From 93820aa2d24e628ff26592c98dc30aa4bd69a928 Mon Sep 17 00:00:00 2001
From: Younes Strittmatter <younes_strittmatter@brown.edu>
Date: Thu, 2 Nov 2023 15:32:14 -0400
Subject: [PATCH] Deployed 7797f3e with MkDocs version: 1.5.3

---
 404.html                                      |  129 +-
 Additional Example/Additional Example.ipynb   |   72 -
 Additional Example/index.html                 | 1407 --------------
 Basic Usage/Basic Usage.ipynb                 |  737 ++++++-
 Basic Usage/index.html                        | 1690 ++++++++++++++++-
 index.html                                    |  131 +-
 index.md                                      |    2 +-
 quickstart/index.html                         |  131 +-
 reference/SUMMARY/index.html                  |  131 +-
 .../src/equation_tree/analysis/index.html     |  129 +-
 .../src/equation_tree/defaults/index.html     |  129 +-
 reference/src/equation_tree/index.html        |  129 +-
 reference/src/equation_tree/prior/index.html  |  217 ++-
 reference/src/equation_tree/sample/index.html |  167 +-
 reference/src/equation_tree/src/index.html    |  129 +-
 .../src/sample_tree_structure/index.html      |  129 +-
 .../equation_tree/src/tree_node/index.html    |  129 +-
 reference/src/equation_tree/tree/index.html   |  633 +++---
 .../equation_tree/util/conversions/index.html |  129 +-
 reference/src/equation_tree/util/index.html   |  129 +-
 .../src/equation_tree/util/io/index.html      |  129 +-
 .../src/equation_tree/util/priors/index.html  |  129 +-
 .../equation_tree/util/type_check/index.html  |  129 +-
 search/search_index.json                      |    2 +-
 sitemap.xml                                   |   15 +-
 sitemap.xml.gz                                |  Bin 381 -> 391 bytes
 .../equation-formats/equation-formats.md      |   16 +
 user-guide/equation-formats/index.html        | 1136 +++++++++++
 user-guide/sampling/index.html                | 1023 ++++++++++
 user-guide/sampling/sampling.md               |    2 +
 30 files changed, 6788 insertions(+), 2272 deletions(-)
 delete mode 100644 Additional Example/Additional Example.ipynb
 delete mode 100644 Additional Example/index.html
 create mode 100644 user-guide/equation-formats/equation-formats.md
 create mode 100644 user-guide/equation-formats/index.html
 create mode 100644 user-guide/sampling/index.html
 create mode 100644 user-guide/sampling/sampling.md

diff --git a/404.html b/404.html
index a27db1d..4ef28e1 100644
--- a/404.html
+++ b/404.html
@@ -295,7 +295,7 @@
             
   
   <span class="md-ellipsis">
-    Tutorials
+    User Guide
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@@ -305,7 +305,7 @@
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           <label class="md-nav__title" for="__nav_3">
             <span class="md-nav__icon md-icon"></span>
-            Tutorials
+            User Guide
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           <ul class="md-nav__list" data-md-scrollfix>
             
@@ -315,11 +315,31 @@
   
   
     <li class="md-nav__item">
-      <a href="/equation-tree/Basic%20Usage/" class="md-nav__link">
+      <a href="/equation-tree/user-guide/sampling/" class="md-nav__link">
         
   
   <span class="md-ellipsis">
-    Basic Usage
+    Sampling
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/equation-tree/user-guide/equation-formats/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Equation Formats
   </span>
   
 
@@ -354,6 +374,69 @@
         <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
         
           
+          <label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
+            
+  
+  <span class="md-ellipsis">
+    Tutorials
+  </span>
+  
+
+            <span class="md-nav__icon md-icon"></span>
+          </label>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            Tutorials
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/equation-tree/Equation Sampling.ipynb" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Equation Sampling
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+    
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
           
           <div class="md-nav__link md-nav__container">
             <a href="/equation-tree/reference/SUMMARY/" class="md-nav__link ">
@@ -367,14 +450,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
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               </label>
             
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-        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
-          <label class="md-nav__title" for="__nav_4">
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
             <span class="md-nav__icon md-icon"></span>
             Code Reference
           </label>
@@ -395,10 +478,10 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1" >
         
           
-          <label class="md-nav__link" for="__nav_4_1" id="__nav_4_1_label" tabindex="0">
+          <label class="md-nav__link" for="__nav_5_1" id="__nav_5_1_label" tabindex="0">
             
   
   <span class="md-ellipsis">
@@ -409,8 +492,8 @@
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-          <label class="md-nav__title" for="__nav_4_1">
+        <nav class="md-nav" data-md-level="2" aria-labelledby="__nav_5_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1">
             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -431,7 +514,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1" >
         
           
           
@@ -447,14 +530,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1" id="__nav_4_1_1_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1" id="__nav_5_1_1_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
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-          <label class="md-nav__title" for="__nav_4_1_1">
+        <nav class="md-nav" data-md-level="3" aria-labelledby="__nav_5_1_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1">
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           </label>
@@ -575,7 +658,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_6" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_6" >
         
           
           
@@ -591,14 +674,14 @@
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-              <label class="md-nav__link " for="__nav_4_1_1_6" id="__nav_4_1_1_6_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1_6" id="__nav_5_1_1_6_label" tabindex="0">
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-          <label class="md-nav__title" for="__nav_4_1_1_6">
+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_6">
             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -667,7 +750,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_7" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_7" >
         
           
           
@@ -683,14 +766,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1_7" id="__nav_4_1_1_7_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1_7" id="__nav_5_1_1_7_label" tabindex="0">
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-          <label class="md-nav__title" for="__nav_4_1_1_7">
+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_7">
             <span class="md-nav__icon md-icon"></span>
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diff --git a/Additional Example/Additional Example.ipynb b/Additional Example/Additional Example.ipynb
deleted file mode 100644
index b211083..0000000
--- a/Additional Example/Additional Example.ipynb	
+++ /dev/null
@@ -1,72 +0,0 @@
-{
- "cells": [
-  {
-   "attachments": {},
-   "cell_type": "markdown",
-   "metadata": {
-    "collapsed": false
-   },
-   "source": [
-    "# Additional Example\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [],
-   "source": [
-    "from autora.equation_tree.equation_tree import Example"
-   ]
-  },
-  {
-   "attachments": {},
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Include inline mathematics like this: $4 < 5$\n",
-    "\n",
-    "Include block mathematics like this (don't forget the empty lines above and below the block):\n",
-    "\n",
-    "$$  \n",
-    "y + 1 = 4 \n",
-    "$$\n",
-    "\n",
-    "... or this:\n",
-    "\n",
-    "\\begin{align}\n",
-    "    p(v_i=1|\\mathbf{h}) & = \\sigma\\left(\\sum_j w_{ij}h_j + b_i\\right) \\\\\n",
-    "    p(h_j=1|\\mathbf{v}) & = \\sigma\\left(\\sum_i w_{ij}v_i + c_j\\right)\n",
-    "\\end{align}"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": []
-  }
- ],
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-   "name": "python3"
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-    "name": "ipython",
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-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython2",
-   "version": "2.7.6"
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- },
- "nbformat": 4,
- "nbformat_minor": 0
-}
diff --git a/Additional Example/index.html b/Additional Example/index.html
deleted file mode 100644
index 817ba2d..0000000
--- a/Additional Example/index.html	
+++ /dev/null
@@ -1,1407 +0,0 @@
-
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-<html lang="en" class="no-js">
-  <head>
-    
-      <meta charset="utf-8">
-      <meta name="viewport" content="width=device-width,initial-scale=1">
-      
-      
-      
-        <link rel="canonical" href="https://autoresearch.github.io/equation-tree/Additional%20Example/">
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-      
-      
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-      <meta name="generator" content="mkdocs-1.5.3, mkdocs-material-9.4.7">
-    
-    
-      
-        <title>Additional Example - AutoRA Equation Tree</title>
-      
-    
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-      <link rel="stylesheet" href="../assets/stylesheets/main.4b4a2bd9.min.css">
-      
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-        <link rel="stylesheet" href="../assets/stylesheets/palette.356b1318.min.css">
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-.highlight-ipynb .cs { color: var(--jp-mirror-editor-comment-color); font-style: italic } /* Comment.Special */
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var(--jp-brand-color1);--jp-input-active-box-shadow-color: rgba(19, 124, 189, .3);--jp-editor-selected-background: #d9d9d9;--jp-editor-selected-focused-background: #d7d4f0;--jp-editor-cursor-color: var(--jp-ui-font-color0);--jp-mirror-editor-keyword-color: #008000;--jp-mirror-editor-atom-color: #88f;--jp-mirror-editor-number-color: #080;--jp-mirror-editor-def-color: #00f;--jp-mirror-editor-variable-color: var(--md-grey-900);--jp-mirror-editor-variable-2-color: #05a;--jp-mirror-editor-variable-3-color: #085;--jp-mirror-editor-punctuation-color: #05a;--jp-mirror-editor-property-color: #05a;--jp-mirror-editor-operator-color: #aa22ff;--jp-mirror-editor-comment-color: #408080;--jp-mirror-editor-string-color: #ba2121;--jp-mirror-editor-string-2-color: #708;--jp-mirror-editor-meta-color: #aa22ff;--jp-mirror-editor-qualifier-color: #555;--jp-mirror-editor-builtin-color: #008000;--jp-mirror-editor-bracket-color: #997;--jp-mirror-editor-tag-color: #170;--jp-mirror-editor-attribute-color: #00c;--jp-mirror-editor-header-color: blue;--jp-mirror-editor-quote-color: #090;--jp-mirror-editor-link-color: #00c;--jp-mirror-editor-error-color: #f00;--jp-mirror-editor-hr-color: #999;--jp-collaborator-color1: #ffad8e;--jp-collaborator-color2: #dac83d;--jp-collaborator-color3: #72dd76;--jp-collaborator-color4: #00e4d0;--jp-collaborator-color5: #45d4ff;--jp-collaborator-color6: #e2b1ff;--jp-collaborator-color7: #ff9de6;--jp-vega-background: white;--jp-sidebar-min-width: 250px;--jp-search-toggle-off-opacity: .5;--jp-search-toggle-hover-opacity: .8;--jp-search-toggle-on-opacity: 1;--jp-search-selected-match-background-color: rgb(245, 200, 0);--jp-search-selected-match-color: black;--jp-search-unselected-match-background-color: var( --jp-inverse-layout-color0 );--jp-search-unselected-match-color: var(--jp-ui-inverse-font-color0);--jp-icon-contrast-color0: var(--md-purple-600);--jp-icon-contrast-color1: var(--md-green-600);--jp-icon-contrast-color2: var(--md-pink-600);--jp-icon-contrast-color3: var(--md-blue-600);--jp-jupyter-icon-color: #f37626;--jp-notebook-icon-color: #f37626;--jp-json-icon-color: var(--md-orange-700);--jp-console-icon-background-color: var(--md-blue-700);--jp-console-icon-color: white;--jp-terminal-icon-background-color: var(--md-grey-800);--jp-terminal-icon-color: var(--md-grey-200);--jp-text-editor-icon-color: var(--md-grey-700);--jp-inspector-icon-color: var(--md-grey-700);--jp-switch-color: var(--md-grey-400);--jp-switch-true-position-color: var(--md-orange-900)}[data-md-color-scheme=slate] .jupyter-wrapper{--jp-shadow-base-lightness: 32;--jp-shadow-umbra-color: rgba( var(--jp-shadow-base-lightness), var(--jp-shadow-base-lightness), var(--jp-shadow-base-lightness), .2 );--jp-shadow-penumbra-color: rgba( var(--jp-shadow-base-lightness), var(--jp-shadow-base-lightness), var(--jp-shadow-base-lightness), .14 );--jp-shadow-ambient-color: rgba( var(--jp-shadow-base-lightness), var(--jp-shadow-base-lightness), var(--jp-shadow-base-lightness), .12 );--jp-elevation-z0: none;--jp-elevation-z1: 0px 2px 1px -1px var(--jp-shadow-umbra-color), 0px 1px 1px 0px var(--jp-shadow-penumbra-color), 0px 1px 3px 0px var(--jp-shadow-ambient-color);--jp-elevation-z2: 0px 3px 1px -2px var(--jp-shadow-umbra-color), 0px 2px 2px 0px var(--jp-shadow-penumbra-color), 0px 1px 5px 0px var(--jp-shadow-ambient-color);--jp-elevation-z4: 0px 2px 4px -1px var(--jp-shadow-umbra-color), 0px 4px 5px 0px var(--jp-shadow-penumbra-color), 0px 1px 10px 0px var(--jp-shadow-ambient-color);--jp-elevation-z6: 0px 3px 5px -1px var(--jp-shadow-umbra-color), 0px 6px 10px 0px var(--jp-shadow-penumbra-color), 0px 1px 18px 0px var(--jp-shadow-ambient-color);--jp-elevation-z8: 0px 5px 5px -3px var(--jp-shadow-umbra-color), 0px 8px 10px 1px var(--jp-shadow-penumbra-color), 0px 3px 14px 2px var(--jp-shadow-ambient-color);--jp-elevation-z12: 0px 7px 8px -4px var(--jp-shadow-umbra-color), 0px 12px 17px 2px var(--jp-shadow-penumbra-color), 0px 5px 22px 4px var(--jp-shadow-ambient-color);--jp-elevation-z16: 0px 8px 10px -5px var(--jp-shadow-umbra-color), 0px 16px 24px 2px var(--jp-shadow-penumbra-color), 0px 6px 30px 5px var(--jp-shadow-ambient-color);--jp-elevation-z20: 0px 10px 13px -6px var(--jp-shadow-umbra-color), 0px 20px 31px 3px var(--jp-shadow-penumbra-color), 0px 8px 38px 7px var(--jp-shadow-ambient-color);--jp-elevation-z24: 0px 11px 15px -7px var(--jp-shadow-umbra-color), 0px 24px 38px 3px var(--jp-shadow-penumbra-color), 0px 9px 46px 8px var(--jp-shadow-ambient-color);--jp-border-width: 1px;--jp-border-color0: var(--md-grey-700);--jp-border-color1: var(--md-grey-700);--jp-border-color2: var(--md-grey-800);--jp-border-color3: var(--md-grey-900);--jp-inverse-border-color: var(--md-grey-600);--jp-border-radius: 2px;--jp-ui-font-scale-factor: 1.2;--jp-ui-font-size0: .83333em;--jp-ui-font-size1: 13px;--jp-ui-font-size2: 1.2em;--jp-ui-font-size3: 1.44em;--jp-ui-font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Helvetica, Arial, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol";--jp-ui-font-color0: rgba(255, 255, 255, 1);--jp-ui-font-color1: rgba(255, 255, 255, .87);--jp-ui-font-color2: rgba(255, 255, 255, .54);--jp-ui-font-color3: rgba(255, 255, 255, .38);--jp-ui-inverse-font-color0: rgba(0, 0, 0, 1);--jp-ui-inverse-font-color1: rgba(0, 0, 0, .8);--jp-ui-inverse-font-color2: rgba(0, 0, 0, .5);--jp-ui-inverse-font-color3: rgba(0, 0, 0, .3);--jp-content-line-height: 1.6;--jp-content-font-scale-factor: 1.2;--jp-content-font-size0: .83333em;--jp-content-font-size1: 14px;--jp-content-font-size2: 1.2em;--jp-content-font-size3: 1.44em;--jp-content-font-size4: 1.728em;--jp-content-font-size5: 2.0736em;--jp-content-presentation-font-size1: 17px;--jp-content-heading-line-height: 1;--jp-content-heading-margin-top: 1.2em;--jp-content-heading-margin-bottom: .8em;--jp-content-heading-font-weight: 500;--jp-content-font-color0: rgba(255, 255, 255, 1);--jp-content-font-color1: rgba(255, 255, 255, 1);--jp-content-font-color2: rgba(255, 255, 255, .7);--jp-content-font-color3: rgba(255, 255, 255, .5);--jp-content-link-color: var(--md-blue-300);--jp-content-font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Helvetica, Arial, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol";--jp-code-font-size: 13px;--jp-code-line-height: 1.3077;--jp-code-padding: 5px;--jp-code-font-family-default: Menlo, Consolas, "DejaVu Sans Mono", monospace;--jp-code-font-family: var(--jp-code-font-family-default);--jp-code-presentation-font-size: 16px;--jp-code-cursor-width0: 1.4px;--jp-code-cursor-width1: 2px;--jp-code-cursor-width2: 4px;--jp-layout-color0: #111111;--jp-layout-color1: var(--md-grey-900);--jp-layout-color2: var(--md-grey-800);--jp-layout-color3: var(--md-grey-700);--jp-layout-color4: var(--md-grey-600);--jp-inverse-layout-color0: white;--jp-inverse-layout-color1: white;--jp-inverse-layout-color2: var(--md-grey-200);--jp-inverse-layout-color3: var(--md-grey-400);--jp-inverse-layout-color4: var(--md-grey-600);--jp-brand-color0: var(--md-blue-700);--jp-brand-color1: var(--md-blue-500);--jp-brand-color2: var(--md-blue-300);--jp-brand-color3: var(--md-blue-100);--jp-brand-color4: var(--md-blue-50);--jp-accent-color0: var(--md-green-700);--jp-accent-color1: var(--md-green-500);--jp-accent-color2: var(--md-green-300);--jp-accent-color3: var(--md-green-100);--jp-warn-color0: var(--md-orange-700);--jp-warn-color1: var(--md-orange-500);--jp-warn-color2: var(--md-orange-300);--jp-warn-color3: var(--md-orange-100);--jp-error-color0: var(--md-red-700);--jp-error-color1: var(--md-red-500);--jp-error-color2: var(--md-red-300);--jp-error-color3: var(--md-red-100);--jp-success-color0: var(--md-green-700);--jp-success-color1: var(--md-green-500);--jp-success-color2: var(--md-green-300);--jp-success-color3: var(--md-green-100);--jp-info-color0: var(--md-cyan-700);--jp-info-color1: var(--md-cyan-500);--jp-info-color2: var(--md-cyan-300);--jp-info-color3: var(--md-cyan-100);--jp-cell-padding: 5px;--jp-cell-collapser-width: 8px;--jp-cell-collapser-min-height: 20px;--jp-cell-collapser-not-active-hover-opacity: .6;--jp-cell-editor-background: var(--jp-layout-color1);--jp-cell-editor-border-color: var(--md-grey-700);--jp-cell-editor-box-shadow: inset 0 0 2px var(--md-blue-300);--jp-cell-editor-active-background: var(--jp-layout-color0);--jp-cell-editor-active-border-color: var(--jp-brand-color1);--jp-cell-prompt-width: 64px;--jp-cell-prompt-font-family: var(--jp-code-font-family-default);--jp-cell-prompt-letter-spacing: 0px;--jp-cell-prompt-opacity: 1;--jp-cell-prompt-not-active-opacity: 1;--jp-cell-prompt-not-active-font-color: var(--md-grey-300);--jp-cell-inprompt-font-color: #307fc1;--jp-cell-outprompt-font-color: #bf5b3d;--jp-notebook-padding: 10px;--jp-notebook-select-background: var(--jp-layout-color1);--jp-notebook-multiselected-color: rgba(33, 150, 243, .24);--jp-notebook-scroll-padding: calc( 100% - var(--jp-code-font-size) * var(--jp-code-line-height) - var(--jp-code-padding) - var(--jp-cell-padding) - 1px );--jp-rendermime-error-background: rgba(244, 67, 54, .28);--jp-rendermime-table-row-background: var(--md-grey-900);--jp-rendermime-table-row-hover-background: rgba(3, 169, 244, .2);--jp-dialog-background: rgba(0, 0, 0, .6);--jp-console-padding: 10px;--jp-toolbar-border-color: var(--jp-border-color2);--jp-toolbar-micro-height: 8px;--jp-toolbar-background: var(--jp-layout-color1);--jp-toolbar-box-shadow: 0px 0px 2px 0px rgba(0, 0, 0, .8);--jp-toolbar-header-margin: 4px 4px 0px 4px;--jp-toolbar-active-background: var(--jp-layout-color0);--jp-statusbar-height: 24px;--jp-input-box-shadow: inset 0 0 2px var(--md-blue-300);--jp-input-active-background: var(--jp-layout-color0);--jp-input-hover-background: var(--jp-layout-color2);--jp-input-background: var(--md-grey-800);--jp-input-border-color: var(--jp-inverse-border-color);--jp-input-active-border-color: var(--jp-brand-color1);--jp-input-active-box-shadow-color: rgba(19, 124, 189, .3);--jp-editor-selected-background: var(--jp-layout-color2);--jp-editor-selected-focused-background: rgba(33, 150, 243, .24);--jp-editor-cursor-color: var(--jp-ui-font-color0);--jp-mirror-editor-keyword-color: var(--md-green-500);--jp-mirror-editor-atom-color: var(--md-blue-300);--jp-mirror-editor-number-color: var(--md-green-400);--jp-mirror-editor-def-color: var(--md-blue-600);--jp-mirror-editor-variable-color: var(--md-grey-300);--jp-mirror-editor-variable-2-color: var(--md-blue-400);--jp-mirror-editor-variable-3-color: var(--md-green-600);--jp-mirror-editor-punctuation-color: var(--md-blue-400);--jp-mirror-editor-property-color: var(--md-blue-400);--jp-mirror-editor-operator-color: #aa22ff;--jp-mirror-editor-comment-color: #408080;--jp-mirror-editor-string-color: #ff7070;--jp-mirror-editor-string-2-color: var(--md-purple-300);--jp-mirror-editor-meta-color: #aa22ff;--jp-mirror-editor-qualifier-color: #555;--jp-mirror-editor-builtin-color: var(--md-green-600);--jp-mirror-editor-bracket-color: #997;--jp-mirror-editor-tag-color: var(--md-green-700);--jp-mirror-editor-attribute-color: var(--md-blue-700);--jp-mirror-editor-header-color: var(--md-blue-500);--jp-mirror-editor-quote-color: var(--md-green-300);--jp-mirror-editor-link-color: var(--md-blue-700);--jp-mirror-editor-error-color: #f00;--jp-mirror-editor-hr-color: #999;--jp-collaborator-color1: #ad4a00;--jp-collaborator-color2: #7b6a00;--jp-collaborator-color3: #007e00;--jp-collaborator-color4: #008772;--jp-collaborator-color5: #0079b9;--jp-collaborator-color6: #8b45c6;--jp-collaborator-color7: #be208b;--jp-vega-background: var(--md-grey-400);--jp-sidebar-min-width: 250px;--jp-search-toggle-off-opacity: .6;--jp-search-toggle-hover-opacity: .8;--jp-search-toggle-on-opacity: 1;--jp-search-selected-match-background-color: rgb(255, 225, 0);--jp-search-selected-match-color: black;--jp-search-unselected-match-background-color: var( --jp-inverse-layout-color0 );--jp-search-unselected-match-color: var(--jp-ui-inverse-font-color0);--jp-scrollbar-background-color: #3f4244;--jp-scrollbar-thumb-color: 88, 96, 97;--jp-scrollbar-endpad: 3px;--jp-scrollbar-thumb-margin: 3.5px;--jp-scrollbar-thumb-radius: 9px;--jp-icon-contrast-color0: var(--md-purple-600);--jp-icon-contrast-color1: var(--md-green-600);--jp-icon-contrast-color2: var(--md-pink-600);--jp-icon-contrast-color3: var(--md-blue-600);--jp-jupyter-icon-color: #f37626;--jp-notebook-icon-color: #f37626;--jp-json-icon-color: var(--md-orange-500);--jp-console-icon-background-color: var(--md-blue-500);--jp-console-icon-color: white;--jp-terminal-icon-background-color: var(--md-grey-200);--jp-terminal-icon-color: var(--md-grey-800);--jp-text-editor-icon-color: var(--md-grey-200);--jp-inspector-icon-color: var(--md-grey-200);--jp-switch-color: var(--md-grey-400);--jp-switch-true-position-color: var(--md-orange-700)}.jupyter-wrapper [data-jp-theme-scrollbars=true]{scrollbar-color:rgb(var(--jp-scrollbar-thumb-color)) var(--jp-scrollbar-background-color)}.jupyter-wrapper [data-jp-theme-scrollbars=true] .CodeMirror-hscrollbar,.jupyter-wrapper [data-jp-theme-scrollbars=true] .CodeMirror-vscrollbar{scrollbar-color:rgba(var(--jp-scrollbar-thumb-color),.5) transparent}.jupyter-wrapper .jp-scrollbar-tiny{scrollbar-color:rgba(var(--jp-scrollbar-thumb-color),.5) transparent;scrollbar-width:thin}.jupyter-wrapper [data-jp-theme-scrollbars=true] ::-webkit-scrollbar,.jupyter-wrapper [data-jp-theme-scrollbars=true] ::-webkit-scrollbar-corner{background:var(--jp-scrollbar-background-color)}.jupyter-wrapper [data-jp-theme-scrollbars=true] ::-webkit-scrollbar-thumb{background:rgb(var(--jp-scrollbar-thumb-color));border:var(--jp-scrollbar-thumb-margin) solid transparent;background-clip:content-box;border-radius:var(--jp-scrollbar-thumb-radius)}.jupyter-wrapper [data-jp-theme-scrollbars=true] ::-webkit-scrollbar-track:horizontal{border-left:var(--jp-scrollbar-endpad) solid var(--jp-scrollbar-background-color);border-right:var(--jp-scrollbar-endpad) solid var(--jp-scrollbar-background-color)}.jupyter-wrapper [data-jp-theme-scrollbars=true] ::-webkit-scrollbar-track:vertical{border-top:var(--jp-scrollbar-endpad) solid var(--jp-scrollbar-background-color);border-bottom:var(--jp-scrollbar-endpad) solid var(--jp-scrollbar-background-color)}.jupyter-wrapper [data-jp-theme-scrollbars=true] .CodeMirror-hscrollbar::-webkit-scrollbar,.jupyter-wrapper [data-jp-theme-scrollbars=true] .CodeMirror-vscrollbar::-webkit-scrollbar,.jupyter-wrapper [data-jp-theme-scrollbars=true] .CodeMirror-hscrollbar::-webkit-scrollbar-corner,.jupyter-wrapper [data-jp-theme-scrollbars=true] .CodeMirror-vscrollbar::-webkit-scrollbar-corner{background-color:transparent}.jupyter-wrapper [data-jp-theme-scrollbars=true] .CodeMirror-hscrollbar::-webkit-scrollbar-thumb,.jupyter-wrapper [data-jp-theme-scrollbars=true] .CodeMirror-vscrollbar::-webkit-scrollbar-thumb{background:rgba(var(--jp-scrollbar-thumb-color),.5);border:var(--jp-scrollbar-thumb-margin) solid transparent;background-clip:content-box;border-radius:var(--jp-scrollbar-thumb-radius)}.jupyter-wrapper [data-jp-theme-scrollbars=true] .CodeMirror-hscrollbar::-webkit-scrollbar-track:horizontal{border-left:var(--jp-scrollbar-endpad) solid transparent;border-right:var(--jp-scrollbar-endpad) solid transparent}.jupyter-wrapper [data-jp-theme-scrollbars=true] .CodeMirror-vscrollbar::-webkit-scrollbar-track:vertical{border-top:var(--jp-scrollbar-endpad) solid transparent;border-bottom:var(--jp-scrollbar-endpad) solid transparent}.jupyter-wrapper .jp-scrollbar-tiny::-webkit-scrollbar,.jupyter-wrapper .jp-scrollbar-tiny::-webkit-scrollbar-corner{background-color:transparent;height:4px;width:4px}.jupyter-wrapper .jp-scrollbar-tiny::-webkit-scrollbar-thumb{background:rgba(var(--jp-scrollbar-thumb-color),.5)}.jupyter-wrapper .jp-scrollbar-tiny::-webkit-scrollbar-track:horizontal{border-left:0px solid transparent;border-right:0px solid transparent}.jupyter-wrapper .jp-scrollbar-tiny::-webkit-scrollbar-track:vertical{border-top:0px solid transparent;border-bottom:0px solid transparent}.jupyter-wrapper .lm-ScrollBar[data-orientation=horizontal]{min-height:16px;max-height:16px;min-width:45px;border-top:1px solid #a0a0a0}.jupyter-wrapper .lm-ScrollBar[data-orientation=vertical]{min-width:16px;max-width:16px;min-height:45px;border-left:1px solid #a0a0a0}.jupyter-wrapper .lm-ScrollBar-button{background-color:#f0f0f0;background-position:center center;min-height:15px;max-height:15px;min-width:15px;max-width:15px}.jupyter-wrapper .lm-ScrollBar-button:hover{background-color:#dadada}.jupyter-wrapper .lm-ScrollBar-button.lm-mod-active{background-color:#cdcdcd}.jupyter-wrapper 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-<div class="jp-Notebook" data-jp-theme-light="true" data-jp-theme-name="JupyterLab Light">
-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
-<div class="jp-Cell-inputWrapper" tabindex="0">
-<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
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-<h1 id="additional-example">Additional Example<a class="anchor-link" href="#additional-example">¶</a></h1>
-</div>
-</div>
-</div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs">
-<div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs">
-<div class="jp-Cell-inputWrapper" tabindex="0">
-<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
-</div>
-<div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
-<div class="CodeMirror cm-s-jupyter">
-<div class="zeroclipboard-container">
-<clipboard-copy for="cell-1">
-<div>
-<span class="notice" hidden="">Copied!</span>
-<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
-<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
-<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
-</svg>
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-</div>
-<div class="highlight-ipynb hl-python"><pre><span></span><span class="kn">from</span> <span class="nn">autora.equation_tree.equation_tree</span> <span class="kn">import</span> <span class="n">Example</span>
-</pre></div>
-<div class="clipboard-copy-txt" id="cell-1">from autora.equation_tree.equation_tree import Example</div>
-</div>
-</div>
-</div>
-</div>
-</div>
-</div>
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-</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
-<p>Include inline mathematics like this: $4 &lt; 5$</p>
-<p>Include block mathematics like this (don't forget the empty lines above and below the block):</p>
-<p>$$  
-y + 1 = 4 
-$$</p>
-<p>... or this:</p>
-<p>\begin{align}
-    p(v_i=1|\mathbf{h}) &amp; = \sigma\left(\sum_j w_{ij}h_j + b_i\right) \\
-    p(h_j=1|\mathbf{v}) &amp; = \sigma\left(\sum_i w_{ij}v_i + c_j\right)
-\end{align}</p>
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-</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
-</div>
-</div>
-</div>
-</div>
-</div> <!-- jp-Notebook -->
-</div> <!-- jupyter-wrapper -->
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diff --git a/Basic Usage/Basic Usage.ipynb b/Basic Usage/Basic Usage.ipynb
index b0a7cca..adc205b 100644
--- a/Basic Usage/Basic Usage.ipynb	
+++ b/Basic Usage/Basic Usage.ipynb	
@@ -7,7 +7,12 @@
     "collapsed": false
    },
    "source": [
-    "# Basic Usage\n"
+    "# Basic Usage\n",
+    "Here, we demonstrate core functionalities of the Equation Tree:\n",
+    "- Basic Functionality for sampling and processing equations\n",
+    "- Advanced settings for sampling equations\n",
+    "\n",
+    "## Installation"
    ]
   },
   {
@@ -21,7 +26,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Requirement already satisfied: equation_tree in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src (0.0.11.dev21+gc4ad4e6.d20230918)\r\n",
+      "Requirement already satisfied: equation_tree in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src (0.0.11.dev27+g1da6b63.d20231102)\r\n",
       "Requirement already satisfied: numpy in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (1.25.2)\r\n",
       "Requirement already satisfied: sympy in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (1.12)\r\n",
       "Requirement already satisfied: importlib_resources in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (6.0.1)\r\n",
@@ -34,26 +39,699 @@
     }
    ],
    "source": [
+    "import random\n",
     "!pip install equation_tree"
    ]
   },
   {
    "cell_type": "markdown",
    "source": [
-    "Include inline mathematics like this: $4 < 5$\n",
+    "## Basic Functionality\n",
     "\n",
-    "Include block mathematics like this (don't forget the empty lines above and below the block):\n",
+    "### Sampling With Default Settings\n",
+    "First, we need to import the functionality. Here we also set a seed to ensure reproducible results."
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "outputs": [],
+   "source": [
+    "from equation_tree import sample\n",
     "\n",
-    "$$  \n",
-    "y + 1 = 4 \n",
-    "$$\n",
+    "# To obtain reproducible results, we set a seed for the following section\n",
+    "import numpy as np\n",
+    "np.random.seed(42)\n",
+    "# Adjusting the input dimension of the equations"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "We use this to sample an equation:"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.\n",
+      "  warnings.warn(\n",
+      "Processing: 100%|██████████| 1/1 [00:00<00:00,  9.77iteration/s]\n"
+     ]
+    }
+   ],
+   "source": [
+    "equation = sample()"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "### Equation Representations And Features\n",
     "\n",
-    "... or this:\n",
+    "First, lets look at the type of the equation"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "list"
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "type(equation)"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "It is a list! This is because we can sample multiple equations in one go:"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Processing:   0%|          | 0/100 [00:00<?, ?iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:51: RuntimeWarning: invalid value encountered in log\n",
+      "  \"log\": lambda a: np.log(a),\n",
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:55: RuntimeWarning: invalid value encountered in arccos\n",
+      "  \"acos\": lambda a: np.arccos(a),\n",
+      "Processing:   7%|▋         | 7/100 [00:00<00:01, 68.58iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:40: RuntimeWarning: invalid value encountered in scalar power\n",
+      "  \"^\": lambda a, b: a**b,\n",
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:52: RuntimeWarning: invalid value encountered in sqrt\n",
+      "  \"sqrt\": lambda a: np.sqrt(a),\n",
+      "Processing:  14%|█▍        | 14/100 [00:00<00:01, 68.71iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:56: RuntimeWarning: invalid value encountered in arcsin\n",
+      "  \"asin\": lambda a: np.arcsin(a),\n",
+      "Processing: 100%|██████████| 100/100 [00:01<00:00, 85.06iteration/s]\n"
+     ]
+    }
+   ],
+   "source": [
+    "equations = sample(n = 100)"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "This returns 100 equations:"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "100"
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(equations)"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "-sin(x_1 - exp(exp(x_1)))"
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "equations[0]"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "-c_2 + tan(c_1*x_1)"
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "equations[42]"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "They are represented as strings, but we can look at other representations as well. For example, prefix notation (for more details on different representations of the equations, see the respective section of the documentation):"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "['-', 'tan', '*', 'c_1', 'x_1', 'c_2']"
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "equations[42].prefix"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "We can also look at features of the equation, for example at the number of constants, the tree depth of the underlying tree, the number of nodes or the tree structure (for more details on these features, see the respective section of the documentation):"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "2"
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "equations[42].n_constants"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "3"
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "equations[42].depth"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "6"
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "equations[42].n_nodes"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "[0, 1, 2, 3, 3, 1]"
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "equations[42].structure"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "### Instantiate Equations\n",
     "\n",
-    "\\begin{align}\n",
-    "    p(v_i=1|\\mathbf{h}) & = \\sigma\\left(\\sum_j w_{ij}h_j + b_i\\right) \\\\\n",
-    "    p(h_j=1|\\mathbf{v}) & = \\sigma\\left(\\sum_i w_{ij}v_i + c_j\\right)\n",
-    "\\end{align}"
+    "Note: the sampled equation are abstract: c_1 are representation of a constant. We can instantiate constants to be numbers:"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "abstract: -c_2 + tan(c_1*x_1) , instantiated: tan(0.2720878822071884*x_1) - 0.4936315339297549\n"
+     ]
+    }
+   ],
+   "source": [
+    "# first we need to import the functionality\n",
+    "from equation_tree import instantiate_constants\n",
+    "import random\n",
+    "\n",
+    "# then we can use a function to instantiate the constants. For example for random constants between 0 and 1:\n",
+    "instantiated_equation = instantiate_constants(equations[42], lambda : random.random())\n",
+    "print(f'abstract: {equations[42]}', f', instantiated: {instantiated_equation}')"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "abstract: c_2*x_1**c_1 , instantiated: x_1\n"
+     ]
+    }
+   ],
+   "source": [
+    "# we can also use other functions (for example all functions to be a constant\n",
+    "instantiated_equation_ = instantiate_constants(equations[41], lambda : 1)\n",
+    "print(f'abstract: {equations[41]}', f', instantiated: {instantiated_equation_}')"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "**We can use arbitrary functions to instantiate the constants.\n",
+    "\n",
+    "### Evaluating Equations\n",
+    "\n",
+    "After instantiating equations, we can also evaluate on arbitrary input:"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "array([-0.21462429,  0.11148855,  0.57008635,  1.41577756])"
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# import functionality\n",
+    "values = instantiated_equation.evaluate({'x_1': [1, 2, 3, 4]})\n",
+    "values"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "array([-0.21462429,  0.11148855,  0.57008635,  1.41577756])"
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# We can also use pandas dataframes as inputs:\n",
+    "\n",
+    "# import functionality\n",
+    "import pandas as pd\n",
+    "\n",
+    "# define the input and get the values\n",
+    "input_df = pd.DataFrame({'x_1': [1, 2, 3, 4]})\n",
+    "instantiated_equation.evaluate(input_df)"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "\n",
+    "## Sample Settings\n",
+    "\n",
+    "When sampling equations, we can control for a variety of features of the underlying distribution.\n",
+    "\n",
+    "### Input Dimensions\n",
+    "\n",
+    "We can manipulate the space on witch the equation is defined. For example, if we want equations that are defined on 2-dimensions, we can write:"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.\n",
+      "  warnings.warn(\n",
+      "Processing:   0%|          | 0/5 [00:00<?, ?iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:55: RuntimeWarning: invalid value encountered in arccos\n",
+      "  \"acos\": lambda a: np.arccos(a),\n",
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:51: RuntimeWarning: invalid value encountered in log\n",
+      "  \"log\": lambda a: np.log(a),\n",
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:56: RuntimeWarning: invalid value encountered in arcsin\n",
+      "  \"asin\": lambda a: np.arcsin(a),\n",
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:52: RuntimeWarning: invalid value encountered in sqrt\n",
+      "  \"sqrt\": lambda a: np.sqrt(a),\n",
+      "Processing: 100%|██████████| 5/5 [00:00<00:00, 112.51iteration/s]\n"
+     ]
+    }
+   ],
+   "source": [
+    "equations_2d = sample(n=5, max_num_variables=2)"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "outputs": [
+    {
+     "data": {
+      "text/plain": "[acos(Abs(acos(x_1))),\n -Abs(x_2) + asin(log(x_1)),\n Max(c_1, x_1),\n Max(x_1, Abs(sqrt(sin(x_1)))),\n cos(x_1*(c_1 + x_2))]"
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "equations_2d"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "**Note: Not all the equations have exactly 2 input variable. Some of them have only one. This is since equations with only one input variable are still defined on 2 (or more dimensions)\n",
+    "\n",
+    "### Equation Complexity\n",
+    "\n",
+    "We can also manipulate the equation complexity (as number of nodes)"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.\n",
+      "  warnings.warn(\n",
+      "Processing:   0%|          | 0/5 [00:00<?, ?iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:55: RuntimeWarning: invalid value encountered in arccos\n",
+      "  \"acos\": lambda a: np.arccos(a),\n",
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:56: RuntimeWarning: invalid value encountered in arcsin\n",
+      "  \"asin\": lambda a: np.arcsin(a),\n",
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:40: RuntimeWarning: invalid value encountered in scalar power\n",
+      "  \"^\": lambda a, b: a**b,\n",
+      "Processing: 100%|██████████| 5/5 [00:00<00:00, 312.27iteration/s]\n",
+      "Processing:   0%|          | 0/5 [00:00<?, ?iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:40: RuntimeWarning: divide by zero encountered in scalar power\n",
+      "  \"^\": lambda a, b: a**b,\n",
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:47: RuntimeWarning: invalid value encountered in sin\n",
+      "  \"sin\": lambda a: np.sin(a),\n",
+      "Processing:  40%|████      | 2/5 [00:00<00:00, 12.82iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:52: RuntimeWarning: invalid value encountered in sqrt\n",
+      "  \"sqrt\": lambda a: np.sqrt(a),\n",
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:51: RuntimeWarning: invalid value encountered in log\n",
+      "  \"log\": lambda a: np.log(a),\n",
+      "Processing: 100%|██████████| 5/5 [00:00<00:00, 21.56iteration/s]\n"
+     ]
+    }
+   ],
+   "source": [
+    "equations_simple = sample(n=5, depth=3)\n",
+    "equations_complex = sample(n=5, depth=8)"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "*** simple equations ***\n",
+      " [acos(exp(x_1)), Max(c_1, x_1), x_1/c_1, asin(exp(x_1)), x_1**c_1] \n",
+      "\n",
+      "*** complex equations ***\n",
+      " [sin(exp(sqrt(1 - sin(x_1)**2)/sin(x_1))**x_1), (x_1 + Min(x_1, sin(x_1)))/sqrt(1 - (x_1 + Min(x_1, sin(x_1)))**2), sqrt(Min(c_1**sin(sin(x_1)), x_1)), -asin(x_1)**x_1 + Min(c_1, x_1), Max(-x_1 + log(x_1), sqrt(Abs(x_1)))]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print('*** simple equations ***\\n', equations_simple, '\\n')\n",
+    "print('*** complex equations ***\\n', equations_complex)"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "### Using Priors\n",
+    "We can also make use of priors to fully customize the sampling. Here, the entries for the structures, features, functions and operators represent the probability of the respective attribute being sampled."
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.\n",
+      "  warnings.warn(\n",
+      "Processing: 100%|██████████| 100/100 [00:00<00:00, 190.81iteration/s]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": "[cos(cos(x_1)),\n sin(sin(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n -x_3 + sin(x_2) + cos(x_1),\n cos(cos(x_1)),\n cos(sin(x_1)),\n sin(cos(x_1)),\n x_1 + x_2,\n sin(cos(x_1)),\n cos(sin(x_1)),\n x_1 + x_2,\n cos(sin(x_1)),\n x_1 - x_2,\n x_1 + x_2,\n sin(sin(x_1)),\n x_1 + x_2,\n sin(cos(x_1)),\n -c_1 + x_1,\n sin(cos(x_1)),\n x_1 + x_2,\n x_1 + x_2,\n x_1 + x_2,\n x_1 + x_2,\n sin(cos(x_1)),\n c_1 + x_1,\n x_1 - x_2,\n x_1 - x_2,\n x_1 + x_2,\n sin(sin(x_1)),\n c_1 + x_1,\n cos(sin(x_1)),\n cos(sin(x_1)),\n cos(sin(x_1)),\n cos(cos(x_1)),\n c_1 + x_1,\n sin(cos(x_1)),\n sin(cos(x_1)),\n x_1 - x_2,\n cos(sin(x_1)),\n cos(sin(x_1)),\n x_1 - x_2,\n cos(cos(x_1)),\n x_1 + x_2,\n x_1 + x_2,\n sin(sin(x_1)),\n c_1 + x_1,\n c_1 + x_1,\n x_1 + x_2,\n x_1 - x_2,\n sin(sin(x_1)),\n cos(cos(x_1)),\n cos(cos(x_1)),\n cos(cos(x_1)),\n sin(cos(x_1)),\n x_1 - x_2,\n sin(sin(x_1)),\n cos(cos(x_1)),\n c_1 + x_1,\n sin(sin(x_1)),\n cos(sin(x_1)),\n cos(sin(x_1)),\n x_1 + x_2,\n cos(sin(x_1)),\n sin(cos(x_1)),\n c_1 + x_1,\n -x_2,\n x_1 - x_2,\n -x_3 + sin(x_1) + sin(x_2),\n c_1 + x_1,\n x_1 + x_2,\n c_1 + x_1,\n c_1 + x_1,\n sin(sin(x_1)),\n cos(cos(x_1)),\n x_1 + x_2,\n c_1 + x_1,\n -x_1 + cos(x_1) + cos(x_2),\n x_1 - x_2,\n cos(sin(x_1)),\n sin(cos(x_1)),\n sin(cos(x_1)),\n sin(cos(x_1)),\n -x_3 + sin(x_1) + cos(x_2),\n x_1 + x_2,\n -x_3 + sin(x_2) + cos(x_1),\n -x_3 + sin(x_1) + sin(x_2),\n c_1 - x_1,\n c_1 + x_1,\n c_1 + x_1,\n cos(cos(x_1)),\n -x_2 + sin(x_2) + cos(x_1),\n c_1 + x_1,\n sin(sin(x_1)),\n c_1 + x_1,\n x_1 + x_2,\n sin(sin(x_1)),\n x_1 + x_2,\n x_1 + x_2,\n cos(sin(x_1)),\n sin(sin(x_1))]"
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "p = {\n",
+    "    'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n",
+    "    'features': {'constants': .2, 'variables': .8},\n",
+    "    'functions': {'sin': .5, 'cos': .5},\n",
+    "    'operators': {'+': .8, '-': .2}\n",
+    "}\n",
+    "equations_with_prior = sample(n=10, prior=p, max_num_variables=10)\n",
+    "equations_with_prior"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "We can also use conditional priors conditioned on the parent node:"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.\n",
+      "  warnings.warn(\n",
+      "Processing: 100%|██████████| 100/100 [00:00<00:00, 128.08iteration/s]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": "[cos(cos(x_1)),\n x_1 - x_2,\n -c_1 + x_1,\n sin(cos(x_1)),\n sin(cos(x_1)),\n c_1 + x_1,\n -c_1 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n cos(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n sin(cos(x_1)),\n c_1 - x_1,\n -x_3 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n c_1 - x_1,\n sin(cos(x_1)),\n cos(cos(x_1)),\n x_1 - x_2,\n -c_1 + sin(x_1) + sin(x_2),\n -x_3 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n c_1 - x_1,\n sin(cos(x_1)),\n x_1 - x_2,\n -x_3 - sin(x_2) + cos(x_1),\n -c_1 + x_1,\n sin(cos(x_1)),\n cos(cos(x_1)),\n sin(cos(x_1)),\n x_1 + x_2,\n cos(cos(x_1)),\n -x_3 + sin(x_1) - sin(x_2),\n c_1 + x_1,\n cos(cos(x_1)),\n cos(cos(x_1)),\n sin(cos(x_1)),\n x_1 - x_2,\n -x_3 + sin(x_1) + sin(x_2),\n -c_1 + x_1,\n c_1 - x_1,\n c_1 + x_1,\n c_1 + x_1,\n cos(cos(x_1)),\n -c_1 + sin(x_1) + sin(x_2),\n c_1 + x_1,\n sin(cos(x_1)),\n sin(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n -x_3 + sin(x_1) - cos(x_2),\n sin(cos(x_1)),\n x_1 - x_2,\n -x_3 + cos(x_1) - cos(x_2),\n x_1 - x_2,\n cos(cos(x_1)),\n sin(cos(x_1)),\n -x_2 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n -c_1 + sin(x_1) + sin(x_2),\n -x_2 + sin(x_1) - cos(x_2),\n cos(cos(x_1)),\n -x_2 + sin(x_1) + sin(x_2),\n -x_3 + sin(x_1) + sin(x_2),\n sin(cos(x_1)),\n cos(cos(x_1)),\n cos(cos(x_1)),\n -c_1 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n cos(cos(x_1)),\n cos(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n cos(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n x_1 + x_2,\n c_1 - x_1,\n -x_1 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n -c_1 + sin(x_1) + sin(x_2),\n c_1 - x_1,\n cos(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n c_1 - x_1,\n -x_3 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n c_1 + x_1,\n x_1 - x_2,\n cos(cos(x_1)),\n c_1 + x_1,\n cos(cos(x_1)),\n sin(cos(x_1)),\n sin(cos(x_1)),\n sin(cos(x_1)),\n sin(cos(x_1)),\n sin(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n c_1 + x_1]"
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "p_ = {\n",
+    "    'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n",
+    "    'features': {'constants': .2, 'variables': .8},\n",
+    "    'functions': {'sin': .5, 'cos': .5},\n",
+    "    'operators': {'+': .5, '-': .5},\n",
+    "    'function_conditionals': {\n",
+    "        'sin': {\n",
+    "            'features': {'constants': 0., 'variables': 1.},\n",
+    "            'functions': {'sin': 0., 'cos': 1.},\n",
+    "            'operators': {'+': .5, '-': .5}\n",
+    "        },\n",
+    "        'cos': {\n",
+    "            'features': {'constants': 0., 'variables': 1.},\n",
+    "            'functions': {'cos': 1., 'sin': 0.},\n",
+    "            'operators': {'+': 0., '-': 1.}\n",
+    "        }\n",
+    "    },\n",
+    "    'operator_conditionals': {\n",
+    "        '+': {\n",
+    "            'features': {'constants': .5, 'variables': .5},\n",
+    "            'functions': {'sin': 1., 'cos': 0.},\n",
+    "            'operators': {'+': 1., '-': 0.}\n",
+    "        },\n",
+    "        '-': {\n",
+    "            'features': {'constants': .3, 'variables': .7},\n",
+    "            'functions': {'cos': .5, 'sin': .5},\n",
+    "            'operators': {'+': .9, '-': .1}\n",
+    "        }\n",
+    "    },\n",
+    "}\n",
+    "equations_with_conditional_prior = sample(n=10, prior=p_, max_num_variables=10)\n",
+    "equations_with_conditional_prior"
    ],
    "metadata": {
     "collapsed": false
@@ -61,8 +739,39 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
-   "source": []
+   "source": [
+    "**WARNING**\n",
+    "If your application is dependent on these priors, you should \"burn\" samples before starting the sampling.\n",
+    "During the sampling process, equations get simplified and invalid equations are discarded. This is likely to lead to disparities between the priors and the sampled frequencies.\n",
+    "To counteract this, the package offers the functionality to \"burn\" samples and adjust the priors so that the outcome frequency match them more closely. To burn samples, use the following code (We don't run it in the notebook since the adjusted priors are saved to disk for future use):\n",
+    "```\n",
+    "burn(\n",
+    "    prior,\n",
+    "    max_number_variables,\n",
+    "    path_to_file,\n",
+    "    number_of_burned_samples,\n",
+    "    learning_rate\n",
+    "    )\n",
+    "```\n",
+    "*this function should be run multiple times. The learning rate defines how much adjusted from previous runs are adjusted.\n",
+    "After burning, you can load the adjusted priors via:\n",
+    "```\n",
+    "    sample(..., file=path_to_file)\n",
+    "```\n",
+    "*multiple adjusted priors can be stored in the same file."
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "outputs": [],
+   "source": [],
+   "metadata": {
+    "collapsed": false
+   }
   }
  ],
  "metadata": {
diff --git a/Basic Usage/index.html b/Basic Usage/index.html
index aedca68..29e7109 100644
--- a/Basic Usage/index.html	
+++ b/Basic Usage/index.html	
@@ -11,10 +11,6 @@
         <link rel="canonical" href="https://autoresearch.github.io/equation-tree/Basic%20Usage/">
       
       
-        <link rel="prev" href="../quickstart/">
-      
-      
-        <link rel="next" href="../reference/SUMMARY/">
       
       
       <link rel="icon" href="../assets/images/favicon.png">
@@ -288,37 +284,35 @@
       
   
   
-    
-  
   
     
     
     
     
     
-    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+    <li class="md-nav__item md-nav__item--nested">
       
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
         
           
           <label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
             
   
   <span class="md-ellipsis">
-    Tutorials
+    User Guide
   </span>
   
 
             <span class="md-nav__icon md-icon"></span>
           </label>
         
-        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="true">
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
           <label class="md-nav__title" for="__nav_3">
             <span class="md-nav__icon md-icon"></span>
-            Tutorials
+            User Guide
           </label>
           <ul class="md-nav__list" data-md-scrollfix>
             
@@ -326,27 +320,100 @@
                 
   
   
-    
   
+    <li class="md-nav__item">
+      <a href="../user-guide/sampling/" class="md-nav__link">
+        
   
-    <li class="md-nav__item md-nav__item--active">
-      
-      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+  <span class="md-ellipsis">
+    Sampling
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../user-guide/equation-formats/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Equation Formats
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
       
+    </li>
+  
+
+    
       
-        
       
+  
+  
+  
+    
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
       
-      <a href="./" class="md-nav__link md-nav__link--active">
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          <label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
+            
+  
+  <span class="md-ellipsis">
+    Tutorials
+  </span>
+  
+
+            <span class="md-nav__icon md-icon"></span>
+          </label>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            Tutorials
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../Equation Sampling.ipynb" class="md-nav__link">
         
   
   <span class="md-ellipsis">
-    Basic Usage
+    Equation Sampling
   </span>
   
 
       </a>
-      
     </li>
   
 
@@ -374,7 +441,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
         
           
           
@@ -390,14 +457,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
           </div>
         
-        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
-          <label class="md-nav__title" for="__nav_4">
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
             <span class="md-nav__icon md-icon"></span>
             Code Reference
           </label>
@@ -418,10 +485,10 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1" >
         
           
-          <label class="md-nav__link" for="__nav_4_1" id="__nav_4_1_label" tabindex="0">
+          <label class="md-nav__link" for="__nav_5_1" id="__nav_5_1_label" tabindex="0">
             
   
   <span class="md-ellipsis">
@@ -432,8 +499,8 @@
             <span class="md-nav__icon md-icon"></span>
           </label>
         
-        <nav class="md-nav" data-md-level="2" aria-labelledby="__nav_4_1_label" aria-expanded="false">
-          <label class="md-nav__title" for="__nav_4_1">
+        <nav class="md-nav" data-md-level="2" aria-labelledby="__nav_5_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1">
             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -454,7 +521,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1" >
         
           
           
@@ -470,14 +537,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1" id="__nav_4_1_1_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1" id="__nav_5_1_1_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
           </div>
         
-        <nav class="md-nav" data-md-level="3" aria-labelledby="__nav_4_1_1_label" aria-expanded="false">
-          <label class="md-nav__title" for="__nav_4_1_1">
+        <nav class="md-nav" data-md-level="3" aria-labelledby="__nav_5_1_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1">
             <span class="md-nav__icon md-icon"></span>
             Equation tree
           </label>
@@ -598,7 +665,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_6" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_6" >
         
           
           
@@ -614,14 +681,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1_6" id="__nav_4_1_1_6_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1_6" id="__nav_5_1_1_6_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
           </div>
         
-        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_4_1_1_6_label" aria-expanded="false">
-          <label class="md-nav__title" for="__nav_4_1_1_6">
+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_6">
             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -690,7 +757,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_7" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_7" >
         
           
           
@@ -706,14 +773,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1_7" id="__nav_4_1_1_7_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1_7" id="__nav_5_1_1_7_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
           </div>
         
-        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_4_1_1_7_label" aria-expanded="false">
-          <label class="md-nav__title" for="__nav_4_1_1_7">
+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_7">
             <span class="md-nav__icon md-icon"></span>
             Util
           </label>
@@ -850,6 +917,96 @@
     
   
   
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      Table of contents
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#installation" class="md-nav__link">
+    Installation
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#basic-functionality" class="md-nav__link">
+    Basic Functionality
+  </a>
+  
+    <nav class="md-nav" aria-label="Basic Functionality">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#sampling-with-default-settings" class="md-nav__link">
+    Sampling With Default Settings
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#equation-representations-and-features" class="md-nav__link">
+    Equation Representations And Features
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#instantiate-equations" class="md-nav__link">
+    Instantiate Equations
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#evaluating-equations" class="md-nav__link">
+    Evaluating Equations
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#sample-settings" class="md-nav__link">
+    Sample Settings
+  </a>
+  
+    <nav class="md-nav" aria-label="Sample Settings">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#input-dimensions" class="md-nav__link">
+    Input Dimensions
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#equation-complexity" class="md-nav__link">
+    Equation Complexity
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#using-priors" class="md-nav__link">
+    Using Priors
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+    </ul>
+  
 </nav>
                   </div>
                 </div>
@@ -1284,7 +1441,12 @@
 </div>
 <div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
 </div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
-<h1 id="basic-usage">Basic Usage<a class="anchor-link" href="#basic-usage">¶</a></h1>
+<h1 id="basic-usage">Basic Usage<a class="anchor-link" href="#basic-usage">¶</a></h1><p>Here, we demonstrate core functionalities of the Equation Tree:</p>
+<ul>
+<li>Basic Functionality for sampling and processing equations</li>
+<li>Advanced settings for sampling equations</li>
+</ul>
+<h2 id="installation">Installation<a class="anchor-link" href="#installation">¶</a></h2>
 </div>
 </div>
 </div>
@@ -1307,9 +1469,11 @@ <h1 id="basic-usage">Basic Usage<a class="anchor-link" href="#basic-usage">¶</a
 </div>
 </clipboard-copy>
 </div>
-<div class="highlight-ipynb hl-python"><pre><span></span><span class="err">!</span><span class="n">pip</span> <span class="n">install</span> <span class="n">equation_tree</span>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="kn">import</span> <span class="nn">random</span>
+<span class="err">!</span><span class="n">pip</span> <span class="n">install</span> <span class="n">equation_tree</span>
 </pre></div>
-<div class="clipboard-copy-txt" id="cell-1">!pip install equation_tree</div>
+<div class="clipboard-copy-txt" id="cell-1">import random
+!pip install equation_tree</div>
 </div>
 </div>
 </div>
@@ -1321,7 +1485,7 @@ <h1 id="basic-usage">Basic Usage<a class="anchor-link" href="#basic-usage">¶</a
 <div class="jp-OutputArea-child">
 <div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
 <div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
-<pre>Requirement already satisfied: equation_tree in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src (0.0.11.dev21+gc4ad4e6.d20230918)
+<pre>Requirement already satisfied: equation_tree in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src (0.0.11.dev27+g1da6b63.d20231102)
 Requirement already satisfied: numpy in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (1.25.2)
 Requirement already satisfied: sympy in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (1.12)
 Requirement already satisfied: importlib_resources in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (6.0.1)
@@ -1343,16 +1507,147 @@ <h1 id="basic-usage">Basic Usage<a class="anchor-link" href="#basic-usage">¶</a
 </div>
 <div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
 </div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
-<p>Include inline mathematics like this: $4 &lt; 5$</p>
-<p>Include block mathematics like this (don't forget the empty lines above and below the block):</p>
-<p>$$  
-y + 1 = 4 
-$$</p>
-<p>... or this:</p>
-<p>\begin{align}
-    p(v_i=1|\mathbf{h}) &amp; = \sigma\left(\sum_j w_{ij}h_j + b_i\right) \\
-    p(h_j=1|\mathbf{v}) &amp; = \sigma\left(\sum_i w_{ij}v_i + c_j\right)
-\end{align}</p>
+<h2 id="basic-functionality">Basic Functionality<a class="anchor-link" href="#basic-functionality">¶</a></h2><h3 id="sampling-with-default-settings">Sampling With Default Settings<a class="anchor-link" href="#sampling-with-default-settings">¶</a></h3><p>First, we need to import the functionality. Here we also set a seed to ensure reproducible results.</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [2]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-2">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="kn">from</span> <span class="nn">equation_tree</span> <span class="kn">import</span> <span class="n">sample</span>
+
+<span class="c1"># To obtain reproducible results, we set a seed for the following section</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
+<span class="c1"># Adjusting the input dimension of the equations</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-2">from equation_tree import sample
+
+# To obtain reproducible results, we set a seed for the following section
+import numpy as np
+np.random.seed(42)
+# Adjusting the input dimension of the equations</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<p>We use this to sample an equation:</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [3]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-3">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">equation</span> <span class="o">=</span> <span class="n">sample</span><span class="p">()</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-3">equation = sample()</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="application/vnd.jupyter.stderr" tabindex="0">
+<pre>/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.
+  warnings.warn(
+Processing: 100%|██████████| 1/1 [00:00&lt;00:00,  9.77iteration/s]
+</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<h3 id="equation-representations-and-features">Equation Representations And Features<a class="anchor-link" href="#equation-representations-and-features">¶</a></h3><p>First, lets look at the type of the equation</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [4]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-4">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="nb">type</span><span class="p">(</span><span class="n">equation</span><span class="p">)</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-4">type(equation)</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[4]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>list</pre>
+</div>
+</div>
 </div>
 </div>
 </div>
@@ -1363,6 +1658,1295 @@ <h1 id="basic-usage">Basic Usage<a class="anchor-link" href="#basic-usage">¶</a
 </div>
 <div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
 </div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<p>It is a list! This is because we can sample multiple equations in one go:</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [5]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-5">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">equations</span> <span class="o">=</span> <span class="n">sample</span><span class="p">(</span><span class="n">n</span> <span class="o">=</span> <span class="mi">100</span><span class="p">)</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-5">equations = sample(n = 100)</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="application/vnd.jupyter.stderr" tabindex="0">
+<pre>Processing:   0%|          | 0/100 [00:00&lt;?, ?iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:51: RuntimeWarning: invalid value encountered in log
+  "log": lambda a: np.log(a),
+/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:55: RuntimeWarning: invalid value encountered in arccos
+  "acos": lambda a: np.arccos(a),
+Processing:   7%|▋         | 7/100 [00:00&lt;00:01, 68.58iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:40: RuntimeWarning: invalid value encountered in scalar power
+  "^": lambda a, b: a**b,
+/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:52: RuntimeWarning: invalid value encountered in sqrt
+  "sqrt": lambda a: np.sqrt(a),
+Processing:  14%|█▍        | 14/100 [00:00&lt;00:01, 68.71iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:56: RuntimeWarning: invalid value encountered in arcsin
+  "asin": lambda a: np.arcsin(a),
+Processing: 100%|██████████| 100/100 [00:01&lt;00:00, 85.06iteration/s]
+</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<p>This returns 100 equations:</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [6]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-6">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="nb">len</span><span class="p">(</span><span class="n">equations</span><span class="p">)</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-6">len(equations)</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[6]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>100</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [7]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-7">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">equations</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-7">equations[0]</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[7]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>-sin(x_1 - exp(exp(x_1)))</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [8]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-8">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">equations</span><span class="p">[</span><span class="mi">42</span><span class="p">]</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-8">equations[42]</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[8]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>-c_2 + tan(c_1*x_1)</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<p>They are represented as strings, but we can look at other representations as well. For example, prefix notation (for more details on different representations of the equations, see the respective section of the documentation):</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [9]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-9">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">equations</span><span class="p">[</span><span class="mi">42</span><span class="p">]</span><span class="o">.</span><span class="n">prefix</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-9">equations[42].prefix</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[9]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>['-', 'tan', '*', 'c_1', 'x_1', 'c_2']</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<p>We can also look at features of the equation, for example at the number of constants, the tree depth of the underlying tree, the number of nodes or the tree structure (for more details on these features, see the respective section of the documentation):</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [10]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-10">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">equations</span><span class="p">[</span><span class="mi">42</span><span class="p">]</span><span class="o">.</span><span class="n">n_constants</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-10">equations[42].n_constants</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[10]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>2</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [11]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-11">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">equations</span><span class="p">[</span><span class="mi">42</span><span class="p">]</span><span class="o">.</span><span class="n">depth</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-11">equations[42].depth</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[11]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>3</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
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+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
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+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">equations</span><span class="p">[</span><span class="mi">42</span><span class="p">]</span><span class="o">.</span><span class="n">n_nodes</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-12">equations[42].n_nodes</div>
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+<pre>6</pre>
+</div>
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+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
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+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">equations</span><span class="p">[</span><span class="mi">42</span><span class="p">]</span><span class="o">.</span><span class="n">structure</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-13">equations[42].structure</div>
+</div>
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+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>[0, 1, 2, 3, 3, 1]</pre>
+</div>
+</div>
+</div>
+</div>
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+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
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+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<h3 id="instantiate-equations">Instantiate Equations<a class="anchor-link" href="#instantiate-equations">¶</a></h3><p>Note: the sampled equation are abstract: c_1 are representation of a constant. We can instantiate constants to be numbers:</p>
+</div>
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+<div class="jp-InputPrompt jp-InputArea-prompt">In [14]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
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+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
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+<div class="highlight-ipynb hl-python"><pre><span></span><span class="c1"># first we need to import the functionality</span>
+<span class="kn">from</span> <span class="nn">equation_tree</span> <span class="kn">import</span> <span class="n">instantiate_constants</span>
+<span class="kn">import</span> <span class="nn">random</span>
+
+<span class="c1"># then we can use a function to instantiate the constants. For example for random constants between 0 and 1:</span>
+<span class="n">instantiated_equation</span> <span class="o">=</span> <span class="n">instantiate_constants</span><span class="p">(</span><span class="n">equations</span><span class="p">[</span><span class="mi">42</span><span class="p">],</span> <span class="k">lambda</span> <span class="p">:</span> <span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">())</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'abstract: </span><span class="si">{</span><span class="n">equations</span><span class="p">[</span><span class="mi">42</span><span class="p">]</span><span class="si">}</span><span class="s1">'</span><span class="p">,</span> <span class="sa">f</span><span class="s1">', instantiated: </span><span class="si">{</span><span class="n">instantiated_equation</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-14"># first we need to import the functionality
+from equation_tree import instantiate_constants
+import random
+
+# then we can use a function to instantiate the constants. For example for random constants between 0 and 1:
+instantiated_equation = instantiate_constants(equations[42], lambda : random.random())
+print(f'abstract: {equations[42]}', f', instantiated: {instantiated_equation}')</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
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+<pre>abstract: -c_2 + tan(c_1*x_1) , instantiated: tan(0.2720878822071884*x_1) - 0.4936315339297549
+</pre>
+</div>
+</div>
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+<div class="jp-InputPrompt jp-InputArea-prompt">In [15]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
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+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
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+<div class="highlight-ipynb hl-python"><pre><span></span><span class="c1"># we can also use other functions (for example all functions to be a constant</span>
+<span class="n">instantiated_equation_</span> <span class="o">=</span> <span class="n">instantiate_constants</span><span class="p">(</span><span class="n">equations</span><span class="p">[</span><span class="mi">41</span><span class="p">],</span> <span class="k">lambda</span> <span class="p">:</span> <span class="mi">1</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'abstract: </span><span class="si">{</span><span class="n">equations</span><span class="p">[</span><span class="mi">41</span><span class="p">]</span><span class="si">}</span><span class="s1">'</span><span class="p">,</span> <span class="sa">f</span><span class="s1">', instantiated: </span><span class="si">{</span><span class="n">instantiated_equation_</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-15"># we can also use other functions (for example all functions to be a constant
+instantiated_equation_ = instantiate_constants(equations[41], lambda : 1)
+print(f'abstract: {equations[41]}', f', instantiated: {instantiated_equation_}')</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
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+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>abstract: c_2*x_1**c_1 , instantiated: x_1
+</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
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+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<p>**We can use arbitrary functions to instantiate the constants.</p>
+<h3 id="evaluating-equations">Evaluating Equations<a class="anchor-link" href="#evaluating-equations">¶</a></h3><p>After instantiating equations, we can also evaluate on arbitrary input:</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
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+<div class="jp-InputPrompt jp-InputArea-prompt">In [16]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
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+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
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+<div class="highlight-ipynb hl-python"><pre><span></span><span class="c1"># import functionality</span>
+<span class="n">values</span> <span class="o">=</span> <span class="n">instantiated_equation</span><span class="o">.</span><span class="n">evaluate</span><span class="p">({</span><span class="s1">'x_1'</span><span class="p">:</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">]})</span>
+<span class="n">values</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-16"># import functionality
+values = instantiated_equation.evaluate({'x_1': [1, 2, 3, 4]})
+values</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[16]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>array([-0.21462429,  0.11148855,  0.57008635,  1.41577756])</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
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+<div class="jp-InputPrompt jp-InputArea-prompt">In [17]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
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+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
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+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="c1"># We can also use pandas dataframes as inputs:</span>
+
+<span class="c1"># import functionality</span>
+<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
+
+<span class="c1"># define the input and get the values</span>
+<span class="n">input_df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">({</span><span class="s1">'x_1'</span><span class="p">:</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">]})</span>
+<span class="n">instantiated_equation</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="n">input_df</span><span class="p">)</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-17"># We can also use pandas dataframes as inputs:
+
+# import functionality
+import pandas as pd
+
+# define the input and get the values
+input_df = pd.DataFrame({'x_1': [1, 2, 3, 4]})
+instantiated_equation.evaluate(input_df)</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[17]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>array([-0.21462429,  0.11148855,  0.57008635,  1.41577756])</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<h2 id="sample-settings">Sample Settings<a class="anchor-link" href="#sample-settings">¶</a></h2><p>When sampling equations, we can control for a variety of features of the underlying distribution.</p>
+<h3 id="input-dimensions">Input Dimensions<a class="anchor-link" href="#input-dimensions">¶</a></h3><p>We can manipulate the space on witch the equation is defined. For example, if we want equations that are defined on 2-dimensions, we can write:</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [25]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
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+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">equations_2d</span> <span class="o">=</span> <span class="n">sample</span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">max_num_variables</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-18">equations_2d = sample(n=5, max_num_variables=2)</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="application/vnd.jupyter.stderr" tabindex="0">
+<pre>/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.
+  warnings.warn(
+Processing:   0%|          | 0/5 [00:00&lt;?, ?iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:55: RuntimeWarning: invalid value encountered in arccos
+  "acos": lambda a: np.arccos(a),
+/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:51: RuntimeWarning: invalid value encountered in log
+  "log": lambda a: np.log(a),
+/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:56: RuntimeWarning: invalid value encountered in arcsin
+  "asin": lambda a: np.arcsin(a),
+/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:52: RuntimeWarning: invalid value encountered in sqrt
+  "sqrt": lambda a: np.sqrt(a),
+Processing: 100%|██████████| 5/5 [00:00&lt;00:00, 112.51iteration/s]
+</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [27]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-19">
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+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
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+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">equations_2d</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-19">equations_2d</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[27]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>[acos(Abs(acos(x_1))),
+ -Abs(x_2) + asin(log(x_1)),
+ Max(c_1, x_1),
+ Max(x_1, Abs(sqrt(sin(x_1)))),
+ cos(x_1*(c_1 + x_2))]</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<p>**Note: Not all the equations have exactly 2 input variable. Some of them have only one. This is since equations with only one input variable are still defined on 2 (or more dimensions)</p>
+<h3 id="equation-complexity">Equation Complexity<a class="anchor-link" href="#equation-complexity">¶</a></h3><p>We can also manipulate the equation complexity (as number of nodes)</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [28]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-20">
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+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">equations_simple</span> <span class="o">=</span> <span class="n">sample</span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">depth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
+<span class="n">equations_complex</span> <span class="o">=</span> <span class="n">sample</span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">depth</span><span class="o">=</span><span class="mi">8</span><span class="p">)</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-20">equations_simple = sample(n=5, depth=3)
+equations_complex = sample(n=5, depth=8)</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="application/vnd.jupyter.stderr" tabindex="0">
+<pre>/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.
+  warnings.warn(
+Processing:   0%|          | 0/5 [00:00&lt;?, ?iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:55: RuntimeWarning: invalid value encountered in arccos
+  "acos": lambda a: np.arccos(a),
+/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:56: RuntimeWarning: invalid value encountered in arcsin
+  "asin": lambda a: np.arcsin(a),
+/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:40: RuntimeWarning: invalid value encountered in scalar power
+  "^": lambda a, b: a**b,
+Processing: 100%|██████████| 5/5 [00:00&lt;00:00, 312.27iteration/s]
+Processing:   0%|          | 0/5 [00:00&lt;?, ?iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:40: RuntimeWarning: divide by zero encountered in scalar power
+  "^": lambda a, b: a**b,
+/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:47: RuntimeWarning: invalid value encountered in sin
+  "sin": lambda a: np.sin(a),
+Processing:  40%|████      | 2/5 [00:00&lt;00:00, 12.82iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:52: RuntimeWarning: invalid value encountered in sqrt
+  "sqrt": lambda a: np.sqrt(a),
+/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:51: RuntimeWarning: invalid value encountered in log
+  "log": lambda a: np.log(a),
+Processing: 100%|██████████| 5/5 [00:00&lt;00:00, 21.56iteration/s]
+</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [29]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-21">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="s1">'*** simple equations ***</span><span class="se">\n</span><span class="s1">'</span><span class="p">,</span> <span class="n">equations_simple</span><span class="p">,</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s1">'*** complex equations ***</span><span class="se">\n</span><span class="s1">'</span><span class="p">,</span> <span class="n">equations_complex</span><span class="p">)</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-21">print('*** simple equations ***\n', equations_simple, '\n')
+print('*** complex equations ***\n', equations_complex)</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>*** simple equations ***
+ [acos(exp(x_1)), Max(c_1, x_1), x_1/c_1, asin(exp(x_1)), x_1**c_1] 
+
+*** complex equations ***
+ [sin(exp(sqrt(1 - sin(x_1)**2)/sin(x_1))**x_1), (x_1 + Min(x_1, sin(x_1)))/sqrt(1 - (x_1 + Min(x_1, sin(x_1)))**2), sqrt(Min(c_1**sin(sin(x_1)), x_1)), -asin(x_1)**x_1 + Min(c_1, x_1), Max(-x_1 + log(x_1), sqrt(Abs(x_1)))]
+</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<h3 id="using-priors">Using Priors<a class="anchor-link" href="#using-priors">¶</a></h3><p>We can also make use of priors to fully customize the sampling. Here, the entries for the structures, features, functions and operators represent the probability of the respective attribute being sampled.</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [34]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-22">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">p</span> <span class="o">=</span> <span class="p">{</span>
+    <span class="s1">'structures'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'[0, 1, 1]'</span><span class="p">:</span> <span class="mf">.3</span><span class="p">,</span> <span class="s1">'[0, 1, 2]'</span><span class="p">:</span> <span class="mf">.3</span><span class="p">,</span> <span class="s1">'[0, 1, 2, 3, 2, 3, 1]'</span><span class="p">:</span> <span class="mf">.4</span><span class="p">},</span>
+    <span class="s1">'features'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'constants'</span><span class="p">:</span> <span class="mf">.2</span><span class="p">,</span> <span class="s1">'variables'</span><span class="p">:</span> <span class="mf">.8</span><span class="p">},</span>
+    <span class="s1">'functions'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'sin'</span><span class="p">:</span> <span class="mf">.5</span><span class="p">,</span> <span class="s1">'cos'</span><span class="p">:</span> <span class="mf">.5</span><span class="p">},</span>
+    <span class="s1">'operators'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'+'</span><span class="p">:</span> <span class="mf">.8</span><span class="p">,</span> <span class="s1">'-'</span><span class="p">:</span> <span class="mf">.2</span><span class="p">}</span>
+<span class="p">}</span>
+<span class="n">equations_with_prior</span> <span class="o">=</span> <span class="n">sample</span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">prior</span><span class="o">=</span><span class="n">p</span><span class="p">,</span> <span class="n">max_num_variables</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
+<span class="n">equations_with_prior</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-22">p = {
+    'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},
+    'features': {'constants': .2, 'variables': .8},
+    'functions': {'sin': .5, 'cos': .5},
+    'operators': {'+': .8, '-': .2}
+}
+equations_with_prior = sample(n=10, prior=p, max_num_variables=10)
+equations_with_prior</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="application/vnd.jupyter.stderr" tabindex="0">
+<pre>/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.
+  warnings.warn(
+Processing: 100%|██████████| 100/100 [00:00&lt;00:00, 190.81iteration/s]
+</pre>
+</div>
+</div>
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[34]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>[cos(cos(x_1)),
+ sin(sin(x_1)),
+ -x_3 + sin(x_1) + sin(x_2),
+ -x_3 + sin(x_2) + cos(x_1),
+ cos(cos(x_1)),
+ cos(sin(x_1)),
+ sin(cos(x_1)),
+ x_1 + x_2,
+ sin(cos(x_1)),
+ cos(sin(x_1)),
+ x_1 + x_2,
+ cos(sin(x_1)),
+ x_1 - x_2,
+ x_1 + x_2,
+ sin(sin(x_1)),
+ x_1 + x_2,
+ sin(cos(x_1)),
+ -c_1 + x_1,
+ sin(cos(x_1)),
+ x_1 + x_2,
+ x_1 + x_2,
+ x_1 + x_2,
+ x_1 + x_2,
+ sin(cos(x_1)),
+ c_1 + x_1,
+ x_1 - x_2,
+ x_1 - x_2,
+ x_1 + x_2,
+ sin(sin(x_1)),
+ c_1 + x_1,
+ cos(sin(x_1)),
+ cos(sin(x_1)),
+ cos(sin(x_1)),
+ cos(cos(x_1)),
+ c_1 + x_1,
+ sin(cos(x_1)),
+ sin(cos(x_1)),
+ x_1 - x_2,
+ cos(sin(x_1)),
+ cos(sin(x_1)),
+ x_1 - x_2,
+ cos(cos(x_1)),
+ x_1 + x_2,
+ x_1 + x_2,
+ sin(sin(x_1)),
+ c_1 + x_1,
+ c_1 + x_1,
+ x_1 + x_2,
+ x_1 - x_2,
+ sin(sin(x_1)),
+ cos(cos(x_1)),
+ cos(cos(x_1)),
+ cos(cos(x_1)),
+ sin(cos(x_1)),
+ x_1 - x_2,
+ sin(sin(x_1)),
+ cos(cos(x_1)),
+ c_1 + x_1,
+ sin(sin(x_1)),
+ cos(sin(x_1)),
+ cos(sin(x_1)),
+ x_1 + x_2,
+ cos(sin(x_1)),
+ sin(cos(x_1)),
+ c_1 + x_1,
+ -x_2,
+ x_1 - x_2,
+ -x_3 + sin(x_1) + sin(x_2),
+ c_1 + x_1,
+ x_1 + x_2,
+ c_1 + x_1,
+ c_1 + x_1,
+ sin(sin(x_1)),
+ cos(cos(x_1)),
+ x_1 + x_2,
+ c_1 + x_1,
+ -x_1 + cos(x_1) + cos(x_2),
+ x_1 - x_2,
+ cos(sin(x_1)),
+ sin(cos(x_1)),
+ sin(cos(x_1)),
+ sin(cos(x_1)),
+ -x_3 + sin(x_1) + cos(x_2),
+ x_1 + x_2,
+ -x_3 + sin(x_2) + cos(x_1),
+ -x_3 + sin(x_1) + sin(x_2),
+ c_1 - x_1,
+ c_1 + x_1,
+ c_1 + x_1,
+ cos(cos(x_1)),
+ -x_2 + sin(x_2) + cos(x_1),
+ c_1 + x_1,
+ sin(sin(x_1)),
+ c_1 + x_1,
+ x_1 + x_2,
+ sin(sin(x_1)),
+ x_1 + x_2,
+ x_1 + x_2,
+ cos(sin(x_1)),
+ sin(sin(x_1))]</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<p>We can also use conditional priors conditioned on the parent node:</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [38]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-23">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+<path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0114.25 11h-7.5A1.75 1.75 0 015 9.25v-7.5zm1.75-.25a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-7.5a.25.25 0 00-.25-.25h-7.5z" fill="currentColor" fill-rule="evenodd"></path>
+</svg>
+</div>
+</clipboard-copy>
+</div>
+<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">p_</span> <span class="o">=</span> <span class="p">{</span>
+    <span class="s1">'structures'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'[0, 1, 1]'</span><span class="p">:</span> <span class="mf">.3</span><span class="p">,</span> <span class="s1">'[0, 1, 2]'</span><span class="p">:</span> <span class="mf">.3</span><span class="p">,</span> <span class="s1">'[0, 1, 2, 3, 2, 3, 1]'</span><span class="p">:</span> <span class="mf">.4</span><span class="p">},</span>
+    <span class="s1">'features'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'constants'</span><span class="p">:</span> <span class="mf">.2</span><span class="p">,</span> <span class="s1">'variables'</span><span class="p">:</span> <span class="mf">.8</span><span class="p">},</span>
+    <span class="s1">'functions'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'sin'</span><span class="p">:</span> <span class="mf">.5</span><span class="p">,</span> <span class="s1">'cos'</span><span class="p">:</span> <span class="mf">.5</span><span class="p">},</span>
+    <span class="s1">'operators'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'+'</span><span class="p">:</span> <span class="mf">.5</span><span class="p">,</span> <span class="s1">'-'</span><span class="p">:</span> <span class="mf">.5</span><span class="p">},</span>
+    <span class="s1">'function_conditionals'</span><span class="p">:</span> <span class="p">{</span>
+        <span class="s1">'sin'</span><span class="p">:</span> <span class="p">{</span>
+            <span class="s1">'features'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'constants'</span><span class="p">:</span> <span class="mf">0.</span><span class="p">,</span> <span class="s1">'variables'</span><span class="p">:</span> <span class="mf">1.</span><span class="p">},</span>
+            <span class="s1">'functions'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'sin'</span><span class="p">:</span> <span class="mf">0.</span><span class="p">,</span> <span class="s1">'cos'</span><span class="p">:</span> <span class="mf">1.</span><span class="p">},</span>
+            <span class="s1">'operators'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'+'</span><span class="p">:</span> <span class="mf">.5</span><span class="p">,</span> <span class="s1">'-'</span><span class="p">:</span> <span class="mf">.5</span><span class="p">}</span>
+        <span class="p">},</span>
+        <span class="s1">'cos'</span><span class="p">:</span> <span class="p">{</span>
+            <span class="s1">'features'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'constants'</span><span class="p">:</span> <span class="mf">0.</span><span class="p">,</span> <span class="s1">'variables'</span><span class="p">:</span> <span class="mf">1.</span><span class="p">},</span>
+            <span class="s1">'functions'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'cos'</span><span class="p">:</span> <span class="mf">1.</span><span class="p">,</span> <span class="s1">'sin'</span><span class="p">:</span> <span class="mf">0.</span><span class="p">},</span>
+            <span class="s1">'operators'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'+'</span><span class="p">:</span> <span class="mf">0.</span><span class="p">,</span> <span class="s1">'-'</span><span class="p">:</span> <span class="mf">1.</span><span class="p">}</span>
+        <span class="p">}</span>
+    <span class="p">},</span>
+    <span class="s1">'operator_conditionals'</span><span class="p">:</span> <span class="p">{</span>
+        <span class="s1">'+'</span><span class="p">:</span> <span class="p">{</span>
+            <span class="s1">'features'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'constants'</span><span class="p">:</span> <span class="mf">.5</span><span class="p">,</span> <span class="s1">'variables'</span><span class="p">:</span> <span class="mf">.5</span><span class="p">},</span>
+            <span class="s1">'functions'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'sin'</span><span class="p">:</span> <span class="mf">1.</span><span class="p">,</span> <span class="s1">'cos'</span><span class="p">:</span> <span class="mf">0.</span><span class="p">},</span>
+            <span class="s1">'operators'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'+'</span><span class="p">:</span> <span class="mf">1.</span><span class="p">,</span> <span class="s1">'-'</span><span class="p">:</span> <span class="mf">0.</span><span class="p">}</span>
+        <span class="p">},</span>
+        <span class="s1">'-'</span><span class="p">:</span> <span class="p">{</span>
+            <span class="s1">'features'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'constants'</span><span class="p">:</span> <span class="mf">.3</span><span class="p">,</span> <span class="s1">'variables'</span><span class="p">:</span> <span class="mf">.7</span><span class="p">},</span>
+            <span class="s1">'functions'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'cos'</span><span class="p">:</span> <span class="mf">.5</span><span class="p">,</span> <span class="s1">'sin'</span><span class="p">:</span> <span class="mf">.5</span><span class="p">},</span>
+            <span class="s1">'operators'</span><span class="p">:</span> <span class="p">{</span><span class="s1">'+'</span><span class="p">:</span> <span class="mf">.9</span><span class="p">,</span> <span class="s1">'-'</span><span class="p">:</span> <span class="mf">.1</span><span class="p">}</span>
+        <span class="p">}</span>
+    <span class="p">},</span>
+<span class="p">}</span>
+<span class="n">equations_with_conditional_prior</span> <span class="o">=</span> <span class="n">sample</span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">prior</span><span class="o">=</span><span class="n">p_</span><span class="p">,</span> <span class="n">max_num_variables</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
+<span class="n">equations_with_conditional_prior</span>
+</pre></div>
+<div class="clipboard-copy-txt" id="cell-23">p_ = {
+    'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},
+    'features': {'constants': .2, 'variables': .8},
+    'functions': {'sin': .5, 'cos': .5},
+    'operators': {'+': .5, '-': .5},
+    'function_conditionals': {
+        'sin': {
+            'features': {'constants': 0., 'variables': 1.},
+            'functions': {'sin': 0., 'cos': 1.},
+            'operators': {'+': .5, '-': .5}
+        },
+        'cos': {
+            'features': {'constants': 0., 'variables': 1.},
+            'functions': {'cos': 1., 'sin': 0.},
+            'operators': {'+': 0., '-': 1.}
+        }
+    },
+    'operator_conditionals': {
+        '+': {
+            'features': {'constants': .5, 'variables': .5},
+            'functions': {'sin': 1., 'cos': 0.},
+            'operators': {'+': 1., '-': 0.}
+        },
+        '-': {
+            'features': {'constants': .3, 'variables': .7},
+            'functions': {'cos': .5, 'sin': .5},
+            'operators': {'+': .9, '-': .1}
+        }
+    },
+}
+equations_with_conditional_prior = sample(n=10, prior=p_, max_num_variables=10)
+equations_with_conditional_prior</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="application/vnd.jupyter.stderr" tabindex="0">
+<pre>/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.
+  warnings.warn(
+Processing: 100%|██████████| 100/100 [00:00&lt;00:00, 128.08iteration/s]
+</pre>
+</div>
+</div>
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[38]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>[cos(cos(x_1)),
+ x_1 - x_2,
+ -c_1 + x_1,
+ sin(cos(x_1)),
+ sin(cos(x_1)),
+ c_1 + x_1,
+ -c_1 + sin(x_1) + sin(x_2),
+ cos(cos(x_1)),
+ cos(cos(x_1)),
+ -x_3 + sin(x_1) + sin(x_2),
+ sin(cos(x_1)),
+ c_1 - x_1,
+ -x_3 + sin(x_1) + sin(x_2),
+ cos(cos(x_1)),
+ -x_3 + sin(x_1) + sin(x_2),
+ cos(cos(x_1)),
+ c_1 - x_1,
+ sin(cos(x_1)),
+ cos(cos(x_1)),
+ x_1 - x_2,
+ -c_1 + sin(x_1) + sin(x_2),
+ -x_3 + sin(x_1) + sin(x_2),
+ cos(cos(x_1)),
+ c_1 - x_1,
+ sin(cos(x_1)),
+ x_1 - x_2,
+ -x_3 - sin(x_2) + cos(x_1),
+ -c_1 + x_1,
+ sin(cos(x_1)),
+ cos(cos(x_1)),
+ sin(cos(x_1)),
+ x_1 + x_2,
+ cos(cos(x_1)),
+ -x_3 + sin(x_1) - sin(x_2),
+ c_1 + x_1,
+ cos(cos(x_1)),
+ cos(cos(x_1)),
+ sin(cos(x_1)),
+ x_1 - x_2,
+ -x_3 + sin(x_1) + sin(x_2),
+ -c_1 + x_1,
+ c_1 - x_1,
+ c_1 + x_1,
+ c_1 + x_1,
+ cos(cos(x_1)),
+ -c_1 + sin(x_1) + sin(x_2),
+ c_1 + x_1,
+ sin(cos(x_1)),
+ sin(cos(x_1)),
+ -x_3 + sin(x_1) + sin(x_2),
+ -x_3 + sin(x_1) - cos(x_2),
+ sin(cos(x_1)),
+ x_1 - x_2,
+ -x_3 + cos(x_1) - cos(x_2),
+ x_1 - x_2,
+ cos(cos(x_1)),
+ sin(cos(x_1)),
+ -x_2 + sin(x_1) + sin(x_2),
+ cos(cos(x_1)),
+ -c_1 + sin(x_1) + sin(x_2),
+ -x_2 + sin(x_1) - cos(x_2),
+ cos(cos(x_1)),
+ -x_2 + sin(x_1) + sin(x_2),
+ -x_3 + sin(x_1) + sin(x_2),
+ sin(cos(x_1)),
+ cos(cos(x_1)),
+ cos(cos(x_1)),
+ -c_1 + sin(x_1) + sin(x_2),
+ cos(cos(x_1)),
+ cos(cos(x_1)),
+ cos(cos(x_1)),
+ -x_3 + sin(x_1) + sin(x_2),
+ cos(cos(x_1)),
+ cos(cos(x_1)),
+ -x_3 + sin(x_1) + sin(x_2),
+ x_1 + x_2,
+ c_1 - x_1,
+ -x_1 + sin(x_1) + sin(x_2),
+ cos(cos(x_1)),
+ -c_1 + sin(x_1) + sin(x_2),
+ c_1 - x_1,
+ cos(cos(x_1)),
+ -x_3 + sin(x_1) + sin(x_2),
+ cos(cos(x_1)),
+ c_1 - x_1,
+ -x_3 + sin(x_1) + sin(x_2),
+ cos(cos(x_1)),
+ -x_3 + sin(x_1) + sin(x_2),
+ c_1 + x_1,
+ x_1 - x_2,
+ cos(cos(x_1)),
+ c_1 + x_1,
+ cos(cos(x_1)),
+ sin(cos(x_1)),
+ sin(cos(x_1)),
+ sin(cos(x_1)),
+ sin(cos(x_1)),
+ sin(cos(x_1)),
+ -x_3 + sin(x_1) + sin(x_2),
+ c_1 + x_1]</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<p><strong>WARNING</strong>
+If your application is dependent on these priors, you should "burn" samples before starting the sampling.
+During the sampling process, equations get simplified and invalid equations are discarded. This is likely to lead to disparities between the priors and the sampled frequencies.
+To counteract this, the package offers the functionality to "burn" samples and adjust the priors so that the outcome frequency match them more closely. To burn samples, use the following code (We don't run it in the notebook since the adjusted priors are saved to disk for future use):</p>
+<pre><code>burn(
+    prior,
+    max_number_variables,
+    path_to_file,
+    number_of_burned_samples,
+    learning_rate
+    )
+</code></pre>
+<p>*this function should be run multiple times. The learning rate defines how much adjusted from previous runs are adjusted.
+After burning, you can load the adjusted priors via:</p>
+<pre><code>    sample(..., file=path_to_file)
+</code></pre>
+<p>*multiple adjusted priors can be stored in the same file.</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs">
+<div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="CodeMirror cm-s-jupyter">
+<div class="zeroclipboard-container">
+<clipboard-copy for="cell-24">
+<div>
+<span class="notice" hidden="">Copied!</span>
+<svg aria-hidden="true" class="clipboard-copy-icon" data-view-component="true" height="20" version="1.1" viewbox="0 0 16 16" width="20">
+<path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 010 1.5h-1.5a.25.25 0 00-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 00.25-.25v-1.5a.75.75 0 011.5 0v1.5A1.75 1.75 0 019.25 16h-7.5A1.75 1.75 0 010 14.25v-7.5z" fill="currentColor" fill-rule="evenodd"></path>
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+</div>
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 </div>
 </div>
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diff --git a/index.html b/index.html
index 3a4b6ce..b922364 100644
--- a/index.html
+++ b/index.html
@@ -372,7 +372,7 @@
             
   
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@@ -392,11 +392,31 @@
   
   
     <li class="md-nav__item">
-      <a href="Basic%20Usage/" class="md-nav__link">
+      <a href="user-guide/sampling/" class="md-nav__link">
         
   
   <span class="md-ellipsis">
-    Basic Usage
+    Sampling
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="user-guide/equation-formats/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Equation Formats
   </span>
   
 
@@ -431,6 +451,69 @@
         <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
         
           
+          <label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
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+            
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="Equation Sampling.ipynb" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Equation Sampling
+  </span>
+  
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+      </a>
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           <div class="md-nav__link md-nav__container">
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@@ -444,14 +527,14 @@
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             <span class="md-nav__icon md-icon"></span>
             Code Reference
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+              <label class="md-nav__link " for="__nav_5_1_1" id="__nav_5_1_1_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_5_1_1">
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             Equation tree
           </label>
@@ -652,7 +735,7 @@
         
         
         
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_6" >
         
           
           
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_7" >
         
           
           
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             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1_7" id="__nav_4_1_1_7_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_7">
             <span class="md-nav__icon md-icon"></span>
             Util
           </label>
@@ -961,7 +1044,7 @@
 <h1 id="equation-tree">Equation Tree</h1>
 <p>The Equation Tree package is an equation toolbox with symbolic regression in mind. It represents
 expressions as incomplete binary trees and has various features tailored towards testing symbolic
-regression algorithms or training models. The main features are:</p>
+regression algorithms or training models. The most notable features are:</p>
 <ul>
 <li>Equation sampling (including priors)</li>
 <li>Feature Extraction from equation distributions</li>
diff --git a/index.md b/index.md
index ad0aee7..ac76ca0 100644
--- a/index.md
+++ b/index.md
@@ -2,7 +2,7 @@
 
 The Equation Tree package is an equation toolbox with symbolic regression in mind. It represents
 expressions as incomplete binary trees and has various features tailored towards testing symbolic
-regression algorithms or training models. The main features are:
+regression algorithms or training models. The most notable features are:
 
 - Equation sampling (including priors)
 - Feature Extraction from equation distributions
diff --git a/quickstart/index.html b/quickstart/index.html
index 1072efb..404f39e 100644
--- a/quickstart/index.html
+++ b/quickstart/index.html
@@ -14,7 +14,7 @@
         <link rel="prev" href="..">
       
       
-        <link rel="next" href="../Basic%20Usage/">
+        <link rel="next" href="../user-guide/sampling/">
       
       
       <link rel="icon" href="../assets/images/favicon.png">
@@ -316,7 +316,7 @@
             
   
   <span class="md-ellipsis">
-    Tutorials
+    User Guide
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           <label class="md-nav__title" for="__nav_3">
             <span class="md-nav__icon md-icon"></span>
-            Tutorials
+            User Guide
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           <ul class="md-nav__list" data-md-scrollfix>
             
@@ -336,11 +336,31 @@
   
   
     <li class="md-nav__item">
-      <a href="../Basic%20Usage/" class="md-nav__link">
+      <a href="../user-guide/sampling/" class="md-nav__link">
         
   
   <span class="md-ellipsis">
-    Basic Usage
+    Sampling
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../user-guide/equation-formats/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Equation Formats
   </span>
   
 
@@ -375,6 +395,69 @@
         <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
         
           
+          <label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
+            
+  
+  <span class="md-ellipsis">
+    Tutorials
+  </span>
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+
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            Tutorials
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../Equation Sampling.ipynb" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Equation Sampling
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
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+      
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+  
+  
+  
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+    
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+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
           
           <div class="md-nav__link md-nav__container">
             <a href="../reference/SUMMARY/" class="md-nav__link ">
@@ -388,14 +471,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
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               </label>
             
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
             <span class="md-nav__icon md-icon"></span>
             Code Reference
           </label>
@@ -416,10 +499,10 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1" >
         
           
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+          <label class="md-nav__link" for="__nav_5_1" id="__nav_5_1_label" tabindex="0">
             
   
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             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -452,7 +535,7 @@
         
         
         
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1" >
         
           
           
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             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1" id="__nav_4_1_1_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1" id="__nav_5_1_1_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_5_1_1">
             <span class="md-nav__icon md-icon"></span>
             Equation tree
           </label>
@@ -596,7 +679,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_6" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_6" >
         
           
           
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             </a>
             
               
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             <span class="md-nav__icon md-icon"></span>
             Src
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@@ -688,7 +771,7 @@
         
         
         
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_7" >
         
           
           
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             </a>
             
               
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+              <label class="md-nav__link " for="__nav_5_1_1_7" id="__nav_5_1_1_7_label" tabindex="0">
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-          <label class="md-nav__title" for="__nav_4_1_1_7">
+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_7">
             <span class="md-nav__icon md-icon"></span>
             Util
           </label>
diff --git a/reference/SUMMARY/index.html b/reference/SUMMARY/index.html
index 2550658..50bc7e1 100644
--- a/reference/SUMMARY/index.html
+++ b/reference/SUMMARY/index.html
@@ -11,7 +11,7 @@
         <link rel="canonical" href="https://autoresearch.github.io/equation-tree/reference/SUMMARY/">
       
       
-        <link rel="prev" href="../../Basic%20Usage/">
+        <link rel="prev" href="../../user-guide/equation-formats/">
       
       
         <link rel="next" href="../src/equation_tree/">
@@ -301,7 +301,7 @@
             
   
   <span class="md-ellipsis">
-    Tutorials
+    User Guide
   </span>
   
 
@@ -310,6 +310,89 @@
         
         <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
           <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            User Guide
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../user-guide/sampling/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Sampling
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../user-guide/equation-formats/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Equation Formats
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+    
+    
+    
+    
+    
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+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          <label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
+            
+  
+  <span class="md-ellipsis">
+    Tutorials
+  </span>
+  
+
+            <span class="md-nav__icon md-icon"></span>
+          </label>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
             <span class="md-nav__icon md-icon"></span>
             Tutorials
           </label>
@@ -321,11 +404,11 @@
   
   
     <li class="md-nav__item">
-      <a href="../../Basic%20Usage/" class="md-nav__link">
+      <a href="../../Equation Sampling.ipynb" class="md-nav__link">
         
   
   <span class="md-ellipsis">
-    Basic Usage
+    Equation Sampling
   </span>
   
 
@@ -359,7 +442,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" checked>
         
           
           
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-              <label class="md-nav__link md-nav__link--active" for="__nav_4" id="__nav_4_label" tabindex="0">
+              <label class="md-nav__link md-nav__link--active" for="__nav_5" id="__nav_5_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5">
             <span class="md-nav__icon md-icon"></span>
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+          <label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
+            
+  
+  <span class="md-ellipsis">
+    Tutorials
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+
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             Tutorials
           </label>
@@ -326,11 +409,11 @@
   
   
     <li class="md-nav__item">
-      <a href="../../../Basic%20Usage/" class="md-nav__link">
+      <a href="../../../Equation Sampling.ipynb" class="md-nav__link">
         
   
   <span class="md-ellipsis">
-    Basic Usage
+    Equation Sampling
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@@ -364,7 +447,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" checked>
         
           
           
@@ -380,14 +463,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
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               </label>
             
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-        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="true">
-          <label class="md-nav__title" for="__nav_4">
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5">
             <span class="md-nav__icon md-icon"></span>
             Code Reference
           </label>
@@ -410,10 +493,10 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1" checked>
         
           
-          <label class="md-nav__link" for="__nav_4_1" id="__nav_4_1_label" tabindex="0">
+          <label class="md-nav__link" for="__nav_5_1" id="__nav_5_1_label" tabindex="0">
             
   
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@@ -424,8 +507,8 @@
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+        <nav class="md-nav" data-md-level="2" aria-labelledby="__nav_5_1_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5_1">
             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -448,7 +531,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1" checked>
         
           
           
@@ -464,14 +547,14 @@
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-              <label class="md-nav__link md-nav__link--active" for="__nav_4_1_1" id="__nav_4_1_1_label" tabindex="0">
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-          <label class="md-nav__title" for="__nav_4_1_1">
+        <nav class="md-nav" data-md-level="3" aria-labelledby="__nav_5_1_1_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5_1_1">
             <span class="md-nav__icon md-icon"></span>
             Equation tree
           </label>
@@ -592,7 +675,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_6" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_6" >
         
           
           
@@ -608,14 +691,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1_6" id="__nav_4_1_1_6_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1_6" id="__nav_5_1_1_6_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_6">
             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -684,7 +767,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_7" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_7" >
         
           
           
@@ -700,14 +783,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1_7" id="__nav_4_1_1_7_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1_7" id="__nav_5_1_1_7_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_7">
             <span class="md-nav__icon md-icon"></span>
             Util
           </label>
diff --git a/reference/src/equation_tree/prior/index.html b/reference/src/equation_tree/prior/index.html
index 3b675db..57b6d22 100644
--- a/reference/src/equation_tree/prior/index.html
+++ b/reference/src/equation_tree/prior/index.html
@@ -306,7 +306,7 @@
             
   
   <span class="md-ellipsis">
-    Tutorials
+    User Guide
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@@ -315,6 +315,89 @@
         
         <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
           <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            User Guide
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+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../../../user-guide/sampling/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Sampling
+  </span>
+  
+
+      </a>
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+  
+
+              
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+              
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+  
+  
+    <li class="md-nav__item">
+      <a href="../../../../user-guide/equation-formats/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    Equation Formats
+  </span>
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+
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+        
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+          <label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
+            
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+  <span class="md-ellipsis">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
             <span class="md-nav__icon md-icon"></span>
             Tutorials
           </label>
@@ -326,11 +409,11 @@
   
   
     <li class="md-nav__item">
-      <a href="../../../../Basic%20Usage/" class="md-nav__link">
+      <a href="../../../../Equation Sampling.ipynb" class="md-nav__link">
         
   
   <span class="md-ellipsis">
-    Basic Usage
+    Equation Sampling
   </span>
   
 
@@ -364,7 +447,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" checked>
         
           
           
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5">
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             Code Reference
           </label>
@@ -410,10 +493,10 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1" checked>
         
           
-          <label class="md-nav__link" for="__nav_4_1" id="__nav_4_1_label" tabindex="0">
+          <label class="md-nav__link" for="__nav_5_1" id="__nav_5_1_label" tabindex="0">
             
   
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+        <nav class="md-nav" data-md-level="2" aria-labelledby="__nav_5_1_label" aria-expanded="true">
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             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -448,7 +531,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1" checked>
         
           
           
@@ -464,14 +547,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1" id="__nav_4_1_1_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1" id="__nav_5_1_1_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
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+        <nav class="md-nav" data-md-level="3" aria-labelledby="__nav_5_1_1_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5_1_1">
             <span class="md-nav__icon md-icon"></span>
             Equation tree
           </label>
@@ -712,7 +795,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_6" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_6" >
         
           
           
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+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_6">
             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -804,7 +887,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_7" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_7" >
         
           
           
@@ -820,14 +903,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1_7" id="__nav_4_1_1_7_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1_7" id="__nav_5_1_1_7_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_7">
             <span class="md-nav__icon md-icon"></span>
             Util
           </label>
@@ -1123,9 +1206,7 @@ <h2 id="src.equation_tree.prior.add" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/prior.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">172</span>
-<span class="normal">173</span>
-<span class="normal">174</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">174</span>
 <span class="normal">175</span>
 <span class="normal">176</span>
 <span class="normal">177</span>
@@ -1146,7 +1227,9 @@ <h2 id="src.equation_tree.prior.add" class="doc doc-heading">
 <span class="normal">192</span>
 <span class="normal">193</span>
 <span class="normal">194</span>
-<span class="normal">195</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="n">prior_a</span><span class="p">,</span> <span class="n">prior_b</span><span class="p">):</span>
+<span class="normal">195</span>
+<span class="normal">196</span>
+<span class="normal">197</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="n">prior_a</span><span class="p">,</span> <span class="n">prior_b</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    &gt;&gt;&gt; import pprint</span>
 <span class="sd">    &gt;&gt;&gt; a = {&#39;a&#39;: {&#39;a_1&#39;: 3, &#39;a_2&#39;: 2}, &#39;b&#39;: {&#39;b_1&#39;: .1, &#39;b_2&#39;: .3}}</span>
@@ -1203,9 +1286,7 @@ <h2 id="src.equation_tree.prior.filter_keys" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/prior.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">124</span>
-<span class="normal">125</span>
-<span class="normal">126</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">126</span>
 <span class="normal">127</span>
 <span class="normal">128</span>
 <span class="normal">129</span>
@@ -1226,7 +1307,9 @@ <h2 id="src.equation_tree.prior.filter_keys" class="doc doc-heading">
 <span class="normal">144</span>
 <span class="normal">145</span>
 <span class="normal">146</span>
-<span class="normal">147</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">filter_keys</span><span class="p">(</span><span class="n">dict_a</span><span class="p">,</span> <span class="n">dict_b</span><span class="p">):</span>
+<span class="normal">147</span>
+<span class="normal">148</span>
+<span class="normal">149</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">filter_keys</span><span class="p">(</span><span class="n">dict_a</span><span class="p">,</span> <span class="n">dict_b</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Examples:</span>
 <span class="sd">        &gt;&gt;&gt; import pprint</span>
@@ -1293,9 +1376,7 @@ <h2 id="src.equation_tree.prior.get_defined_functions" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/prior.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">389</span>
-<span class="normal">390</span>
-<span class="normal">391</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">391</span>
 <span class="normal">392</span>
 <span class="normal">393</span>
 <span class="normal">394</span>
@@ -1312,7 +1393,9 @@ <h2 id="src.equation_tree.prior.get_defined_functions" class="doc doc-heading">
 <span class="normal">405</span>
 <span class="normal">406</span>
 <span class="normal">407</span>
-<span class="normal">408</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">get_defined_functions</span><span class="p">(</span><span class="n">prior</span><span class="p">):</span>
+<span class="normal">408</span>
+<span class="normal">409</span>
+<span class="normal">410</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">get_defined_functions</span><span class="p">(</span><span class="n">prior</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Examples:</span>
 <span class="sd">        &gt;&gt;&gt; test_prior = {</span>
@@ -1375,9 +1458,7 @@ <h2 id="src.equation_tree.prior.get_defined_operators" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/prior.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">411</span>
-<span class="normal">412</span>
-<span class="normal">413</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">413</span>
 <span class="normal">414</span>
 <span class="normal">415</span>
 <span class="normal">416</span>
@@ -1394,7 +1475,9 @@ <h2 id="src.equation_tree.prior.get_defined_operators" class="doc doc-heading">
 <span class="normal">427</span>
 <span class="normal">428</span>
 <span class="normal">429</span>
-<span class="normal">430</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">get_defined_operators</span><span class="p">(</span><span class="n">prior</span><span class="p">):</span>
+<span class="normal">430</span>
+<span class="normal">431</span>
+<span class="normal">432</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">get_defined_operators</span><span class="p">(</span><span class="n">prior</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Examples:</span>
 <span class="sd">        &gt;&gt;&gt; test_prior = {</span>
@@ -1466,9 +1549,7 @@ <h2 id="src.equation_tree.prior.multiply" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/prior.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">239</span>
-<span class="normal">240</span>
-<span class="normal">241</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">241</span>
 <span class="normal">242</span>
 <span class="normal">243</span>
 <span class="normal">244</span>
@@ -1509,7 +1590,9 @@ <h2 id="src.equation_tree.prior.multiply" class="doc doc-heading">
 <span class="normal">279</span>
 <span class="normal">280</span>
 <span class="normal">281</span>
-<span class="normal">282</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">multiply</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
+<span class="normal">282</span>
+<span class="normal">283</span>
+<span class="normal">284</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">multiply</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Examples:</span>
 <span class="sd">        &gt;&gt;&gt; import pprint</span>
@@ -1594,9 +1677,7 @@ <h2 id="src.equation_tree.prior.prior_from_space" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/prior.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">26</span>
-<span class="normal">27</span>
-<span class="normal">28</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">28</span>
 <span class="normal">29</span>
 <span class="normal">30</span>
 <span class="normal">31</span>
@@ -1615,7 +1696,9 @@ <h2 id="src.equation_tree.prior.prior_from_space" class="doc doc-heading">
 <span class="normal">44</span>
 <span class="normal">45</span>
 <span class="normal">46</span>
-<span class="normal">47</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">prior_from_space</span><span class="p">(</span><span class="n">space</span><span class="p">):</span>
+<span class="normal">47</span>
+<span class="normal">48</span>
+<span class="normal">49</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">prior_from_space</span><span class="p">(</span><span class="n">space</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Uniform prior from a list of strings</span>
 <span class="sd">    Examples:</span>
@@ -1661,9 +1744,7 @@ <h2 id="src.equation_tree.prior.re_normalize" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/prior.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">104</span>
-<span class="normal">105</span>
-<span class="normal">106</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">106</span>
 <span class="normal">107</span>
 <span class="normal">108</span>
 <span class="normal">109</span>
@@ -1678,7 +1759,9 @@ <h2 id="src.equation_tree.prior.re_normalize" class="doc doc-heading">
 <span class="normal">118</span>
 <span class="normal">119</span>
 <span class="normal">120</span>
-<span class="normal">121</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">re_normalize</span><span class="p">(</span><span class="n">target</span><span class="p">,</span> <span class="n">origin</span><span class="p">):</span>
+<span class="normal">121</span>
+<span class="normal">122</span>
+<span class="normal">123</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">re_normalize</span><span class="p">(</span><span class="n">target</span><span class="p">,</span> <span class="n">origin</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot; &quot;&quot;&quot;</span>
     <span class="n">tmp_t</span> <span class="o">=</span> <span class="n">copy</span><span class="o">.</span><span class="n">deepcopy</span><span class="p">(</span><span class="n">target</span><span class="p">)</span>
     <span class="n">tmp_o</span> <span class="o">=</span> <span class="n">copy</span><span class="o">.</span><span class="n">deepcopy</span><span class="p">(</span><span class="n">origin</span><span class="p">)</span>
@@ -1729,9 +1812,7 @@ <h2 id="src.equation_tree.prior.scalar_multiply" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/prior.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">150</span>
-<span class="normal">151</span>
-<span class="normal">152</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">152</span>
 <span class="normal">153</span>
 <span class="normal">154</span>
 <span class="normal">155</span>
@@ -1748,7 +1829,9 @@ <h2 id="src.equation_tree.prior.scalar_multiply" class="doc doc-heading">
 <span class="normal">166</span>
 <span class="normal">167</span>
 <span class="normal">168</span>
-<span class="normal">169</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">scalar_multiply</span><span class="p">(</span><span class="n">scalar</span><span class="p">,</span> <span class="n">prior</span><span class="p">):</span>
+<span class="normal">169</span>
+<span class="normal">170</span>
+<span class="normal">171</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">scalar_multiply</span><span class="p">(</span><span class="n">scalar</span><span class="p">,</span> <span class="n">prior</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Examples:</span>
 <span class="sd">        &gt;&gt;&gt; import pprint</span>
@@ -1801,9 +1884,7 @@ <h2 id="src.equation_tree.prior.structure_prior_from_depth" class="doc doc-headi
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/prior.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">50</span>
-<span class="normal">51</span>
-<span class="normal">52</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">52</span>
 <span class="normal">53</span>
 <span class="normal">54</span>
 <span class="normal">55</span>
@@ -1817,7 +1898,9 @@ <h2 id="src.equation_tree.prior.structure_prior_from_depth" class="doc doc-headi
 <span class="normal">63</span>
 <span class="normal">64</span>
 <span class="normal">65</span>
-<span class="normal">66</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">structure_prior_from_depth</span><span class="p">(</span><span class="n">depth</span><span class="p">):</span>
+<span class="normal">66</span>
+<span class="normal">67</span>
+<span class="normal">68</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">structure_prior_from_depth</span><span class="p">(</span><span class="n">depth</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Uniform structure prior for a given depth</span>
 <span class="sd">    Examples:</span>
@@ -1885,9 +1968,7 @@ <h2 id="src.equation_tree.prior.structure_prior_from_max_depth" class="doc doc-h
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/prior.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 69</span>
-<span class="normal"> 70</span>
-<span class="normal"> 71</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 71</span>
 <span class="normal"> 72</span>
 <span class="normal"> 73</span>
 <span class="normal"> 74</span>
@@ -1917,7 +1998,9 @@ <h2 id="src.equation_tree.prior.structure_prior_from_max_depth" class="doc doc-h
 <span class="normal"> 98</span>
 <span class="normal"> 99</span>
 <span class="normal">100</span>
-<span class="normal">101</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">structure_prior_from_max_depth</span><span class="p">(</span><span class="n">max_depth</span><span class="p">):</span>
+<span class="normal">101</span>
+<span class="normal">102</span>
+<span class="normal">103</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">structure_prior_from_max_depth</span><span class="p">(</span><span class="n">max_depth</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Uniform structure prior up to a given depth (from min depth 3)</span>
 <span class="sd">    Examples:</span>
@@ -1980,9 +2063,7 @@ <h2 id="src.equation_tree.prior.subtract" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/prior.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">198</span>
-<span class="normal">199</span>
-<span class="normal">200</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">200</span>
 <span class="normal">201</span>
 <span class="normal">202</span>
 <span class="normal">203</span>
@@ -2018,7 +2099,9 @@ <h2 id="src.equation_tree.prior.subtract" class="doc doc-heading">
 <span class="normal">233</span>
 <span class="normal">234</span>
 <span class="normal">235</span>
-<span class="normal">236</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">subtract</span><span class="p">(</span><span class="n">minuend</span><span class="p">,</span> <span class="n">subtrahend</span><span class="p">):</span>
+<span class="normal">236</span>
+<span class="normal">237</span>
+<span class="normal">238</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">subtract</span><span class="p">(</span><span class="n">minuend</span><span class="p">,</span> <span class="n">subtrahend</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Minuend - Subtrahend</span>
 <span class="sd">    Examples:</span>
diff --git a/reference/src/equation_tree/sample/index.html b/reference/src/equation_tree/sample/index.html
index 1d28274..f73b2e5 100644
--- a/reference/src/equation_tree/sample/index.html
+++ b/reference/src/equation_tree/sample/index.html
@@ -306,7 +306,7 @@
             
   
   <span class="md-ellipsis">
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+    User Guide
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         <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
           <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            User Guide
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../../../user-guide/sampling/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Sampling
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../../../user-guide/equation-formats/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Equation Formats
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+    
+    
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+    
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+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          <label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
+            
+  
+  <span class="md-ellipsis">
+    Tutorials
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+  
+
+            <span class="md-nav__icon md-icon"></span>
+          </label>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
             <span class="md-nav__icon md-icon"></span>
             Tutorials
           </label>
@@ -326,11 +409,11 @@
   
   
     <li class="md-nav__item">
-      <a href="../../../../Basic%20Usage/" class="md-nav__link">
+      <a href="../../../../Equation Sampling.ipynb" class="md-nav__link">
         
   
   <span class="md-ellipsis">
-    Basic Usage
+    Equation Sampling
   </span>
   
 
@@ -364,7 +447,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" checked>
         
           
           
@@ -380,14 +463,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
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               </label>
             
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-        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="true">
-          <label class="md-nav__title" for="__nav_4">
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5">
             <span class="md-nav__icon md-icon"></span>
             Code Reference
           </label>
@@ -410,10 +493,10 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1" checked>
         
           
-          <label class="md-nav__link" for="__nav_4_1" id="__nav_4_1_label" tabindex="0">
+          <label class="md-nav__link" for="__nav_5_1" id="__nav_5_1_label" tabindex="0">
             
   
   <span class="md-ellipsis">
@@ -424,8 +507,8 @@
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-          <label class="md-nav__title" for="__nav_4_1">
+        <nav class="md-nav" data-md-level="2" aria-labelledby="__nav_5_1_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5_1">
             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -448,7 +531,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1" checked>
         
           
           
@@ -464,14 +547,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1" id="__nav_4_1_1_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1" id="__nav_5_1_1_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
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-          <label class="md-nav__title" for="__nav_4_1_1">
+        <nav class="md-nav" data-md-level="3" aria-labelledby="__nav_5_1_1_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5_1_1">
             <span class="md-nav__icon md-icon"></span>
             Equation tree
           </label>
@@ -642,7 +725,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_6" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_6" >
         
           
           
@@ -658,14 +741,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1_6" id="__nav_4_1_1_6_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1_6" id="__nav_5_1_1_6_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
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-          <label class="md-nav__title" for="__nav_4_1_1_6">
+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_6">
             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -734,7 +817,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_7" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_7" >
         
           
           
@@ -750,14 +833,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1_7" id="__nav_4_1_1_7_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1_7" id="__nav_5_1_1_7_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
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-        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_4_1_1_7_label" aria-expanded="false">
-          <label class="md-nav__title" for="__nav_4_1_1_7">
+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_7">
             <span class="md-nav__icon md-icon"></span>
             Util
           </label>
@@ -971,24 +1054,7 @@ <h2 id="src.equation_tree.sample.sample_tree_raw_from_priors" class="doc doc-hea
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/sample.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">203</span>
-<span class="normal">204</span>
-<span class="normal">205</span>
-<span class="normal">206</span>
-<span class="normal">207</span>
-<span class="normal">208</span>
-<span class="normal">209</span>
-<span class="normal">210</span>
-<span class="normal">211</span>
-<span class="normal">212</span>
-<span class="normal">213</span>
-<span class="normal">214</span>
-<span class="normal">215</span>
-<span class="normal">216</span>
-<span class="normal">217</span>
-<span class="normal">218</span>
-<span class="normal">219</span>
-<span class="normal">220</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">220</span>
 <span class="normal">221</span>
 <span class="normal">222</span>
 <span class="normal">223</span>
@@ -1065,7 +1131,24 @@ <h2 id="src.equation_tree.sample.sample_tree_raw_from_priors" class="doc doc-hea
 <span class="normal">294</span>
 <span class="normal">295</span>
 <span class="normal">296</span>
-<span class="normal">297</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">sample_tree_raw_from_priors</span><span class="p">(</span>
+<span class="normal">297</span>
+<span class="normal">298</span>
+<span class="normal">299</span>
+<span class="normal">300</span>
+<span class="normal">301</span>
+<span class="normal">302</span>
+<span class="normal">303</span>
+<span class="normal">304</span>
+<span class="normal">305</span>
+<span class="normal">306</span>
+<span class="normal">307</span>
+<span class="normal">308</span>
+<span class="normal">309</span>
+<span class="normal">310</span>
+<span class="normal">311</span>
+<span class="normal">312</span>
+<span class="normal">313</span>
+<span class="normal">314</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">sample_tree_raw_from_priors</span><span class="p">(</span>
     <span class="n">max_num_constants</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span>
     <span class="n">max_num_variables</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
     <span class="n">feature_priors</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">Dict</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
diff --git a/reference/src/equation_tree/src/index.html b/reference/src/equation_tree/src/index.html
index 504ab0f..d31e05b 100644
--- a/reference/src/equation_tree/src/index.html
+++ b/reference/src/equation_tree/src/index.html
@@ -306,7 +306,7 @@
             
   
   <span class="md-ellipsis">
-    Tutorials
+    User Guide
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@@ -315,6 +315,89 @@
         
         <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
           <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            User Guide
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../../../user-guide/sampling/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
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@@ -893,7 +976,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_7" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_7" >
         
           
           
@@ -909,14 +992,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1_7" id="__nav_4_1_1_7_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1_7" id="__nav_5_1_1_7_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
           </div>
         
-        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_4_1_1_7_label" aria-expanded="false">
-          <label class="md-nav__title" for="__nav_4_1_1_7">
+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_7">
             <span class="md-nav__icon md-icon"></span>
             Util
           </label>
diff --git a/reference/src/equation_tree/tree/index.html b/reference/src/equation_tree/tree/index.html
index b15dd08..c0ea4b4 100644
--- a/reference/src/equation_tree/tree/index.html
+++ b/reference/src/equation_tree/tree/index.html
@@ -306,7 +306,7 @@
             
   
   <span class="md-ellipsis">
-    Tutorials
+    User Guide
   </span>
   
 
@@ -315,6 +315,89 @@
         
         <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
           <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            User Guide
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../../../user-guide/sampling/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Sampling
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../../../user-guide/equation-formats/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Equation Formats
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+    
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          <label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
+            
+  
+  <span class="md-ellipsis">
+    Tutorials
+  </span>
+  
+
+            <span class="md-nav__icon md-icon"></span>
+          </label>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
             <span class="md-nav__icon md-icon"></span>
             Tutorials
           </label>
@@ -326,11 +409,11 @@
   
   
     <li class="md-nav__item">
-      <a href="../../../../Basic%20Usage/" class="md-nav__link">
+      <a href="../../../../Equation Sampling.ipynb" class="md-nav__link">
         
   
   <span class="md-ellipsis">
-    Basic Usage
+    Equation Sampling
   </span>
   
 
@@ -364,7 +447,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" checked>
         
           
           
@@ -380,14 +463,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
           </div>
         
-        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="true">
-          <label class="md-nav__title" for="__nav_4">
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5">
             <span class="md-nav__icon md-icon"></span>
             Code Reference
           </label>
@@ -410,10 +493,10 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1" checked>
         
           
-          <label class="md-nav__link" for="__nav_4_1" id="__nav_4_1_label" tabindex="0">
+          <label class="md-nav__link" for="__nav_5_1" id="__nav_5_1_label" tabindex="0">
             
   
   <span class="md-ellipsis">
@@ -424,8 +507,8 @@
             <span class="md-nav__icon md-icon"></span>
           </label>
         
-        <nav class="md-nav" data-md-level="2" aria-labelledby="__nav_4_1_label" aria-expanded="true">
-          <label class="md-nav__title" for="__nav_4_1">
+        <nav class="md-nav" data-md-level="2" aria-labelledby="__nav_5_1_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5_1">
             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -448,7 +531,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1" checked>
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1" checked>
         
           
           
@@ -464,14 +547,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1" id="__nav_4_1_1_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1" id="__nav_5_1_1_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
           </div>
         
-        <nav class="md-nav" data-md-level="3" aria-labelledby="__nav_4_1_1_label" aria-expanded="true">
-          <label class="md-nav__title" for="__nav_4_1_1">
+        <nav class="md-nav" data-md-level="3" aria-labelledby="__nav_5_1_1_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5_1_1">
             <span class="md-nav__icon md-icon"></span>
             Equation tree
           </label>
@@ -1026,7 +1109,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_6" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_6" >
         
           
           
@@ -1042,14 +1125,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1_6" id="__nav_4_1_1_6_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1_6" id="__nav_5_1_1_6_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
           </div>
         
-        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_4_1_1_6_label" aria-expanded="false">
-          <label class="md-nav__title" for="__nav_4_1_1_6">
+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_6">
             <span class="md-nav__icon md-icon"></span>
             Src
           </label>
@@ -1118,7 +1201,7 @@
         
         
         
-        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4_1_1_7" >
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5_1_1_7" >
         
           
           
@@ -1134,14 +1217,14 @@
             </a>
             
               
-              <label class="md-nav__link " for="__nav_4_1_1_7" id="__nav_4_1_1_7_label" tabindex="0">
+              <label class="md-nav__link " for="__nav_5_1_1_7" id="__nav_5_1_1_7_label" tabindex="0">
                 <span class="md-nav__icon md-icon"></span>
               </label>
             
           </div>
         
-        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_4_1_1_7_label" aria-expanded="false">
-          <label class="md-nav__title" for="__nav_4_1_1_7">
+        <nav class="md-nav" data-md-level="4" aria-labelledby="__nav_5_1_1_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5_1_1_7">
             <span class="md-nav__icon md-icon"></span>
             Util
           </label>
@@ -3204,7 +3287,20 @@ <h2 id="src.equation_tree.tree.EquationTree" class="doc doc-heading">
 <span class="normal">1529</span>
 <span class="normal">1530</span>
 <span class="normal">1531</span>
-<span class="normal">1532</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">class</span> <span class="nc">EquationTree</span><span class="p">:</span>
+<span class="normal">1532</span>
+<span class="normal">1533</span>
+<span class="normal">1534</span>
+<span class="normal">1535</span>
+<span class="normal">1536</span>
+<span class="normal">1537</span>
+<span class="normal">1538</span>
+<span class="normal">1539</span>
+<span class="normal">1540</span>
+<span class="normal">1541</span>
+<span class="normal">1542</span>
+<span class="normal">1543</span>
+<span class="normal">1544</span>
+<span class="normal">1545</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">class</span> <span class="nc">EquationTree</span><span class="p">:</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Equation tree that represents an equation as binary tree.</span>
 <span class="sd">    &quot;&quot;&quot;</span>
@@ -3326,6 +3422,9 @@ <h2 id="src.equation_tree.tree.EquationTree" class="doc doc-heading">
 
         <span class="bp">self</span><span class="o">.</span><span class="n">_build</span><span class="p">()</span>
 
+    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">sympy_expr</span><span class="p">)</span>
+
     <span class="nd">@classmethod</span>
     <span class="k">def</span> <span class="nf">from_prefix</span><span class="p">(</span>
         <span class="bp">cls</span><span class="p">,</span>
@@ -3490,6 +3589,8 @@ <h2 id="src.equation_tree.tree.EquationTree" class="doc doc-heading">
         <span class="n">root</span> <span class="o">=</span> <span class="n">sample_tree_full</span><span class="p">(</span><span class="n">prior</span><span class="p">,</span> <span class="n">max_variables_unique</span><span class="p">)</span>
         <span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
 
+
+
     <span class="nd">@classmethod</span>
     <span class="k">def</span> <span class="nf">from_priors</span><span class="p">(</span>
         <span class="bp">cls</span><span class="p">,</span>
@@ -3765,6 +3866,14 @@ <h2 id="src.equation_tree.tree.EquationTree" class="doc doc-heading">
         <span class="n">ev</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">evaluation</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]</span>
         <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">isfinite</span><span class="p">(</span><span class="n">ev</span><span class="p">)</span> <span class="o">&amp;</span> <span class="o">~</span><span class="n">np</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">ev</span><span class="p">))</span>
 
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">depth</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="nb">max</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">structure</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">n_nodes</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">structure</span><span class="p">)</span>
+
     <span class="nd">@property</span>
     <span class="k">def</span> <span class="nf">info</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
 <span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
@@ -5081,40 +5190,40 @@ <h3 id="src.equation_tree.tree.EquationTree.check_possible" class="doc doc-headi
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">966</span>
-<span class="normal">967</span>
-<span class="normal">968</span>
-<span class="normal">969</span>
-<span class="normal">970</span>
-<span class="normal">971</span>
-<span class="normal">972</span>
-<span class="normal">973</span>
-<span class="normal">974</span>
-<span class="normal">975</span>
-<span class="normal">976</span>
-<span class="normal">977</span>
-<span class="normal">978</span>
-<span class="normal">979</span>
-<span class="normal">980</span>
-<span class="normal">981</span>
-<span class="normal">982</span>
-<span class="normal">983</span>
-<span class="normal">984</span>
-<span class="normal">985</span>
-<span class="normal">986</span>
-<span class="normal">987</span>
-<span class="normal">988</span>
-<span class="normal">989</span>
-<span class="normal">990</span>
-<span class="normal">991</span>
-<span class="normal">992</span>
-<span class="normal">993</span>
-<span class="normal">994</span>
-<span class="normal">995</span>
-<span class="normal">996</span>
-<span class="normal">997</span>
-<span class="normal">998</span>
-<span class="normal">999</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">check_possible</span><span class="p">(</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 979</span>
+<span class="normal"> 980</span>
+<span class="normal"> 981</span>
+<span class="normal"> 982</span>
+<span class="normal"> 983</span>
+<span class="normal"> 984</span>
+<span class="normal"> 985</span>
+<span class="normal"> 986</span>
+<span class="normal"> 987</span>
+<span class="normal"> 988</span>
+<span class="normal"> 989</span>
+<span class="normal"> 990</span>
+<span class="normal"> 991</span>
+<span class="normal"> 992</span>
+<span class="normal"> 993</span>
+<span class="normal"> 994</span>
+<span class="normal"> 995</span>
+<span class="normal"> 996</span>
+<span class="normal"> 997</span>
+<span class="normal"> 998</span>
+<span class="normal"> 999</span>
+<span class="normal">1000</span>
+<span class="normal">1001</span>
+<span class="normal">1002</span>
+<span class="normal">1003</span>
+<span class="normal">1004</span>
+<span class="normal">1005</span>
+<span class="normal">1006</span>
+<span class="normal">1007</span>
+<span class="normal">1008</span>
+<span class="normal">1009</span>
+<span class="normal">1010</span>
+<span class="normal">1011</span>
+<span class="normal">1012</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">check_possible</span><span class="p">(</span>
     <span class="bp">self</span><span class="p">,</span>
     <span class="n">feature_priors</span><span class="p">:</span> <span class="n">Dict</span><span class="p">,</span>
     <span class="n">function_priors</span><span class="p">:</span> <span class="n">Dict</span><span class="p">,</span>
@@ -5289,20 +5398,7 @@ <h3 id="src.equation_tree.tree.EquationTree.check_validity" class="doc doc-headi
 </details>
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">897</span>
-<span class="normal">898</span>
-<span class="normal">899</span>
-<span class="normal">900</span>
-<span class="normal">901</span>
-<span class="normal">902</span>
-<span class="normal">903</span>
-<span class="normal">904</span>
-<span class="normal">905</span>
-<span class="normal">906</span>
-<span class="normal">907</span>
-<span class="normal">908</span>
-<span class="normal">909</span>
-<span class="normal">910</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">910</span>
 <span class="normal">911</span>
 <span class="normal">912</span>
 <span class="normal">913</span>
@@ -5346,7 +5442,20 @@ <h3 id="src.equation_tree.tree.EquationTree.check_validity" class="doc doc-headi
 <span class="normal">951</span>
 <span class="normal">952</span>
 <span class="normal">953</span>
-<span class="normal">954</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">check_validity</span><span class="p">(</span>
+<span class="normal">954</span>
+<span class="normal">955</span>
+<span class="normal">956</span>
+<span class="normal">957</span>
+<span class="normal">958</span>
+<span class="normal">959</span>
+<span class="normal">960</span>
+<span class="normal">961</span>
+<span class="normal">962</span>
+<span class="normal">963</span>
+<span class="normal">964</span>
+<span class="normal">965</span>
+<span class="normal">966</span>
+<span class="normal">967</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">check_validity</span><span class="p">(</span>
     <span class="bp">self</span><span class="p">,</span>
     <span class="n">zero_representations</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;0&quot;</span><span class="p">],</span>
     <span class="n">log_representations</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;log&quot;</span><span class="p">,</span> <span class="s2">&quot;Log&quot;</span><span class="p">],</span>
@@ -5511,20 +5620,7 @@ <h4 id="src.equation_tree.tree.EquationTree.evaluate--or-pandas-dataframe">Or pa
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">663</span>
-<span class="normal">664</span>
-<span class="normal">665</span>
-<span class="normal">666</span>
-<span class="normal">667</span>
-<span class="normal">668</span>
-<span class="normal">669</span>
-<span class="normal">670</span>
-<span class="normal">671</span>
-<span class="normal">672</span>
-<span class="normal">673</span>
-<span class="normal">674</span>
-<span class="normal">675</span>
-<span class="normal">676</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">676</span>
 <span class="normal">677</span>
 <span class="normal">678</span>
 <span class="normal">679</span>
@@ -5617,7 +5713,20 @@ <h4 id="src.equation_tree.tree.EquationTree.evaluate--or-pandas-dataframe">Or pa
 <span class="normal">766</span>
 <span class="normal">767</span>
 <span class="normal">768</span>
-<span class="normal">769</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">evaluate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">variables</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">]):</span>
+<span class="normal">769</span>
+<span class="normal">770</span>
+<span class="normal">771</span>
+<span class="normal">772</span>
+<span class="normal">773</span>
+<span class="normal">774</span>
+<span class="normal">775</span>
+<span class="normal">776</span>
+<span class="normal">777</span>
+<span class="normal">778</span>
+<span class="normal">779</span>
+<span class="normal">780</span>
+<span class="normal">781</span>
+<span class="normal">782</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">evaluate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">variables</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">]):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Examples:</span>
 <span class="sd">        &gt;&gt;&gt; expr = sympify(&#39;x_a + 3 * y&#39;)</span>
@@ -5758,20 +5867,7 @@ <h3 id="src.equation_tree.tree.EquationTree.export_to_srbench" class="doc doc-he
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">864</span>
-<span class="normal">865</span>
-<span class="normal">866</span>
-<span class="normal">867</span>
-<span class="normal">868</span>
-<span class="normal">869</span>
-<span class="normal">870</span>
-<span class="normal">871</span>
-<span class="normal">872</span>
-<span class="normal">873</span>
-<span class="normal">874</span>
-<span class="normal">875</span>
-<span class="normal">876</span>
-<span class="normal">877</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">877</span>
 <span class="normal">878</span>
 <span class="normal">879</span>
 <span class="normal">880</span>
@@ -5789,7 +5885,20 @@ <h3 id="src.equation_tree.tree.EquationTree.export_to_srbench" class="doc doc-he
 <span class="normal">892</span>
 <span class="normal">893</span>
 <span class="normal">894</span>
-<span class="normal">895</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">export_to_srbench</span><span class="p">(</span>
+<span class="normal">895</span>
+<span class="normal">896</span>
+<span class="normal">897</span>
+<span class="normal">898</span>
+<span class="normal">899</span>
+<span class="normal">900</span>
+<span class="normal">901</span>
+<span class="normal">902</span>
+<span class="normal">903</span>
+<span class="normal">904</span>
+<span class="normal">905</span>
+<span class="normal">906</span>
+<span class="normal">907</span>
+<span class="normal">908</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">export_to_srbench</span><span class="p">(</span>
     <span class="bp">self</span><span class="p">,</span>
     <span class="n">folder</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span>
     <span class="n">data_file_name</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="nb">str</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
@@ -5989,10 +6098,7 @@ <h4 id="src.equation_tree.tree.EquationTree.from_prefix--the-tree-expression-is-
 </details>
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">189</span>
-<span class="normal">190</span>
-<span class="normal">191</span>
-<span class="normal">192</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">192</span>
 <span class="normal">193</span>
 <span class="normal">194</span>
 <span class="normal">195</span>
@@ -6045,7 +6151,10 @@ <h4 id="src.equation_tree.tree.EquationTree.from_prefix--the-tree-expression-is-
 <span class="normal">242</span>
 <span class="normal">243</span>
 <span class="normal">244</span>
-<span class="normal">245</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="nd">@classmethod</span>
+<span class="normal">245</span>
+<span class="normal">246</span>
+<span class="normal">247</span>
+<span class="normal">248</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="nd">@classmethod</span>
 <span class="k">def</span> <span class="nf">from_prefix</span><span class="p">(</span>
     <span class="bp">cls</span><span class="p">,</span>
     <span class="n">prefix_notation</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="nb">str</span><span class="p">],</span>
@@ -6250,10 +6359,7 @@ <h4 id="src.equation_tree.tree.EquationTree.from_prior--note-this-would-be-disca
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">267</span>
-<span class="normal">268</span>
-<span class="normal">269</span>
-<span class="normal">270</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">270</span>
 <span class="normal">271</span>
 <span class="normal">272</span>
 <span class="normal">273</span>
@@ -6334,7 +6440,10 @@ <h4 id="src.equation_tree.tree.EquationTree.from_prior--note-this-would-be-disca
 <span class="normal">348</span>
 <span class="normal">349</span>
 <span class="normal">350</span>
-<span class="normal">351</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="nd">@classmethod</span>
+<span class="normal">351</span>
+<span class="normal">352</span>
+<span class="normal">353</span>
+<span class="normal">354</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="nd">@classmethod</span>
 <span class="k">def</span> <span class="nf">from_prior</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">prior</span><span class="p">:</span> <span class="n">Dict</span><span class="p">,</span> <span class="n">max_variables_unique</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Initiate a tree from a prior</span>
@@ -6506,10 +6615,7 @@ <h3 id="src.equation_tree.tree.EquationTree.from_prior_fast" class="doc doc-head
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">252</span>
-<span class="normal">253</span>
-<span class="normal">254</span>
-<span class="normal">255</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">255</span>
 <span class="normal">256</span>
 <span class="normal">257</span>
 <span class="normal">258</span>
@@ -6519,7 +6625,10 @@ <h3 id="src.equation_tree.tree.EquationTree.from_prior_fast" class="doc doc-head
 <span class="normal">262</span>
 <span class="normal">263</span>
 <span class="normal">264</span>
-<span class="normal">265</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="nd">@classmethod</span>
+<span class="normal">265</span>
+<span class="normal">266</span>
+<span class="normal">267</span>
+<span class="normal">268</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="nd">@classmethod</span>
 <span class="k">def</span> <span class="nf">from_prior_fast</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">prior</span><span class="p">:</span> <span class="n">Dict</span><span class="p">,</span> <span class="n">tree_depth</span><span class="p">,</span> <span class="n">max_variables_unique</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Initiate a tree from a prior with fast sampling</span>
@@ -6684,12 +6793,7 @@ <h3 id="src.equation_tree.tree.EquationTree.from_priors" class="doc doc-heading"
 </details>
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">353</span>
-<span class="normal">354</span>
-<span class="normal">355</span>
-<span class="normal">356</span>
-<span class="normal">357</span>
-<span class="normal">358</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">358</span>
 <span class="normal">359</span>
 <span class="normal">360</span>
 <span class="normal">361</span>
@@ -6744,7 +6848,12 @@ <h3 id="src.equation_tree.tree.EquationTree.from_priors" class="doc doc-heading"
 <span class="normal">410</span>
 <span class="normal">411</span>
 <span class="normal">412</span>
-<span class="normal">413</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="nd">@classmethod</span>
+<span class="normal">413</span>
+<span class="normal">414</span>
+<span class="normal">415</span>
+<span class="normal">416</span>
+<span class="normal">417</span>
+<span class="normal">418</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="nd">@classmethod</span>
 <span class="k">def</span> <span class="nf">from_priors</span><span class="p">(</span>
     <span class="bp">cls</span><span class="p">,</span>
     <span class="n">feature_priors</span><span class="o">=</span><span class="p">{},</span>
@@ -6913,12 +7022,7 @@ <h4 id="src.equation_tree.tree.EquationTree.from_sympy--numbers-dont-get-standar
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">415</span>
-<span class="normal">416</span>
-<span class="normal">417</span>
-<span class="normal">418</span>
-<span class="normal">419</span>
-<span class="normal">420</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">420</span>
 <span class="normal">421</span>
 <span class="normal">422</span>
 <span class="normal">423</span>
@@ -7011,7 +7115,12 @@ <h4 id="src.equation_tree.tree.EquationTree.from_sympy--numbers-dont-get-standar
 <span class="normal">510</span>
 <span class="normal">511</span>
 <span class="normal">512</span>
-<span class="normal">513</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="nd">@classmethod</span>
+<span class="normal">513</span>
+<span class="normal">514</span>
+<span class="normal">515</span>
+<span class="normal">516</span>
+<span class="normal">517</span>
+<span class="normal">518</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="nd">@classmethod</span>
 <span class="k">def</span> <span class="nf">from_sympy</span><span class="p">(</span>
     <span class="bp">cls</span><span class="p">,</span>
     <span class="n">expression</span><span class="p">,</span>
@@ -7134,20 +7243,7 @@ <h3 id="src.equation_tree.tree.EquationTree.get_evaluation" class="doc doc-headi
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1331</span>
-<span class="normal">1332</span>
-<span class="normal">1333</span>
-<span class="normal">1334</span>
-<span class="normal">1335</span>
-<span class="normal">1336</span>
-<span class="normal">1337</span>
-<span class="normal">1338</span>
-<span class="normal">1339</span>
-<span class="normal">1340</span>
-<span class="normal">1341</span>
-<span class="normal">1342</span>
-<span class="normal">1343</span>
-<span class="normal">1344</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1344</span>
 <span class="normal">1345</span>
 <span class="normal">1346</span>
 <span class="normal">1347</span>
@@ -7162,7 +7258,20 @@ <h3 id="src.equation_tree.tree.EquationTree.get_evaluation" class="doc doc-headi
 <span class="normal">1356</span>
 <span class="normal">1357</span>
 <span class="normal">1358</span>
-<span class="normal">1359</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">get_evaluation</span><span class="p">(</span>
+<span class="normal">1359</span>
+<span class="normal">1360</span>
+<span class="normal">1361</span>
+<span class="normal">1362</span>
+<span class="normal">1363</span>
+<span class="normal">1364</span>
+<span class="normal">1365</span>
+<span class="normal">1366</span>
+<span class="normal">1367</span>
+<span class="normal">1368</span>
+<span class="normal">1369</span>
+<span class="normal">1370</span>
+<span class="normal">1371</span>
+<span class="normal">1372</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">get_evaluation</span><span class="p">(</span>
     <span class="bp">self</span><span class="p">,</span> <span class="n">min_val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="n">num_samples</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">100</span>
 <span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
@@ -7224,20 +7333,7 @@ <h3 id="src.equation_tree.tree.EquationTree.save_samples" class="doc doc-heading
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">771</span>
-<span class="normal">772</span>
-<span class="normal">773</span>
-<span class="normal">774</span>
-<span class="normal">775</span>
-<span class="normal">776</span>
-<span class="normal">777</span>
-<span class="normal">778</span>
-<span class="normal">779</span>
-<span class="normal">780</span>
-<span class="normal">781</span>
-<span class="normal">782</span>
-<span class="normal">783</span>
-<span class="normal">784</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">784</span>
 <span class="normal">785</span>
 <span class="normal">786</span>
 <span class="normal">787</span>
@@ -7279,7 +7375,20 @@ <h3 id="src.equation_tree.tree.EquationTree.save_samples" class="doc doc-heading
 <span class="normal">823</span>
 <span class="normal">824</span>
 <span class="normal">825</span>
-<span class="normal">826</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">save_samples</span><span class="p">(</span>
+<span class="normal">826</span>
+<span class="normal">827</span>
+<span class="normal">828</span>
+<span class="normal">829</span>
+<span class="normal">830</span>
+<span class="normal">831</span>
+<span class="normal">832</span>
+<span class="normal">833</span>
+<span class="normal">834</span>
+<span class="normal">835</span>
+<span class="normal">836</span>
+<span class="normal">837</span>
+<span class="normal">838</span>
+<span class="normal">839</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">save_samples</span><span class="p">(</span>
     <span class="bp">self</span><span class="p">,</span>
     <span class="n">path</span><span class="p">,</span>
     <span class="n">num_samples</span><span class="p">,</span>
@@ -7435,20 +7544,7 @@ <h4 id="src.equation_tree.tree.EquationTree.simplify---x_1-c_1-2">['^', '-', 'x_
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1162</span>
-<span class="normal">1163</span>
-<span class="normal">1164</span>
-<span class="normal">1165</span>
-<span class="normal">1166</span>
-<span class="normal">1167</span>
-<span class="normal">1168</span>
-<span class="normal">1169</span>
-<span class="normal">1170</span>
-<span class="normal">1171</span>
-<span class="normal">1172</span>
-<span class="normal">1173</span>
-<span class="normal">1174</span>
-<span class="normal">1175</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1175</span>
 <span class="normal">1176</span>
 <span class="normal">1177</span>
 <span class="normal">1178</span>
@@ -7602,7 +7698,20 @@ <h4 id="src.equation_tree.tree.EquationTree.simplify---x_1-c_1-2">['^', '-', 'x_
 <span class="normal">1326</span>
 <span class="normal">1327</span>
 <span class="normal">1328</span>
-<span class="normal">1329</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">simplify</span><span class="p">(</span>
+<span class="normal">1329</span>
+<span class="normal">1330</span>
+<span class="normal">1331</span>
+<span class="normal">1332</span>
+<span class="normal">1333</span>
+<span class="normal">1334</span>
+<span class="normal">1335</span>
+<span class="normal">1336</span>
+<span class="normal">1337</span>
+<span class="normal">1338</span>
+<span class="normal">1339</span>
+<span class="normal">1340</span>
+<span class="normal">1341</span>
+<span class="normal">1342</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">simplify</span><span class="p">(</span>
     <span class="bp">self</span><span class="p">,</span>
     <span class="n">function_test</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">Callable</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
     <span class="n">operator_test</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">Callable</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
@@ -7827,20 +7936,7 @@ <h4 id="src.equation_tree.tree.EquationTree.standardize--then-we-create-the-node
 </details>
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1106</span>
-<span class="normal">1107</span>
-<span class="normal">1108</span>
-<span class="normal">1109</span>
-<span class="normal">1110</span>
-<span class="normal">1111</span>
-<span class="normal">1112</span>
-<span class="normal">1113</span>
-<span class="normal">1114</span>
-<span class="normal">1115</span>
-<span class="normal">1116</span>
-<span class="normal">1117</span>
-<span class="normal">1118</span>
-<span class="normal">1119</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1119</span>
 <span class="normal">1120</span>
 <span class="normal">1121</span>
 <span class="normal">1122</span>
@@ -7881,7 +7977,20 @@ <h4 id="src.equation_tree.tree.EquationTree.standardize--then-we-create-the-node
 <span class="normal">1157</span>
 <span class="normal">1158</span>
 <span class="normal">1159</span>
-<span class="normal">1160</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">standardize</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="normal">1160</span>
+<span class="normal">1161</span>
+<span class="normal">1162</span>
+<span class="normal">1163</span>
+<span class="normal">1164</span>
+<span class="normal">1165</span>
+<span class="normal">1166</span>
+<span class="normal">1167</span>
+<span class="normal">1168</span>
+<span class="normal">1169</span>
+<span class="normal">1170</span>
+<span class="normal">1171</span>
+<span class="normal">1172</span>
+<span class="normal">1173</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">standardize</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Standardize variable and constant names</span>
 
@@ -7996,20 +8105,7 @@ <h2 id="src.equation_tree.tree.instantiate_constants" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1535</span>
-<span class="normal">1536</span>
-<span class="normal">1537</span>
-<span class="normal">1538</span>
-<span class="normal">1539</span>
-<span class="normal">1540</span>
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-<span class="normal">1543</span>
-<span class="normal">1544</span>
-<span class="normal">1545</span>
-<span class="normal">1546</span>
-<span class="normal">1547</span>
-<span class="normal">1548</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1548</span>
 <span class="normal">1549</span>
 <span class="normal">1550</span>
 <span class="normal">1551</span>
@@ -8039,7 +8135,20 @@ <h2 id="src.equation_tree.tree.instantiate_constants" class="doc doc-heading">
 <span class="normal">1575</span>
 <span class="normal">1576</span>
 <span class="normal">1577</span>
-<span class="normal">1578</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">instantiate_constants</span><span class="p">(</span><span class="n">tree</span><span class="p">,</span> <span class="n">fct</span><span class="p">:</span> <span class="n">Callable</span><span class="p">):</span>
+<span class="normal">1578</span>
+<span class="normal">1579</span>
+<span class="normal">1580</span>
+<span class="normal">1581</span>
+<span class="normal">1582</span>
+<span class="normal">1583</span>
+<span class="normal">1584</span>
+<span class="normal">1585</span>
+<span class="normal">1586</span>
+<span class="normal">1587</span>
+<span class="normal">1588</span>
+<span class="normal">1589</span>
+<span class="normal">1590</span>
+<span class="normal">1591</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">instantiate_constants</span><span class="p">(</span><span class="n">tree</span><span class="p">,</span> <span class="n">fct</span><span class="p">:</span> <span class="n">Callable</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Examples:</span>
 <span class="sd">        &gt;&gt;&gt; expr = sympify(&#39;e ** (- e **( x + y))&#39;)</span>
@@ -8109,16 +8218,16 @@ <h2 id="src.equation_tree.tree.normalized_tree_distance" class="doc doc-heading"
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1581</span>
-<span class="normal">1582</span>
-<span class="normal">1583</span>
-<span class="normal">1584</span>
-<span class="normal">1585</span>
-<span class="normal">1586</span>
-<span class="normal">1587</span>
-<span class="normal">1588</span>
-<span class="normal">1589</span>
-<span class="normal">1590</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">normalized_tree_distance</span><span class="p">(</span><span class="n">e_a</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">,</span> <span class="n">e_b</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">):</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1594</span>
+<span class="normal">1595</span>
+<span class="normal">1596</span>
+<span class="normal">1597</span>
+<span class="normal">1598</span>
+<span class="normal">1599</span>
+<span class="normal">1600</span>
+<span class="normal">1601</span>
+<span class="normal">1602</span>
+<span class="normal">1603</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">normalized_tree_distance</span><span class="p">(</span><span class="n">e_a</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">,</span> <span class="n">e_b</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Normalized edit distance between two trees according to</span>
 <span class="sd">    `Li, Y., &amp; Chenguang, Z. (2011). A metric normalization of tree edit distance.</span>
@@ -8181,20 +8290,7 @@ <h2 id="src.equation_tree.tree.prediction_distance" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1593</span>
-<span class="normal">1594</span>
-<span class="normal">1595</span>
-<span class="normal">1596</span>
-<span class="normal">1597</span>
-<span class="normal">1598</span>
-<span class="normal">1599</span>
-<span class="normal">1600</span>
-<span class="normal">1601</span>
-<span class="normal">1602</span>
-<span class="normal">1603</span>
-<span class="normal">1604</span>
-<span class="normal">1605</span>
-<span class="normal">1606</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1606</span>
 <span class="normal">1607</span>
 <span class="normal">1608</span>
 <span class="normal">1609</span>
@@ -8217,7 +8313,20 @@ <h2 id="src.equation_tree.tree.prediction_distance" class="doc doc-heading">
 <span class="normal">1626</span>
 <span class="normal">1627</span>
 <span class="normal">1628</span>
-<span class="normal">1629</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">prediction_distance</span><span class="p">(</span>
+<span class="normal">1629</span>
+<span class="normal">1630</span>
+<span class="normal">1631</span>
+<span class="normal">1632</span>
+<span class="normal">1633</span>
+<span class="normal">1634</span>
+<span class="normal">1635</span>
+<span class="normal">1636</span>
+<span class="normal">1637</span>
+<span class="normal">1638</span>
+<span class="normal">1639</span>
+<span class="normal">1640</span>
+<span class="normal">1641</span>
+<span class="normal">1642</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">prediction_distance</span><span class="p">(</span>
     <span class="n">e_a</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">,</span> <span class="n">e_b</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">,</span> <span class="n">X</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">dict</span><span class="p">,</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">]</span>
 <span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
@@ -8303,20 +8412,7 @@ <h2 id="src.equation_tree.tree.symbolic_solution_diff" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1632</span>
-<span class="normal">1633</span>
-<span class="normal">1634</span>
-<span class="normal">1635</span>
-<span class="normal">1636</span>
-<span class="normal">1637</span>
-<span class="normal">1638</span>
-<span class="normal">1639</span>
-<span class="normal">1640</span>
-<span class="normal">1641</span>
-<span class="normal">1642</span>
-<span class="normal">1643</span>
-<span class="normal">1644</span>
-<span class="normal">1645</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1645</span>
 <span class="normal">1646</span>
 <span class="normal">1647</span>
 <span class="normal">1648</span>
@@ -8336,7 +8432,20 @@ <h2 id="src.equation_tree.tree.symbolic_solution_diff" class="doc doc-heading">
 <span class="normal">1662</span>
 <span class="normal">1663</span>
 <span class="normal">1664</span>
-<span class="normal">1665</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">symbolic_solution_diff</span><span class="p">(</span><span class="n">e_a</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">,</span> <span class="n">e_b</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">):</span>
+<span class="normal">1665</span>
+<span class="normal">1666</span>
+<span class="normal">1667</span>
+<span class="normal">1668</span>
+<span class="normal">1669</span>
+<span class="normal">1670</span>
+<span class="normal">1671</span>
+<span class="normal">1672</span>
+<span class="normal">1673</span>
+<span class="normal">1674</span>
+<span class="normal">1675</span>
+<span class="normal">1676</span>
+<span class="normal">1677</span>
+<span class="normal">1678</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">symbolic_solution_diff</span><span class="p">(</span><span class="n">e_a</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">,</span> <span class="n">e_b</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Symbolic solution with difference constant based on</span>
 <span class="sd">    `La Cava, W. et al (2021).</span>
@@ -8419,20 +8528,7 @@ <h2 id="src.equation_tree.tree.symbolic_solution_quot" class="doc doc-heading">
 
           <details class="quote">
             <summary>Source code in <code>src/equation_tree/tree.py</code></summary>
-            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1668</span>
-<span class="normal">1669</span>
-<span class="normal">1670</span>
-<span class="normal">1671</span>
-<span class="normal">1672</span>
-<span class="normal">1673</span>
-<span class="normal">1674</span>
-<span class="normal">1675</span>
-<span class="normal">1676</span>
-<span class="normal">1677</span>
-<span class="normal">1678</span>
-<span class="normal">1679</span>
-<span class="normal">1680</span>
-<span class="normal">1681</span>
+            <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1681</span>
 <span class="normal">1682</span>
 <span class="normal">1683</span>
 <span class="normal">1684</span>
@@ -8453,7 +8549,20 @@ <h2 id="src.equation_tree.tree.symbolic_solution_quot" class="doc doc-heading">
 <span class="normal">1699</span>
 <span class="normal">1700</span>
 <span class="normal">1701</span>
-<span class="normal">1702</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">symbolic_solution_quot</span><span class="p">(</span><span class="n">e_a</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">,</span> <span class="n">e_b</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">):</span>
+<span class="normal">1702</span>
+<span class="normal">1703</span>
+<span class="normal">1704</span>
+<span class="normal">1705</span>
+<span class="normal">1706</span>
+<span class="normal">1707</span>
+<span class="normal">1708</span>
+<span class="normal">1709</span>
+<span class="normal">1710</span>
+<span class="normal">1711</span>
+<span class="normal">1712</span>
+<span class="normal">1713</span>
+<span class="normal">1714</span>
+<span class="normal">1715</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">symbolic_solution_quot</span><span class="p">(</span><span class="n">e_a</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">,</span> <span class="n">e_b</span><span class="p">:</span> <span class="n">EquationTree</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Symbolic solution with quotient constant based on</span>
 <span class="sd">    `La Cava, W. et al (2021).</span>
diff --git a/reference/src/equation_tree/util/conversions/index.html b/reference/src/equation_tree/util/conversions/index.html
index 1913b72..e2020b6 100644
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+++ b/reference/src/equation_tree/util/conversions/index.html
@@ -306,7 +306,7 @@
             
   
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+    Sampling
+  </span>
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+
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+  
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+      <a href="../../../../../user-guide/equation-formats/" class="md-nav__link">
+        
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+  </span>
+  
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@@ -326,11 +409,11 @@
   
   
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+      <a href="../../../../../Equation Sampling.ipynb" class="md-nav__link">
         
   
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+    Equation Sampling
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             <span class="md-nav__icon md-icon"></span>
             Util
           </label>
diff --git a/reference/src/equation_tree/util/index.html b/reference/src/equation_tree/util/index.html
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diff --git a/search/search_index.json b/search/search_index.json
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-{"config":{"lang":["en"],"separator":"[\\s\\-]+","pipeline":["stopWordFilter"]},"docs":[{"location":"","title":"Equation Tree","text":"<p>The Equation Tree package is an equation toolbox with symbolic regression in mind. It represents expressions as incomplete binary trees and has various features tailored towards testing symbolic regression algorithms or training models. The main features are:</p> <ul> <li>Equation sampling (including priors)</li> <li>Feature Extraction from equation distributions</li> <li>Distance metrics between equations</li> </ul>"},{"location":"#equation-sampling","title":"Equation Sampling","text":"<p>coming soon</p>"},{"location":"#feature-extraction","title":"Feature Extraction","text":"<p>coming soon</p>"},{"location":"#distance-metrics","title":"Distance Metrics","text":"<p>coming soon</p>"},{"location":"#about","title":"About","text":"<p>This project is in active development by the Autonomous Empirical Research Group (package developer: Younes Strittmatter, PI: Sebastian Musslick. This research program is supported by Schmidt Science Fellows, in partnership with the Rhodes Trust, as well as the Carney BRAINSTORM program at Brown University.</p>"},{"location":"Additional%20Example/","title":"Additional Example","text":"In\u00a0[\u00a0]: Copied! <pre>from autora.equation_tree.equation_tree import Example\n</pre> from autora.equation_tree.equation_tree import Example <p>Include inline mathematics like this: $4 &lt; 5$</p> <p>Include block mathematics like this (don't forget the empty lines above and below the block):</p> <p>$$   y + 1 = 4  $$</p> <p>... or this:</p> <p>\\begin{align}     p(v_i=1|\\mathbf{h}) &amp; = \\sigma\\left(\\sum_j w_{ij}h_j + b_i\\right) \\\\     p(h_j=1|\\mathbf{v}) &amp; = \\sigma\\left(\\sum_i w_{ij}v_i + c_j\\right) \\end{align}</p>"},{"location":"Additional%20Example/#additional-example","title":"Additional Example\u00b6","text":""},{"location":"Basic%20Usage/","title":"Basic Usage","text":"In\u00a0[1]: Copied! <pre>!pip install equation_tree\n</pre> !pip install equation_tree <pre>Requirement already satisfied: equation_tree in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src (0.0.11.dev21+gc4ad4e6.d20230918)\r\nRequirement already satisfied: numpy in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (1.25.2)\r\nRequirement already satisfied: sympy in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (1.12)\r\nRequirement already satisfied: importlib_resources in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (6.0.1)\r\nRequirement already satisfied: tqdm in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (4.66.1)\r\nRequirement already satisfied: mpmath&gt;=0.19 in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from sympy-&gt;equation_tree) (1.3.0)\r\n\r\n[notice] A new release of pip is available: 23.1.2 -&gt; 23.3.1\r\n[notice] To update, run: pip install --upgrade pip\r\n</pre> <p>Include inline mathematics like this: $4 &lt; 5$</p> <p>Include block mathematics like this (don't forget the empty lines above and below the block):</p> <p>$$   y + 1 = 4  $$</p> <p>... or this:</p> <p>\\begin{align}     p(v_i=1|\\mathbf{h}) &amp; = \\sigma\\left(\\sum_j w_{ij}h_j + b_i\\right) \\\\     p(h_j=1|\\mathbf{v}) &amp; = \\sigma\\left(\\sum_i w_{ij}v_i + c_j\\right) \\end{align}</p>"},{"location":"Basic%20Usage/#basic-usage","title":"Basic Usage\u00b6","text":""},{"location":"quickstart/","title":"Quickstart Guide","text":"<p>You will need:</p> <ul> <li><code>python</code> 3.8 or greater: https://www.python.org/downloads/</li> </ul> <pre><code>pip install -U equation-tree\n</code></pre> <p>Check your installation by running: <pre><code>python -c \"from equation_tree import EquationTree\"\n</code></pre></p>"},{"location":"reference/SUMMARY/","title":"Code Reference","text":"<ul> <li>src<ul> <li>equation_tree<ul> <li>analysis</li> <li>defaults</li> <li>prior</li> <li>sample</li> <li>src<ul> <li>sample_tree_structure</li> <li>tree_node</li> </ul> </li> <li>tree</li> <li>util<ul> <li>conversions</li> <li>io</li> <li>priors</li> <li>type_check</li> </ul> </li> </ul> </li> </ul> </li> </ul>"},{"location":"reference/src/equation_tree/","title":"Equation tree","text":""},{"location":"reference/src/equation_tree/analysis/","title":"Analysis","text":""},{"location":"reference/src/equation_tree/analysis/#src.equation_tree.analysis.get_counts","title":"<code>get_counts(trees)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; import numpy as np\n&gt;&gt;&gt; import pprint\n&gt;&gt;&gt; np.random.seed(42)\n&gt;&gt;&gt; p = {\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .5, 'variables': .5},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': .5, '-': .5},\n...     'function_conditionals': {\n...                             'sin': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': .5, 'cos': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             },\n...                             'cos': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             }\n...                         },\n...     'operator_conditionals': {\n...                             '+': {\n...                                 'features': {'constants': .5, 'variables': .5},\n...                                 'functions': {'sin': .5, 'cos': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             },\n...                             '-': {\n...                                 'features': {'constants': .5, 'variables': .5},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             }\n...                         },\n... }\n&gt;&gt;&gt; pprint.pprint(p)\n{'features': {'constants': 0.5, 'variables': 0.5},\n 'function_conditionals': {'cos': {'features': {'constants': 0.0,\n                                                'variables': 1.0},\n                                   'functions': {'cos': 0.5, 'sin': 0.5},\n                                   'operators': {'+': 0.5, '-': 0.5}},\n                           'sin': {'features': {'constants': 0.0,\n                                                'variables': 1.0},\n                                   'functions': {'cos': 0.5, 'sin': 0.5},\n                                   'operators': {'+': 0.5, '-': 0.5}}},\n 'functions': {'cos': 0.5, 'sin': 0.5},\n 'operator_conditionals': {'+': {'features': {'constants': 0.5,\n                                              'variables': 0.5},\n                                 'functions': {'cos': 0.5, 'sin': 0.5},\n                                 'operators': {'+': 0.5, '-': 0.5}},\n                           '-': {'features': {'constants': 0.5,\n                                              'variables': 0.5},\n                                 'functions': {'cos': 0.5, 'sin': 0.5},\n                                 'operators': {'+': 0.5, '-': 0.5}}},\n 'operators': {'+': 0.5, '-': 0.5},\n 'structures': {'[0, 1, 1]': 0.3,\n                '[0, 1, 2, 3, 2, 3, 1]': 0.4,\n                '[0, 1, 2]': 0.3}}\n</code></pre> <pre><code>&gt;&gt;&gt; tree_list = [EquationTree.from_prior(p, 4) for _ in range(100)]\n&gt;&gt;&gt; len(tree_list)\n100\n&gt;&gt;&gt; example_tree = tree_list[2]\n&gt;&gt;&gt; example_tree.expr\n['+', '-', 'sin', 'x_1', 'cos', 'x_2', 'c_1']\n&gt;&gt;&gt; example_tree.sympy_expr\nc_1 + sin(x_1) - cos(x_2)\n&gt;&gt;&gt; pprint.pprint(example_tree.info)\n{'depth': 3,\n 'features': {'constants': 1, 'variables': 2},\n 'function_conditionals': {'cos': {'features': {'constants': 0, 'variables': 1},\n                                   'functions': {},\n                                   'operators': {}},\n                           'sin': {'features': {'constants': 0, 'variables': 1},\n                                   'functions': {},\n                                   'operators': {}}},\n 'functions': {'cos': 1, 'sin': 1},\n 'max_depth': 7,\n 'operator_conditionals': {'+': {'features': {'constants': 1, 'variables': 0},\n                                 'functions': {},\n                                 'operators': {'-': 1}},\n                           '-': {'features': {'constants': 0, 'variables': 0},\n                                 'functions': {'cos': 1, 'sin': 1},\n                                 'operators': {}}},\n 'operators': {'+': 1, '-': 1},\n 'structures': [0, 1, 2, 3, 2, 3, 1]}\n</code></pre> <pre><code>&gt;&gt;&gt; counts = get_counts(tree_list)\n&gt;&gt;&gt; pprint.pprint(counts)\n{'depth': {1: 32, 2: 27, 3: 41},\n 'features': {'constants': 44, 'variables': 170},\n 'function_conditionals': {'cos': {'features': {'constants': 0,\n                                                'variables': 54},\n                                   'functions': {'cos': 7, 'sin': 6},\n                                   'operators': {}},\n                           'sin': {'features': {'constants': 0,\n                                                'variables': 55},\n                                   'functions': {'cos': 7, 'sin': 7},\n                                   'operators': {}}},\n 'functions': {'cos': 67, 'sin': 69},\n 'max_depth': {3: 59, 7: 41},\n 'operator_conditionals': {'+': {'features': {'constants': 24, 'variables': 29},\n                                 'functions': {'cos': 27, 'sin': 21},\n                                 'operators': {'+': 14, '-': 9}},\n                           '-': {'features': {'constants': 20, 'variables': 32},\n                                 'functions': {'cos': 13, 'sin': 21},\n                                 'operators': {'+': 10, '-': 8}}},\n 'operators': {'+': 62, '-': 52},\n 'structures': {'[0, 1, 1]': 32, '[0, 1, 2, 3, 2, 3, 1]': 41, '[0, 1, 2]': 27}}\n</code></pre> Source code in <code>src/equation_tree/analysis.py</code> <pre><code>def get_counts(trees: List[EquationTree]):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; import numpy as np\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; np.random.seed(42)\n        &gt;&gt;&gt; p = {\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .5, 'variables': .5},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': .5, '-': .5},\n        ...     'function_conditionals': {\n        ...                             'sin': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': .5, 'cos': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             },\n        ...                             'cos': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             }\n        ...                         },\n        ...     'operator_conditionals': {\n        ...                             '+': {\n        ...                                 'features': {'constants': .5, 'variables': .5},\n        ...                                 'functions': {'sin': .5, 'cos': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             },\n        ...                             '-': {\n        ...                                 'features': {'constants': .5, 'variables': .5},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             }\n        ...                         },\n        ... }\n        &gt;&gt;&gt; pprint.pprint(p)\n        {'features': {'constants': 0.5, 'variables': 0.5},\n         'function_conditionals': {'cos': {'features': {'constants': 0.0,\n                                                        'variables': 1.0},\n                                           'functions': {'cos': 0.5, 'sin': 0.5},\n                                           'operators': {'+': 0.5, '-': 0.5}},\n                                   'sin': {'features': {'constants': 0.0,\n                                                        'variables': 1.0},\n                                           'functions': {'cos': 0.5, 'sin': 0.5},\n                                           'operators': {'+': 0.5, '-': 0.5}}},\n         'functions': {'cos': 0.5, 'sin': 0.5},\n         'operator_conditionals': {'+': {'features': {'constants': 0.5,\n                                                      'variables': 0.5},\n                                         'functions': {'cos': 0.5, 'sin': 0.5},\n                                         'operators': {'+': 0.5, '-': 0.5}},\n                                   '-': {'features': {'constants': 0.5,\n                                                      'variables': 0.5},\n                                         'functions': {'cos': 0.5, 'sin': 0.5},\n                                         'operators': {'+': 0.5, '-': 0.5}}},\n         'operators': {'+': 0.5, '-': 0.5},\n         'structures': {'[0, 1, 1]': 0.3,\n                        '[0, 1, 2, 3, 2, 3, 1]': 0.4,\n                        '[0, 1, 2]': 0.3}}\n\n\n        &gt;&gt;&gt; tree_list = [EquationTree.from_prior(p, 4) for _ in range(100)]\n        &gt;&gt;&gt; len(tree_list)\n        100\n        &gt;&gt;&gt; example_tree = tree_list[2]\n        &gt;&gt;&gt; example_tree.expr\n        ['+', '-', 'sin', 'x_1', 'cos', 'x_2', 'c_1']\n        &gt;&gt;&gt; example_tree.sympy_expr\n        c_1 + sin(x_1) - cos(x_2)\n        &gt;&gt;&gt; pprint.pprint(example_tree.info)\n        {'depth': 3,\n         'features': {'constants': 1, 'variables': 2},\n         'function_conditionals': {'cos': {'features': {'constants': 0, 'variables': 1},\n                                           'functions': {},\n                                           'operators': {}},\n                                   'sin': {'features': {'constants': 0, 'variables': 1},\n                                           'functions': {},\n                                           'operators': {}}},\n         'functions': {'cos': 1, 'sin': 1},\n         'max_depth': 7,\n         'operator_conditionals': {'+': {'features': {'constants': 1, 'variables': 0},\n                                         'functions': {},\n                                         'operators': {'-': 1}},\n                                   '-': {'features': {'constants': 0, 'variables': 0},\n                                         'functions': {'cos': 1, 'sin': 1},\n                                         'operators': {}}},\n         'operators': {'+': 1, '-': 1},\n         'structures': [0, 1, 2, 3, 2, 3, 1]}\n\n        &gt;&gt;&gt; counts = get_counts(tree_list)\n        &gt;&gt;&gt; pprint.pprint(counts)\n        {'depth': {1: 32, 2: 27, 3: 41},\n         'features': {'constants': 44, 'variables': 170},\n         'function_conditionals': {'cos': {'features': {'constants': 0,\n                                                        'variables': 54},\n                                           'functions': {'cos': 7, 'sin': 6},\n                                           'operators': {}},\n                                   'sin': {'features': {'constants': 0,\n                                                        'variables': 55},\n                                           'functions': {'cos': 7, 'sin': 7},\n                                           'operators': {}}},\n         'functions': {'cos': 67, 'sin': 69},\n         'max_depth': {3: 59, 7: 41},\n         'operator_conditionals': {'+': {'features': {'constants': 24, 'variables': 29},\n                                         'functions': {'cos': 27, 'sin': 21},\n                                         'operators': {'+': 14, '-': 9}},\n                                   '-': {'features': {'constants': 20, 'variables': 32},\n                                         'functions': {'cos': 13, 'sin': 21},\n                                         'operators': {'+': 10, '-': 8}}},\n         'operators': {'+': 62, '-': 52},\n         'structures': {'[0, 1, 1]': 32, '[0, 1, 2, 3, 2, 3, 1]': 41, '[0, 1, 2]': 27}}\n    \"\"\"\n    info: Dict = {}\n    max_depth: Dict = {}\n    depth: Dict = {}\n    structures: Dict = {}\n    features: Dict = {}\n    functions: Dict = {}\n    operators: Dict = {}\n    function_conditionals: Dict = {}\n    operator_conditionals: Dict = {}\n    for t in trees:\n        _info = t.info\n        if \"max_depth\" in _info.keys():\n            _update(max_depth, _info[\"max_depth\"])\n        if \"depth\" in _info.keys():\n            _update(depth, _info[\"depth\"])\n        if \"structures\" in _info.keys():\n            _update(structures, str(_info[\"structures\"]))\n        if \"features\" in _info.keys():\n            for key, val in _info[\"features\"].items():\n                _update(features, key, val)\n        if \"functions\" in _info.keys():\n            for key, val in _info[\"functions\"].items():\n                _update(functions, key, val)\n        if \"operators\" in _info.keys():\n            for key, val in _info[\"operators\"].items():\n                _update(operators, key, val)\n        if \"function_conditionals\" in _info.keys():\n            fnc_con_dict = _info[\"function_conditionals\"]\n            for k, fnc_dict in fnc_con_dict.items():\n                if k not in function_conditionals.keys():\n                    function_conditionals[k] = {\n                        \"features\": {},\n                        \"functions\": {},\n                        \"operators\": {},\n                    }\n                fnc_dct_features = fnc_dict[\"features\"]\n                fnc_fct_functions = fnc_dict[\"functions\"]\n                fnc_fct_operators = fnc_dict[\"operators\"]\n                for key, val in fnc_dct_features.items():\n                    _update(function_conditionals[k][\"features\"], key, val)\n                for key, val in fnc_fct_functions.items():\n                    _update(function_conditionals[k][\"functions\"], key, val)\n                for key, val in fnc_fct_operators.items():\n                    _update(function_conditionals[k][\"operators\"], key, val)\n        if \"operator_conditionals\" in _info.keys():\n            op_con_dict = _info[\"operator_conditionals\"]\n            for k, op_dict in op_con_dict.items():\n                if k not in operator_conditionals.keys():\n                    operator_conditionals[k] = {\n                        \"features\": {},\n                        \"functions\": {},\n                        \"operators\": {},\n                    }\n                op_dct_features = op_dict[\"features\"]\n                op_fct_functions = op_dict[\"functions\"]\n                op_fct_operators = op_dict[\"operators\"]\n                for key, val in op_dct_features.items():\n                    _update(operator_conditionals[k][\"features\"], key, val)\n                for key, val in op_fct_functions.items():\n                    _update(operator_conditionals[k][\"functions\"], key, val)\n                for key, val in op_fct_operators.items():\n                    _update(operator_conditionals[k][\"operators\"], key, val)\n\n    info[\"max_depth\"] = max_depth\n    info[\"depth\"] = depth\n    info[\"structures\"] = structures\n    info[\"features\"] = features\n    info[\"functions\"] = functions\n    info[\"operators\"] = operators\n    info[\"function_conditionals\"] = function_conditionals\n    info[\"operator_conditionals\"] = operator_conditionals\n    return info\n</code></pre>"},{"location":"reference/src/equation_tree/analysis/#src.equation_tree.analysis.get_frequencies","title":"<code>get_frequencies(trees)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; import numpy as np\n&gt;&gt;&gt; import pprint\n&gt;&gt;&gt; np.random.seed(42)\n&gt;&gt;&gt; p = {\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .5, 'variables': .5},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': .5, '-': .5},\n...     'function_conditionals': {\n...                             'sin': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': .5, 'cos': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             },\n...                             'cos': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             }\n...                         },\n...     'operator_conditionals': {\n...                             '+': {\n...                                 'features': {'constants': .5, 'variables': .5},\n...                                 'functions': {'sin': .5, 'cos': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             },\n...                             '-': {\n...                                 'features': {'constants': .5, 'variables': .5},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             }\n...                         },\n... }\n&gt;&gt;&gt; pprint.pprint(p)\n{'features': {'constants': 0.5, 'variables': 0.5},\n 'function_conditionals': {'cos': {'features': {'constants': 0.0,\n                                                'variables': 1.0},\n                                   'functions': {'cos': 0.5, 'sin': 0.5},\n                                   'operators': {'+': 0.5, '-': 0.5}},\n                           'sin': {'features': {'constants': 0.0,\n                                                'variables': 1.0},\n                                   'functions': {'cos': 0.5, 'sin': 0.5},\n                                   'operators': {'+': 0.5, '-': 0.5}}},\n 'functions': {'cos': 0.5, 'sin': 0.5},\n 'operator_conditionals': {'+': {'features': {'constants': 0.5,\n                                              'variables': 0.5},\n                                 'functions': {'cos': 0.5, 'sin': 0.5},\n                                 'operators': {'+': 0.5, '-': 0.5}},\n                           '-': {'features': {'constants': 0.5,\n                                              'variables': 0.5},\n                                 'functions': {'cos': 0.5, 'sin': 0.5},\n                                 'operators': {'+': 0.5, '-': 0.5}}},\n 'operators': {'+': 0.5, '-': 0.5},\n 'structures': {'[0, 1, 1]': 0.3,\n                '[0, 1, 2, 3, 2, 3, 1]': 0.4,\n                '[0, 1, 2]': 0.3}}\n</code></pre> <pre><code>&gt;&gt;&gt; tree_list = [EquationTree.from_prior(p, 4) for _ in range(100)]\n&gt;&gt;&gt; len(tree_list)\n100\n&gt;&gt;&gt; example_tree = tree_list[2]\n&gt;&gt;&gt; example_tree.expr\n['+', '-', 'sin', 'x_1', 'cos', 'x_2', 'c_1']\n&gt;&gt;&gt; example_tree.sympy_expr\nc_1 + sin(x_1) - cos(x_2)\n&gt;&gt;&gt; pprint.pprint(example_tree.info)\n{'depth': 3,\n 'features': {'constants': 1, 'variables': 2},\n 'function_conditionals': {'cos': {'features': {'constants': 0, 'variables': 1},\n                                   'functions': {},\n                                   'operators': {}},\n                           'sin': {'features': {'constants': 0, 'variables': 1},\n                                   'functions': {},\n                                   'operators': {}}},\n 'functions': {'cos': 1, 'sin': 1},\n 'max_depth': 7,\n 'operator_conditionals': {'+': {'features': {'constants': 1, 'variables': 0},\n                                 'functions': {},\n                                 'operators': {'-': 1}},\n                           '-': {'features': {'constants': 0, 'variables': 0},\n                                 'functions': {'cos': 1, 'sin': 1},\n                                 'operators': {}}},\n 'operators': {'+': 1, '-': 1},\n 'structures': [0, 1, 2, 3, 2, 3, 1]}\n</code></pre> <pre><code>&gt;&gt;&gt; frequencies = get_frequencies(tree_list)\n&gt;&gt;&gt; pprint.pprint(frequencies)\n{'depth': {1: 0.32, 2: 0.27, 3: 0.41},\n 'features': {'constants': 0.205607476635514, 'variables': 0.794392523364486},\n 'function_conditionals': {'cos': {'features': {'constants': 0.0,\n                                                'variables': 1.0},\n                                   'functions': {'cos': 0.5384615384615384,\n                                                 'sin': 0.46153846153846156},\n                                   'operators': {}},\n                           'sin': {'features': {'constants': 0.0,\n                                                'variables': 1.0},\n                                   'functions': {'cos': 0.5, 'sin': 0.5},\n                                   'operators': {}}},\n 'functions': {'cos': 0.49264705882352944, 'sin': 0.5073529411764706},\n 'max_depth': {3: 0.59, 7: 0.41},\n 'operator_conditionals': {'+': {'features': {'constants': 0.4528301886792453,\n                                              'variables': 0.5471698113207547},\n                                 'functions': {'cos': 0.5625, 'sin': 0.4375},\n                                 'operators': {'+': 0.6086956521739131,\n                                               '-': 0.391304347826087}},\n                           '-': {'features': {'constants': 0.38461538461538464,\n                                              'variables': 0.6153846153846154},\n                                 'functions': {'cos': 0.38235294117647056,\n                                               'sin': 0.6176470588235294},\n                                 'operators': {'+': 0.5555555555555556,\n                                               '-': 0.4444444444444444}}},\n 'operators': {'+': 0.543859649122807, '-': 0.45614035087719296},\n 'structures': {'[0, 1, 1]': 0.32,\n                '[0, 1, 2, 3, 2, 3, 1]': 0.41,\n                '[0, 1, 2]': 0.27}}\n</code></pre> Source code in <code>src/equation_tree/analysis.py</code> <pre><code>def get_frequencies(trees: List[EquationTree]):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; import numpy as np\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; np.random.seed(42)\n        &gt;&gt;&gt; p = {\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .5, 'variables': .5},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': .5, '-': .5},\n        ...     'function_conditionals': {\n        ...                             'sin': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': .5, 'cos': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             },\n        ...                             'cos': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             }\n        ...                         },\n        ...     'operator_conditionals': {\n        ...                             '+': {\n        ...                                 'features': {'constants': .5, 'variables': .5},\n        ...                                 'functions': {'sin': .5, 'cos': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             },\n        ...                             '-': {\n        ...                                 'features': {'constants': .5, 'variables': .5},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             }\n        ...                         },\n        ... }\n        &gt;&gt;&gt; pprint.pprint(p)\n        {'features': {'constants': 0.5, 'variables': 0.5},\n         'function_conditionals': {'cos': {'features': {'constants': 0.0,\n                                                        'variables': 1.0},\n                                           'functions': {'cos': 0.5, 'sin': 0.5},\n                                           'operators': {'+': 0.5, '-': 0.5}},\n                                   'sin': {'features': {'constants': 0.0,\n                                                        'variables': 1.0},\n                                           'functions': {'cos': 0.5, 'sin': 0.5},\n                                           'operators': {'+': 0.5, '-': 0.5}}},\n         'functions': {'cos': 0.5, 'sin': 0.5},\n         'operator_conditionals': {'+': {'features': {'constants': 0.5,\n                                                      'variables': 0.5},\n                                         'functions': {'cos': 0.5, 'sin': 0.5},\n                                         'operators': {'+': 0.5, '-': 0.5}},\n                                   '-': {'features': {'constants': 0.5,\n                                                      'variables': 0.5},\n                                         'functions': {'cos': 0.5, 'sin': 0.5},\n                                         'operators': {'+': 0.5, '-': 0.5}}},\n         'operators': {'+': 0.5, '-': 0.5},\n         'structures': {'[0, 1, 1]': 0.3,\n                        '[0, 1, 2, 3, 2, 3, 1]': 0.4,\n                        '[0, 1, 2]': 0.3}}\n\n\n        &gt;&gt;&gt; tree_list = [EquationTree.from_prior(p, 4) for _ in range(100)]\n        &gt;&gt;&gt; len(tree_list)\n        100\n        &gt;&gt;&gt; example_tree = tree_list[2]\n        &gt;&gt;&gt; example_tree.expr\n        ['+', '-', 'sin', 'x_1', 'cos', 'x_2', 'c_1']\n        &gt;&gt;&gt; example_tree.sympy_expr\n        c_1 + sin(x_1) - cos(x_2)\n        &gt;&gt;&gt; pprint.pprint(example_tree.info)\n        {'depth': 3,\n         'features': {'constants': 1, 'variables': 2},\n         'function_conditionals': {'cos': {'features': {'constants': 0, 'variables': 1},\n                                           'functions': {},\n                                           'operators': {}},\n                                   'sin': {'features': {'constants': 0, 'variables': 1},\n                                           'functions': {},\n                                           'operators': {}}},\n         'functions': {'cos': 1, 'sin': 1},\n         'max_depth': 7,\n         'operator_conditionals': {'+': {'features': {'constants': 1, 'variables': 0},\n                                         'functions': {},\n                                         'operators': {'-': 1}},\n                                   '-': {'features': {'constants': 0, 'variables': 0},\n                                         'functions': {'cos': 1, 'sin': 1},\n                                         'operators': {}}},\n         'operators': {'+': 1, '-': 1},\n         'structures': [0, 1, 2, 3, 2, 3, 1]}\n\n        &gt;&gt;&gt; frequencies = get_frequencies(tree_list)\n        &gt;&gt;&gt; pprint.pprint(frequencies)\n        {'depth': {1: 0.32, 2: 0.27, 3: 0.41},\n         'features': {'constants': 0.205607476635514, 'variables': 0.794392523364486},\n         'function_conditionals': {'cos': {'features': {'constants': 0.0,\n                                                        'variables': 1.0},\n                                           'functions': {'cos': 0.5384615384615384,\n                                                         'sin': 0.46153846153846156},\n                                           'operators': {}},\n                                   'sin': {'features': {'constants': 0.0,\n                                                        'variables': 1.0},\n                                           'functions': {'cos': 0.5, 'sin': 0.5},\n                                           'operators': {}}},\n         'functions': {'cos': 0.49264705882352944, 'sin': 0.5073529411764706},\n         'max_depth': {3: 0.59, 7: 0.41},\n         'operator_conditionals': {'+': {'features': {'constants': 0.4528301886792453,\n                                                      'variables': 0.5471698113207547},\n                                         'functions': {'cos': 0.5625, 'sin': 0.4375},\n                                         'operators': {'+': 0.6086956521739131,\n                                                       '-': 0.391304347826087}},\n                                   '-': {'features': {'constants': 0.38461538461538464,\n                                                      'variables': 0.6153846153846154},\n                                         'functions': {'cos': 0.38235294117647056,\n                                                       'sin': 0.6176470588235294},\n                                         'operators': {'+': 0.5555555555555556,\n                                                       '-': 0.4444444444444444}}},\n         'operators': {'+': 0.543859649122807, '-': 0.45614035087719296},\n         'structures': {'[0, 1, 1]': 0.32,\n                        '[0, 1, 2, 3, 2, 3, 1]': 0.41,\n                        '[0, 1, 2]': 0.27}}\n    \"\"\"\n    info: Dict = {}\n    max_depth: Dict = {}\n    depth: Dict = {}\n    structures: Dict = {}\n    features: Dict = {}\n    functions: Dict = {}\n    operators: Dict = {}\n    function_conditionals: Dict = {}\n    operator_conditionals: Dict = {}\n    for t in trees:\n        _info = t.info\n        if \"max_depth\" in _info.keys():\n            _update(max_depth, _info[\"max_depth\"])\n        if \"depth\" in _info.keys():\n            _update(depth, _info[\"depth\"])\n        if \"structures\" in _info.keys():\n            _update(structures, str(_info[\"structures\"]))\n        if \"features\" in _info.keys():\n            for key, val in _info[\"features\"].items():\n                _update(features, key, val)\n        if \"functions\" in _info.keys():\n            for key, val in _info[\"functions\"].items():\n                _update(functions, key, val)\n        if \"operators\" in _info.keys():\n            for key, val in _info[\"operators\"].items():\n                _update(operators, key, val)\n        if \"function_conditionals\" in _info.keys():\n            fnc_con_dict = _info[\"function_conditionals\"]\n            for k, fnc_dict in fnc_con_dict.items():\n                if k not in function_conditionals.keys():\n                    function_conditionals[k] = {\n                        \"features\": {},\n                        \"functions\": {},\n                        \"operators\": {},\n                    }\n                fnc_dct_features = fnc_dict[\"features\"]\n                fnc_fct_functions = fnc_dict[\"functions\"]\n                fnc_fct_operators = fnc_dict[\"operators\"]\n                for key, val in fnc_dct_features.items():\n                    _update(function_conditionals[k][\"features\"], key, val)\n                for key, val in fnc_fct_functions.items():\n                    _update(function_conditionals[k][\"functions\"], key, val)\n                for key, val in fnc_fct_operators.items():\n                    _update(function_conditionals[k][\"operators\"], key, val)\n        if \"operator_conditionals\" in _info.keys():\n            op_con_dict = _info[\"operator_conditionals\"]\n            for k, op_dict in op_con_dict.items():\n                if k not in operator_conditionals.keys():\n                    operator_conditionals[k] = {\n                        \"features\": {},\n                        \"functions\": {},\n                        \"operators\": {},\n                    }\n                op_dct_features = op_dict[\"features\"]\n                op_fct_functions = op_dict[\"functions\"]\n                op_fct_operators = op_dict[\"operators\"]\n                for key, val in op_dct_features.items():\n                    _update(operator_conditionals[k][\"features\"], key, val)\n                for key, val in op_fct_functions.items():\n                    _update(operator_conditionals[k][\"functions\"], key, val)\n                for key, val in op_fct_operators.items():\n                    _update(operator_conditionals[k][\"operators\"], key, val)\n    for k_c in function_conditionals:\n        for k in [\"features\", \"functions\", \"operators\"]:\n            if k in function_conditionals[k_c]:\n                function_conditionals[k_c][k] = normalized_dict(\n                    function_conditionals[k_c][k]\n                )\n    for k_c in operator_conditionals:\n        for k in [\"features\", \"functions\", \"operators\"]:\n            if k in operator_conditionals[k_c]:\n                operator_conditionals[k_c][k] = normalized_dict(\n                    operator_conditionals[k_c][k]\n                )\n\n    info[\"max_depth\"] = normalized_dict(max_depth)\n    info[\"depth\"] = normalized_dict(depth)\n    info[\"structures\"] = normalized_dict(structures)\n    info[\"features\"] = normalized_dict(features)\n    info[\"functions\"] = normalized_dict(functions)\n    info[\"operators\"] = normalized_dict(operators)\n    info[\"function_conditionals\"] = function_conditionals\n    info[\"operator_conditionals\"] = operator_conditionals\n    return info\n</code></pre>"},{"location":"reference/src/equation_tree/defaults/","title":"Defaults","text":""},{"location":"reference/src/equation_tree/prior/","title":"Prior","text":""},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.add","title":"<code>add(prior_a, prior_b)</code>","text":"<p>import pprint a = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}} b = {'a': {'a_1': 2, 'a_2': 4}, 'c': {'b_1': 3, 'b_2': 3}} pprint.pprint(add(a, b)) {'a': {'a_1': 5, 'a_2': 6},  'b': {'b_1': 0.1, 'b_2': 0.3},  'c': {'b_1': 3, 'b_2': 3}}</p> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def add(prior_a, prior_b):\n    \"\"\"\n    &gt;&gt;&gt; import pprint\n    &gt;&gt;&gt; a = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}}\n    &gt;&gt;&gt; b = {'a': {'a_1': 2, 'a_2': 4}, 'c': {'b_1': 3, 'b_2': 3}}\n    &gt;&gt;&gt; pprint.pprint(add(a, b))\n    {'a': {'a_1': 5, 'a_2': 6},\n     'b': {'b_1': 0.1, 'b_2': 0.3},\n     'c': {'b_1': 3, 'b_2': 3}}\n\n    \"\"\"\n    tmp_a = copy.deepcopy(prior_a)\n    tmp_b = copy.deepcopy(prior_b)\n\n    def _rec_add(a, b):\n        for k, val in a.items():\n            if k in b.keys():\n                if isinstance(val, dict) and isinstance(b[k], dict):\n                    _rec_add(a[k], b[k])\n                elif not isinstance(val, dict) and not isinstance(b[k], dict):\n                    a[k] += b[k]\n\n    _rec_add(tmp_a, tmp_b)\n    return append(tmp_a, tmp_b)\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.filter_keys","title":"<code>filter_keys(dict_a, dict_b)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; import pprint\n&gt;&gt;&gt; a = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}, 'c': {}}\n&gt;&gt;&gt; b = {'a': {'a_1': 2, 'a_2': 4}, 'b': {'b_1': 3, 'c_1': 3}}\n&gt;&gt;&gt; pprint.pprint(filter_keys(a, b))\n{'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': 0.1}}\n</code></pre> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def filter_keys(dict_a, dict_b):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; a = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}, 'c': {}}\n        &gt;&gt;&gt; b = {'a': {'a_1': 2, 'a_2': 4}, 'b': {'b_1': 3, 'c_1': 3}}\n        &gt;&gt;&gt; pprint.pprint(filter_keys(a, b))\n        {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': 0.1}}\n    \"\"\"\n    tmp_a = copy.deepcopy(dict_a)\n    tmp_b = copy.deepcopy(dict_b)\n\n    def _rec_f_key(a, b):\n        for k in list(a.keys()):\n            if k in b.keys():\n                if isinstance(a[k], dict) and isinstance(b[k], dict):\n                    _rec_f_key(a[k], b[k])\n                else:\n                    a[k] = a[k]\n            else:\n                del a[k]\n\n    _rec_f_key(tmp_a, tmp_b)\n    return tmp_a\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.get_defined_functions","title":"<code>get_defined_functions(prior)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; test_prior = {\n...     'functions': {'sin': 2},\n...     'function_conditionals': {'sin': {'features': {'constants': 0, 'variables': 2},\n...                                   'functions': {},\n...                                       'operators': {}}},\n...     'operator_conditionals': {'+': {'features': {'constants': 0, 'variables': 1},\n...                                     'functions': {'cos': 2},\n...                                     'operators': {'-': 1}},\n...                               '-': {'features': {'constants': 0, 'variables': 0},\n...                                     'functions': {'sin': 2, 'abs': 1},\n...                                     'operators': {}}},\n...     'operators': {'+': 1, '-': 1},\n...     'structure': [0, 1, 2, 3, 2, 3, 1]}\n&gt;&gt;&gt; set(get_defined_functions(test_prior)) == set(['sin', 'abs', 'cos'])\nTrue\n</code></pre> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def get_defined_functions(prior):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; test_prior = {\n        ...     'functions': {'sin': 2},\n        ...     'function_conditionals': {'sin': {'features': {'constants': 0, 'variables': 2},\n        ...                                   'functions': {},\n        ...                                       'operators': {}}},\n        ...     'operator_conditionals': {'+': {'features': {'constants': 0, 'variables': 1},\n        ...                                     'functions': {'cos': 2},\n        ...                                     'operators': {'-': 1}},\n        ...                               '-': {'features': {'constants': 0, 'variables': 0},\n        ...                                     'functions': {'sin': 2, 'abs': 1},\n        ...                                     'operators': {}}},\n        ...     'operators': {'+': 1, '-': 1},\n        ...     'structure': [0, 1, 2, 3, 2, 3, 1]}\n        &gt;&gt;&gt; set(get_defined_functions(test_prior)) == set(['sin', 'abs', 'cos'])\n        True\n    \"\"\"\n    return _get_defined(prior, \"functions\", \"function_conditionals\")\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.get_defined_operators","title":"<code>get_defined_operators(prior)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; test_prior = {\n...     'function_conditionals': {'sin': {'features': {'constants': 0, 'variables': 2},\n...                                   'functions': {},\n...                                       'operators': {}}},\n...     'functions': {'sin': 2},\n...     'operator_conditionals': {'+': {'features': {'constants': 0, 'variables': 1},\n...                                     'functions': {'cos': 2},\n...                                     'operators': {'**': 1}},\n...                               '/': {'features': {'constants': 0, 'variables': 0},\n...                                     'functions': {'sin': 2},\n...                                     'operators': {}}},\n...     'operators': {'+': 1, '-': 1},\n...     'structure': [0, 1, 2, 3, 2, 3, 1]}\n&gt;&gt;&gt; set(get_defined_operators(test_prior)) == set(['+', '/', '**', '-'])\nTrue\n</code></pre> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def get_defined_operators(prior):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; test_prior = {\n        ...     'function_conditionals': {'sin': {'features': {'constants': 0, 'variables': 2},\n        ...                                   'functions': {},\n        ...                                       'operators': {}}},\n        ...     'functions': {'sin': 2},\n        ...     'operator_conditionals': {'+': {'features': {'constants': 0, 'variables': 1},\n        ...                                     'functions': {'cos': 2},\n        ...                                     'operators': {'**': 1}},\n        ...                               '/': {'features': {'constants': 0, 'variables': 0},\n        ...                                     'functions': {'sin': 2},\n        ...                                     'operators': {}}},\n        ...     'operators': {'+': 1, '-': 1},\n        ...     'structure': [0, 1, 2, 3, 2, 3, 1]}\n        &gt;&gt;&gt; set(get_defined_operators(test_prior)) == set(['+', '/', '**', '-'])\n        True\n    \"\"\"\n    return _get_defined(prior, \"operators\", \"operator_conditionals\")\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.multiply","title":"<code>multiply(a, b)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; import pprint\n&gt;&gt;&gt; prior_a = {'a':\n...                 {'a_1':  .2, 'a_2': .8},\n...             'b': {\n...                 'b_1' : {'b_1_1': .25, 'b_1_2': .5, 'b_1_3': .25}\n...             }\n...         }\n&gt;&gt;&gt; prior_b = {'a':\n...                 {'a_1':  4, 'a_2': 1},\n...             'b': {\n...                 'b_1' : {'b_1_1': 4 , 'b_1_2': 1, 'b_1_3': 4}\n...             },\n...             'c': {'c_1': .9, 'c_2': .1}\n...         }\n&gt;&gt;&gt; product = multiply(prior_a, prior_b)\n&gt;&gt;&gt; pprint.pprint(product)\n{'a': {'a_1': 0.8, 'a_2': 0.8},\n 'b': {'b_1': {'b_1_1': 1.0, 'b_1_2': 0.5, 'b_1_3': 1.0}},\n 'c': {'c_1': 0.9, 'c_2': 0.1}}\n&gt;&gt;&gt; normalize(product)\n&gt;&gt;&gt; pprint.pprint(product)\n{'a': {'a_1': 0.5, 'a_2': 0.5},\n 'b': {'b_1': {'b_1_1': 0.4, 'b_1_2': 0.2, 'b_1_3': 0.4}},\n 'c': {'c_1': 0.9, 'c_2': 0.1}}\n</code></pre> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def multiply(a, b):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; prior_a = {'a':\n        ...                 {'a_1':  .2, 'a_2': .8},\n        ...             'b': {\n        ...                 'b_1' : {'b_1_1': .25, 'b_1_2': .5, 'b_1_3': .25}\n        ...             }\n        ...         }\n        &gt;&gt;&gt; prior_b = {'a':\n        ...                 {'a_1':  4, 'a_2': 1},\n        ...             'b': {\n        ...                 'b_1' : {'b_1_1': 4 , 'b_1_2': 1, 'b_1_3': 4}\n        ...             },\n        ...             'c': {'c_1': .9, 'c_2': .1}\n        ...         }\n        &gt;&gt;&gt; product = multiply(prior_a, prior_b)\n        &gt;&gt;&gt; pprint.pprint(product)\n        {'a': {'a_1': 0.8, 'a_2': 0.8},\n         'b': {'b_1': {'b_1_1': 1.0, 'b_1_2': 0.5, 'b_1_3': 1.0}},\n         'c': {'c_1': 0.9, 'c_2': 0.1}}\n        &gt;&gt;&gt; normalize(product)\n        &gt;&gt;&gt; pprint.pprint(product)\n        {'a': {'a_1': 0.5, 'a_2': 0.5},\n         'b': {'b_1': {'b_1_1': 0.4, 'b_1_2': 0.2, 'b_1_3': 0.4}},\n         'c': {'c_1': 0.9, 'c_2': 0.1}}\n    \"\"\"\n    tmp_a = copy.deepcopy(a)\n    tmp_b = copy.deepcopy(b)\n\n    def _multiply(_a, _b):\n        for k, val in _a.items():\n            if k in _b.keys():\n                if isinstance(val, dict) and isinstance(_b[k], dict):\n                    _multiply(val, _b[k])\n                elif not isinstance(val, dict) and not isinstance(_b[k], dict):\n                    res = val * _b[k]\n                    _a[k] = res\n\n    _multiply(tmp_a, tmp_b)\n    tmp_a = append(tmp_a, tmp_b)\n\n    return tmp_a\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.prior_from_space","title":"<code>prior_from_space(space)</code>","text":"<p>Uniform prior from a list of strings Examples:     &gt;&gt;&gt; import pprint     &gt;&gt;&gt; operator_space = ['+', '-', '', '/', '^']     &gt;&gt;&gt; operator_prior = prior_from_space(operator_space)     &gt;&gt;&gt; pprint.pprint(operator_prior)     {'': 0.2, '+': 0.2, '-': 0.2, '/': 0.2, '^': 0.2}</p> <pre><code>&gt;&gt;&gt; function_space = ['sin', 'cos', 'tan', 'exp', 'log', 'sqrt', 'abs']\n&gt;&gt;&gt; function_prior = prior_from_space(function_space)\n&gt;&gt;&gt; pprint.pprint(function_prior)\n{'abs': 0.14285714285714285,\n 'cos': 0.14285714285714285,\n 'exp': 0.14285714285714285,\n 'log': 0.14285714285714285,\n 'sin': 0.14285714285714285,\n 'sqrt': 0.14285714285714285,\n 'tan': 0.14285714285714285}\n</code></pre> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def prior_from_space(space):\n    \"\"\"\n    Uniform prior from a list of strings\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; operator_space = ['+', '-', '*', '/', '^']\n        &gt;&gt;&gt; operator_prior = prior_from_space(operator_space)\n        &gt;&gt;&gt; pprint.pprint(operator_prior)\n        {'*': 0.2, '+': 0.2, '-': 0.2, '/': 0.2, '^': 0.2}\n\n        &gt;&gt;&gt; function_space = ['sin', 'cos', 'tan', 'exp', 'log', 'sqrt', 'abs']\n        &gt;&gt;&gt; function_prior = prior_from_space(function_space)\n        &gt;&gt;&gt; pprint.pprint(function_prior)\n        {'abs': 0.14285714285714285,\n         'cos': 0.14285714285714285,\n         'exp': 0.14285714285714285,\n         'log': 0.14285714285714285,\n         'sin': 0.14285714285714285,\n         'sqrt': 0.14285714285714285,\n         'tan': 0.14285714285714285}\n    \"\"\"\n    return priors_from_space(space)\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.re_normalize","title":"<code>re_normalize(target, origin)</code>","text":"Source code in <code>src/equation_tree/prior.py</code> <pre><code>def re_normalize(target, origin):\n    \"\"\" \"\"\"\n    tmp_t = copy.deepcopy(target)\n    tmp_o = copy.deepcopy(origin)\n\n    def _rec_re_normalize(t, p):\n        for k, val in t.items():\n            if isinstance(val, dict) and isinstance(p[k], dict):\n                _rec_re_normalize(t[k], p[k])\n            elif not isinstance(val, dict):\n                if not isinstance(p[k], dict) and val &lt;= 0 &lt; p[k]:\n                    t[k] = MIN\n                elif val &lt;= 0:\n                    t[k] = 0\n\n    _rec_re_normalize(tmp_t, tmp_o)\n    normalize(tmp_t)\n    return tmp_t\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.scalar_multiply","title":"<code>scalar_multiply(scalar, prior)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; import pprint\n&gt;&gt;&gt; m = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}}\n&gt;&gt;&gt; s = 2\n&gt;&gt;&gt; pprint.pprint(scalar_multiply(s, m))\n{'a': {'a_1': 6, 'a_2': 4}, 'b': {'b_1': 0.2, 'b_2': 0.6}}\n</code></pre> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def scalar_multiply(scalar, prior):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; m = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}}\n        &gt;&gt;&gt; s = 2\n        &gt;&gt;&gt; pprint.pprint(scalar_multiply(s, m))\n        {'a': {'a_1': 6, 'a_2': 4}, 'b': {'b_1': 0.2, 'b_2': 0.6}}\n    \"\"\"\n    tmp_p = copy.deepcopy(prior)\n\n    def _rec_s_mult(s, p):\n        for k, val in p.items():\n            if isinstance(val, dict):\n                _rec_s_mult(s, p[k])\n            else:\n                p[k] *= s\n\n    _rec_s_mult(scalar, tmp_p)\n    return tmp_p\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.structure_prior_from_depth","title":"<code>structure_prior_from_depth(depth)</code>","text":"<p>Uniform structure prior for a given depth Examples:     &gt;&gt;&gt; import pprint     &gt;&gt;&gt; pprint.pprint(structure_prior_from_depth(3))     {'[0, 1, 1]': 0.5, '[0, 1, 2]': 0.5}     &gt;&gt;&gt; pprint.pprint(structure_prior_from_depth(4))     {'[0, 1, 1, 2]': 0.25,      '[0, 1, 2, 1]': 0.25,      '[0, 1, 2, 2]': 0.25,      '[0, 1, 2, 3]': 0.25}</p> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def structure_prior_from_depth(depth):\n    \"\"\"\n    Uniform structure prior for a given depth\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; pprint.pprint(structure_prior_from_depth(3))\n        {'[0, 1, 1]': 0.5, '[0, 1, 2]': 0.5}\n        &gt;&gt;&gt; pprint.pprint(structure_prior_from_depth(4))\n        {'[0, 1, 1, 2]': 0.25,\n         '[0, 1, 2, 1]': 0.25,\n         '[0, 1, 2, 2]': 0.25,\n         '[0, 1, 2, 3]': 0.25}\n\n    \"\"\"\n    structures = _gen_tree_structures(depth)\n    structures = [s for s in structures if len(s) == depth]\n    return prior_from_space([str(s) for s in structures])\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.structure_prior_from_max_depth","title":"<code>structure_prior_from_max_depth(max_depth)</code>","text":"<p>Uniform structure prior up to a given depth (from min depth 3) Examples:     &gt;&gt;&gt; import pprint     &gt;&gt;&gt; pprint.pprint(structure_prior_from_max_depth(3))     {'[0, 1, 1]': 0.5, '[0, 1, 2]': 0.5}     &gt;&gt;&gt; pprint.pprint(structure_prior_from_max_depth(4))     {'[0, 1, 1, 2]': 0.16666666666666666,      '[0, 1, 1]': 0.16666666666666666,      '[0, 1, 2, 1]': 0.16666666666666666,      '[0, 1, 2, 2]': 0.16666666666666666,      '[0, 1, 2, 3]': 0.16666666666666666,      '[0, 1, 2]': 0.16666666666666666}     &gt;&gt;&gt; pprint.pprint(structure_prior_from_max_depth(5))     {'[0, 1, 1, 2, 2]': 0.06666666666666667,      '[0, 1, 1, 2, 3]': 0.06666666666666667,      '[0, 1, 1, 2]': 0.06666666666666667,      '[0, 1, 1]': 0.06666666666666667,      '[0, 1, 2, 1, 2]': 0.06666666666666667,      '[0, 1, 2, 1]': 0.06666666666666667,      '[0, 1, 2, 2, 1]': 0.06666666666666667,      '[0, 1, 2, 2, 3]': 0.06666666666666667,      '[0, 1, 2, 2]': 0.06666666666666667,      '[0, 1, 2, 3, 1]': 0.06666666666666667,      '[0, 1, 2, 3, 2]': 0.06666666666666667,      '[0, 1, 2, 3, 3]': 0.06666666666666667,      '[0, 1, 2, 3, 4]': 0.06666666666666667,      '[0, 1, 2, 3]': 0.06666666666666667,      '[0, 1, 2]': 0.06666666666666667}</p> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def structure_prior_from_max_depth(max_depth):\n    \"\"\"\n    Uniform structure prior up to a given depth (from min depth 3)\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; pprint.pprint(structure_prior_from_max_depth(3))\n        {'[0, 1, 1]': 0.5, '[0, 1, 2]': 0.5}\n        &gt;&gt;&gt; pprint.pprint(structure_prior_from_max_depth(4))\n        {'[0, 1, 1, 2]': 0.16666666666666666,\n         '[0, 1, 1]': 0.16666666666666666,\n         '[0, 1, 2, 1]': 0.16666666666666666,\n         '[0, 1, 2, 2]': 0.16666666666666666,\n         '[0, 1, 2, 3]': 0.16666666666666666,\n         '[0, 1, 2]': 0.16666666666666666}\n        &gt;&gt;&gt; pprint.pprint(structure_prior_from_max_depth(5))\n        {'[0, 1, 1, 2, 2]': 0.06666666666666667,\n         '[0, 1, 1, 2, 3]': 0.06666666666666667,\n         '[0, 1, 1, 2]': 0.06666666666666667,\n         '[0, 1, 1]': 0.06666666666666667,\n         '[0, 1, 2, 1, 2]': 0.06666666666666667,\n         '[0, 1, 2, 1]': 0.06666666666666667,\n         '[0, 1, 2, 2, 1]': 0.06666666666666667,\n         '[0, 1, 2, 2, 3]': 0.06666666666666667,\n         '[0, 1, 2, 2]': 0.06666666666666667,\n         '[0, 1, 2, 3, 1]': 0.06666666666666667,\n         '[0, 1, 2, 3, 2]': 0.06666666666666667,\n         '[0, 1, 2, 3, 3]': 0.06666666666666667,\n         '[0, 1, 2, 3, 4]': 0.06666666666666667,\n         '[0, 1, 2, 3]': 0.06666666666666667,\n         '[0, 1, 2]': 0.06666666666666667}\n    \"\"\"\n    structures = _gen_tree_structures(max_depth)\n    return prior_from_space([str(s) for s in structures])\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.subtract","title":"<code>subtract(minuend, subtrahend)</code>","text":"<p>Minuend - Subtrahend Examples:     &gt;&gt;&gt; import pprint     &gt;&gt;&gt; m = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}}     &gt;&gt;&gt; s = {'a': {'a_1': 2, 'a_2': 4}}     &gt;&gt;&gt; pprint.pprint(subtract(m, s))     {'a': {'a_1': 1, 'a_2': -2}, 'b': {'b_1': 0.0, 'b_2': 0.0}}</p> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def subtract(minuend, subtrahend):\n    \"\"\"\n    Minuend - Subtrahend\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; m = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}}\n        &gt;&gt;&gt; s = {'a': {'a_1': 2, 'a_2': 4}}\n        &gt;&gt;&gt; pprint.pprint(subtract(m, s))\n        {'a': {'a_1': 1, 'a_2': -2}, 'b': {'b_1': 0.0, 'b_2': 0.0}}\n\n    \"\"\"\n    tmp_m = copy.deepcopy(minuend)\n    tmp_s = copy.deepcopy(subtrahend)\n\n    def _rec_sub(m, s):\n        for k, val in m.items():\n            if k in s.keys():\n                if isinstance(val, dict) and isinstance(s[k], dict):\n                    _rec_sub(val, s[k])\n                elif (\n                    not isinstance(val, dict)\n                    and is_numeric(val)\n                    and not isinstance(s[k], dict)\n                    and is_numeric(s[k])\n                ):\n                    m[k] -= s[k]\n                else:\n                    if not isinstance(val, dict):\n                        m[k] = 0.0\n                    else:\n                        _set_zero(m[k])\n            else:\n                if not isinstance(val, dict):\n                    m[k] = 0.0\n                else:\n                    _set_zero(m[k])\n\n    _rec_sub(tmp_m, tmp_s)\n    return tmp_m\n</code></pre>"},{"location":"reference/src/equation_tree/sample/","title":"Sample","text":""},{"location":"reference/src/equation_tree/sample/#src.equation_tree.sample.sample_tree_raw_from_priors","title":"<code>sample_tree_raw_from_priors(max_num_constants=0, max_num_variables=1, feature_priors=None, function_priors=DEFAULT_FUNCTION_SPACE, operator_priors=DEFAULT_OPERATOR_SPACE, structure_priors={})</code>","text":"<p>Sample a tree from priors, simplify and check if valid tree</p> Source code in <code>src/equation_tree/sample.py</code> <pre><code>def sample_tree_raw_from_priors(\n    max_num_constants: int = 0,\n    max_num_variables: int = 1,\n    feature_priors: Optional[Dict] = None,\n    function_priors: PriorType = DEFAULT_FUNCTION_SPACE,\n    operator_priors: PriorType = DEFAULT_OPERATOR_SPACE,\n    structure_priors: PriorType = {},\n):\n    \"\"\"\n    Sample a tree from priors, simplify and check if valid tree\n    \"\"\"\n    # Assertions\n    if max_num_constants + max_num_variables &lt; 1:\n        raise Exception(\"Can not sample tree without leafs\")\n\n    # Get feature priors\n    if feature_priors is not None:\n        for key in feature_priors:\n            if not (is_variable_formatted(key) or is_constant_formatted(key)):\n                raise Exception(\n                    \"Use standard formats for feature priors: x_{int} for variables, \"\n                    \"c_{int} for constants.\"\n                )\n        _feature_priors = feature_priors.copy()\n    else:\n        _feature_space = [f\"x_{i}\" for i in range(1, max_num_variables + 1)] + [\n            f\"c_{i}\" for i in range(1, max_num_constants + 1)\n        ]\n        _feature_priors = priors_from_space(_feature_space)\n\n    # Convert priors if space is given\n    if isinstance(function_priors, List):\n        _function_priors = priors_from_space(function_priors)\n    else:\n        _function_priors = function_priors.copy()\n\n    if isinstance(operator_priors, List):\n        _operator_priors = priors_from_space(operator_priors)\n    else:\n        _operator_priors = operator_priors.copy()\n\n    if isinstance(structure_priors, List):\n        _structure_priors = priors_from_space(structure_priors)\n    else:\n        _structure_priors = structure_priors.copy()\n\n    # Create tree\n    equation_tree = EquationTree.from_priors(\n        feature_priors=_feature_priors,\n        function_priors=_function_priors,\n        operator_priors=_operator_priors,\n        structure_priors=_structure_priors,\n    )\n\n    # Check if tree is valid\n    if not equation_tree.check_validity():\n        return None\n\n    equation_tree.simplify(\n        function_test=lambda x: x in _function_priors.keys(),\n        operator_test=lambda x: x in _operator_priors.keys(),\n    )\n\n    # Check is nan\n    if equation_tree.is_nan:\n        return None\n\n    # Check if duplicate constants\n    if (\n        equation_tree.n_non_numeric_constants\n        &gt; equation_tree.n_non_numeric_constants_unique\n    ):\n        return None\n\n    # Check if more constants than max:\n    if equation_tree.n_constants &gt; max_num_constants:\n        return None\n\n    # Check if more variables than max:\n    if equation_tree.n_variables &gt; max_num_variables:\n        return None\n\n    if not equation_tree.check_validity():\n        return None\n\n    if not equation_tree.check_possible(\n        _feature_priors, _function_priors, _operator_priors, _structure_priors\n    ):\n        return None\n\n    equation_tree.get_evaluation()\n    if not equation_tree.has_valid_value:\n        return None\n\n    return equation_tree\n</code></pre>"},{"location":"reference/src/equation_tree/tree/","title":"Tree","text":""},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree","title":"<code>EquationTree</code>","text":"<p>Equation tree that represents an equation as binary tree.</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>class EquationTree:\n    \"\"\"\n    Equation tree that represents an equation as binary tree.\n    \"\"\"\n\n    def __init__(self, node: TreeNode):\n        \"\"\"\n        Initializes a tree from a TreeNode\n\n        Examples:\n            # We can inititlize from a single node\n            &gt;&gt;&gt; node_root = TreeNode(kind=NodeKind.VARIABLE, attribute=\"x\")\n            &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n            &gt;&gt;&gt; equation_tree.expr\n            ['x']\n            &gt;&gt;&gt; equation_tree.structure\n            [0]\n            &gt;&gt;&gt; equation_tree.variables\n            ['x']\n\n            # Or from a node with children\n            &gt;&gt;&gt; node_left = TreeNode(kind=NodeKind.VARIABLE, attribute=\"x\")\n            &gt;&gt;&gt; node_right = TreeNode(kind=NodeKind.CONSTANT, attribute=\"c\")\n            &gt;&gt;&gt; node_root = TreeNode(kind=NodeKind.OPERATOR, attribute=\"+\", \\\n                            left=node_left, right=node_right)\n            &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n            &gt;&gt;&gt; equation_tree.expr\n            ['+', 'x', 'c']\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 1]\n            &gt;&gt;&gt; equation_tree.variables\n            ['x']\n            &gt;&gt;&gt; equation_tree.constants\n            ['c']\n            &gt;&gt;&gt; equation_tree.operators\n            ['+']\n\n            # We can first sample a node and children and initialize from that\n            &gt;&gt;&gt; np.random.seed(42)\n            &gt;&gt;&gt; max_depth = 12\n            &gt;&gt;&gt; structure_priors = {'[0, 1, 2, 1, 2, 3]': .5, '[0, 1, 2, 2, 1, 2, 3]': .5}\n            &gt;&gt;&gt; feature_priors = {\"x_1\": 0.5, \"c_1\": 0.5}\n            &gt;&gt;&gt; function_priors = {\"sin\": 0.5, \"cos\": 0.5}\n            &gt;&gt;&gt; operator_priors = {\"+\": 0.5, \"-\": 0.5}\n            &gt;&gt;&gt; node_root = sample_tree(feature_priors, function_priors,\n            ...     operator_priors, structure_priors)\n            &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n            &gt;&gt;&gt; equation_tree.expr\n            ['-', 'cos', 'c_1', 'sin', 'sin', 'x_1']\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2, 1, 2, 3]\n            &gt;&gt;&gt; equation_tree.variables\n            ['x_1']\n            &gt;&gt;&gt; equation_tree.n_variables\n            1\n            &gt;&gt;&gt; equation_tree.n_variables_unique\n            1\n            &gt;&gt;&gt; equation_tree.constants\n            ['c_1']\n            &gt;&gt;&gt; equation_tree.n_constants\n            1\n            &gt;&gt;&gt; equation_tree.n_constants_unique\n            1\n            &gt;&gt;&gt; equation_tree.n_leafs\n            2\n            &gt;&gt;&gt; equation_tree.operators\n            ['-']\n            &gt;&gt;&gt; equation_tree.functions\n            ['cos', 'sin', 'sin']\n\n            # First we create test functions that test weather an attribute is a variable,\n            # a constant, a function, or an operater\n            &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n            &gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n            &gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n            &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n\n            # here we use the prefix notation\n            &gt;&gt;&gt; prefix_notation = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n\n            # then we create the node root\n            &gt;&gt;&gt; node_root = node_from_prefix(\n            ...     prefix_notation=prefix_notation,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     function_test=is_function,\n            ...     operator_test=is_operator\n            ...     )\n\n            # and initialize the tree\n            &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2, 2, 1, 2, 3, 2, 3]\n            &gt;&gt;&gt; equation_tree.variables\n            ['x', 'y', 'z']\n            &gt;&gt;&gt; equation_tree.constants\n            ['1']\n            &gt;&gt;&gt; equation_tree.operators\n            ['+', '-', '*']\n            &gt;&gt;&gt; equation_tree.functions\n            ['sin', 'cos']\n\n            # The tree expression is the same as the prefix notation\n            &gt;&gt;&gt; equation_tree.expr == prefix_notation\n            True\n        \"\"\"\n\n        self.root: Union[TreeNode, None] = node\n\n        self.structure: List[int] = []\n\n        self.expr: List[str] = list()\n\n        self.variables: List[str] = list()\n        self.functions: List[str] = list()\n        self.operators: List[str] = list()\n        self.constants: List[str] = list()\n\n        self.evaluation = None\n\n        self._build()\n\n    @classmethod\n    def from_prefix(\n        cls,\n        prefix_notation: List[str],\n        function_test: Callable = lambda _: False,\n        operator_test: Callable = lambda _: False,\n        variable_test: Callable = lambda _: False,\n        constant_test: Callable = lambda _: False,\n    ):\n        \"\"\"\n        Instantiate a tree from prefix notation\n\n        Args:\n            prefix_notation: The equation in prefix notation\n            function_test: A function that tests if the attribute is a function\n            operator_test: A function that tests if the attribute is an operator\n            variable_test: A function that tests if the attribute is a variable\n            constant_test: A function that tests if the attribute is a constant\n\n        Example:\n            &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n            &gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n            &gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n            &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n            &gt;&gt;&gt; prefix = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n\n            # then we create the node root\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     prefix_notation=prefix,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     function_test=is_function,\n            ...     operator_test=is_operator\n            ...     )\n\n            # and initialize the tree\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2, 2, 1, 2, 3, 2, 3]\n            &gt;&gt;&gt; equation_tree.variables\n            ['x', 'y', 'z']\n            &gt;&gt;&gt; equation_tree.constants\n            ['1']\n            &gt;&gt;&gt; equation_tree.operators\n            ['+', '-', '*']\n            &gt;&gt;&gt; equation_tree.functions\n            ['sin', 'cos']\n\n            # The tree expression is the same as the prefix notation\n            &gt;&gt;&gt; equation_tree.expr == prefix\n            True\n\n\n        \"\"\"\n        root = node_from_prefix(\n            prefix_notation, function_test, operator_test, variable_test, constant_test\n        )\n        return cls(root)\n\n    @classmethod\n    def from_full_prior(cls, prior):\n        root = sample_tree_full(prior)\n        return cls(root)\n\n    @classmethod\n    def from_prior_fast(cls, prior: Dict, tree_depth, max_variables_unique: int):\n        \"\"\"\n        Initiate a tree from a prior with fast sampling\n        Attention: structure prior is not supported\n\n        Args:\n            prior: The priors in dictionary form (structure priors are not needed)\n            tree_depth: depth of the tree\n            max_variables_unique: The maximum number of unique variables (a tree can have less then\n                this number)\n        \"\"\"\n        root = sample_tree_full_fast(prior, tree_depth, max_variables_unique)\n        return cls(root)\n\n    @classmethod\n    def from_prior(cls, prior: Dict, max_variables_unique: int):\n        \"\"\"\n        Initiate a tree from a prior\n\n        Args:\n            prior: The priors in dictionary form\n            max_variables_unique: The maximum number of unique variables (a tree can have less then\n                this number)\n\n        Examples:\n            &gt;&gt;&gt; np.random.seed(42)\n\n            # We can set priors for features, functions, operators\n            # and also conditionals based the parent\n            &gt;&gt;&gt; p = {\n            ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n            ...     'features': {'constants': .2, 'variables': .8},\n            ...     'functions': {'sin': .5, 'cos': .5},\n            ...     'operators': {'+': 1., '-': .0},\n            ...     'function_conditionals': {\n            ...                             'sin': {\n            ...                                 'features': {'constants': 0., 'variables': 1.},\n            ...                                 'functions': {'sin': 0., 'cos': 1.},\n            ...                                 'operators': {'+': 0., '-': 1.}\n            ...                             },\n            ...                             'cos': {\n            ...                                 'features': {'constants': 0., 'variables': 1.},\n            ...                                 'functions': {'cos': 1., 'sin': 0.},\n            ...                                 'operators': {'+': 0., '-': 1.}\n            ...                             }\n            ...                         },\n            ...     'operator_conditionals': {\n            ...                             '+': {\n            ...                                 'features': {'constants': .5, 'variables': .5},\n            ...                                 'functions': {'sin': 1., 'cos': 0.},\n            ...                                 'operators': {'+': 1., '-': 0.}\n            ...                             },\n            ...                             '-': {\n            ...                                 'features': {'constants': .3, 'variables': .7},\n            ...                                 'functions': {'cos': .5, 'sin': .5},\n            ...                                 'operators': {'+': .9, '-': .1}\n            ...                             }\n            ...                         },\n            ... }\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2]\n            &gt;&gt;&gt; equation_tree.expr\n            ['cos', 'cos', 'x_1']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2]\n            &gt;&gt;&gt; equation_tree.expr\n            ['sin', 'cos', 'x_1']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 1]\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2, 3, 2, 3, 1]\n            &gt;&gt;&gt; equation_tree.expr\n            ['+', '+', 'sin', 'x_1', 'sin', 'x_2', 'x_2']\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            x_2 + sin(x_1) + sin(x_2)\n\n            # Without conditionals, the unconditioned priors are the fallback option\n            &gt;&gt;&gt; p = {\n            ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n            ...     'features': {'constants': .2, 'variables': .8},\n            ...     'functions': {'sin': .5, 'cos': .5},\n            ...     'operators': {'+': .5, '-': .5},\n            ... }\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2, 3, 2, 3, 1]\n            &gt;&gt;&gt; equation_tree.expr\n            ['+', '-', 'cos', 'c_1', 'cos', 'c_2', 'c_3']\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            c_3 + cos(c_1) - cos(c_2)\n\n            # Note: this would be discarded in a future step as unnecesarry complex\n        \"\"\"\n        root = sample_tree_full(prior, max_variables_unique)\n        return cls(root)\n\n    @classmethod\n    def from_priors(\n        cls,\n        feature_priors={},\n        function_priors={},\n        operator_priors={},\n        structure_priors={},\n    ):\n        \"\"\"\n        Instantiate a tree from priors\n\n        Attention\n            - use standard notation here:   variables should be in form x_{number}\n                                            constants should be in form c_{number}\n\n        Args:\n            max_depth: Maximum depth of the tree\n            feature_priors: The priors for the features (variables + constants)\n            function_priors: The priors for the functions\n            operator_priors: The priors for the operators\n            structure_priors: The priors for the tree structures\n\n        Example:\n            &gt;&gt;&gt; np.random.seed(42)\n            &gt;&gt;&gt; max_depth = 12\n            &gt;&gt;&gt; feature_priors = {\"x_1\": 0.5, \"c_1\": 0.5}\n            &gt;&gt;&gt; function_priors = {\"sin\": 0.5, \"cos\": 0.5}\n            &gt;&gt;&gt; operator_priors = {\"+\": 0.5, \"-\": 0.5}\n            &gt;&gt;&gt; structure_priors = {'[0, 1, 2, 3, 4, 5, 5, 2, 3, 4, 4]': 1}\n            &gt;&gt;&gt; equation_tree = EquationTree.from_priors(\n            ...     feature_priors, function_priors, operator_priors, structure_priors)\n            &gt;&gt;&gt; equation_tree.expr\n            ['cos', '-', 'cos', 'sin', '+', 'x_1', 'c_1', 'cos', '-', 'x_1', 'c_1']\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2, 3, 4, 5, 5, 2, 3, 4, 4]\n            &gt;&gt;&gt; equation_tree.variables\n            ['x_1', 'x_1']\n            &gt;&gt;&gt; equation_tree.n_variables\n            2\n            &gt;&gt;&gt; equation_tree.n_variables_unique\n            1\n            &gt;&gt;&gt; equation_tree.constants\n            ['c_1', 'c_1']\n            &gt;&gt;&gt; equation_tree.n_constants\n            2\n            &gt;&gt;&gt; equation_tree.n_constants_unique\n            1\n            &gt;&gt;&gt; equation_tree.n_leafs\n            4\n            &gt;&gt;&gt; equation_tree.operators\n            ['-', '+', '-']\n            &gt;&gt;&gt; equation_tree.functions\n            ['cos', 'cos', 'sin', 'cos']\n        \"\"\"\n        root = sample_tree(\n            feature_priors,\n            function_priors,\n            operator_priors,\n            structure_priors,\n        )\n        return cls(root)\n\n    @classmethod\n    def from_sympy(\n        cls,\n        expression,\n        function_test: Callable = lambda _: False,\n        operator_test: Callable = lambda _: False,\n        variable_test: Callable = lambda _: False,\n        constant_test: Callable = lambda _: False,\n    ):\n        \"\"\"\n        Instantiate a tree from a sympy function\n\n        Attention:\n            - constant and variable names get standardized\n            - unary minus get converted to binary minus\n\n        Examples:\n            &gt;&gt;&gt; expr = sympify('x_a + B * y')\n            &gt;&gt;&gt; expr\n            B*y + x_a\n            &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*']\n            &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n            &gt;&gt;&gt; is_constant = lambda x : x == 'B'\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant\n            ... )\n            &gt;&gt;&gt; equation_tree.expr\n            ['+', '*', 'c_1', 'x_2', 'x_1']\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            c_1*x_2 + x_1\n\n            # Numbers don't get standardized but are constants\n            &gt;&gt;&gt; expr = sympify('x_a + 2 * y')\n            &gt;&gt;&gt; expr\n            x_a + 2*y\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant\n            ... )\n            &gt;&gt;&gt; equation_tree.expr\n            ['+', 'x_1', '*', '2', 'x_2']\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            x_1 + 2*x_2\n            &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**']\n            &gt;&gt;&gt; is_variable = lambda x: '_' in x\n            &gt;&gt;&gt; is_constant = lambda x: x == 'B'\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     sympify('B*x_1**2'),\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant\n            ... )\n\n            &gt;&gt;&gt; expr = sympify('min(x_1, x_2)')\n            &gt;&gt;&gt; expr\n            Min(x_1, x_2)\n            &gt;&gt;&gt; is_operator = lambda x : x in ['min']\n            &gt;&gt;&gt; is_variable = lambda x : x in ['x_1', 'x_2']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ... )\n            &gt;&gt;&gt; equation_tree.expr\n            ['min', 'x_1', 'x_2']\n\n            &gt;&gt;&gt; expr = sympify('x_1**2')\n            &gt;&gt;&gt; expr\n            x_1**2\n            &gt;&gt;&gt; is_operator = lambda x : x in ['*', '/', '**', '+']\n            &gt;&gt;&gt; is_variable = lambda x : x in ['x_1']\n            &gt;&gt;&gt; is_function = lambda x : x in ['squared']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ...     function_test=is_function\n            ... )\n            &gt;&gt;&gt; equation_tree.expr\n            ['squared', 'x_1']\n\n        \"\"\"\n        standard = standardize_sympy(expression, variable_test, constant_test)\n        standard = unary_minus_to_binary(standard, operator_test)\n        standard = op_const_to_func(standard)\n        prefix = infix_to_prefix(str(standard), function_test, operator_test)\n        root = node_from_prefix(\n            prefix,\n            function_test,\n            operator_test,\n            lambda x: \"x_\" in x,\n            lambda x: \"c_\" in x,\n        )\n        return cls(root)\n\n    @property\n    def constants_unique(self):\n        return list(set(self.constants))\n\n    @property\n    def n_constants(self):\n        return len(self.constants)\n\n    @property\n    def n_constants_unique(self):\n        return len(set(self.constants))\n\n    @property\n    def non_numeric_constants(self):\n        return [\n            c for c in self.constants if not is_numeric(c) and not is_known_constant(c)\n        ]\n\n    @property\n    def non_numeric_constants_unique(self):\n        return list(set(self.non_numeric_constants))\n\n    @property\n    def n_non_numeric_constants_unique(self):\n        return len(self.non_numeric_constants_unique)\n\n    @property\n    def n_non_numeric_constants(self):\n        return len(self.non_numeric_constants)\n\n    @property\n    def variables_unique(self):\n        return list(set(self.variables))\n\n    @property\n    def n_variables(self):\n        return len(self.variables)\n\n    @property\n    def n_variables_unique(self):\n        return len(set(self.variables))\n\n    @property\n    def functions_unique(self):\n        return list(set(self.functions))\n\n    @property\n    def operators_unique(self):\n        return list(set(self.operators))\n\n    @property\n    def n_leafs(self):\n        return self.n_constants + self.n_variables\n\n    # TODO: implement this\n    @property\n    def standard_structure(self):\n        return self.structure\n\n    @property\n    def prefix(self):\n        return self.expr\n\n    @property\n    def infix(self):\n        return prefix_to_infix(\n            self.prefix, lambda x: x in self.functions, lambda x: x in self.operators\n        )\n\n    @property\n    def sympy_expr(self):\n        _infix = func_to_op_const(self.infix)\n        sympy_expr = sympify(_infix)\n        if sympy_expr.free_symbols:\n            symbol_names = [str(symbol) for symbol in sympy_expr.free_symbols]\n            real_symbols = symbols(\" \".join(symbol_names), real=True)\n            if not isinstance(real_symbols, list) and not isinstance(\n                real_symbols, tuple\n            ):\n                real_symbols = [real_symbols]\n            subs_dict = {old: new for old, new in zip(symbol_names, real_symbols)}\n            sympy_expr = sympy_expr.subs(subs_dict)\n        return sympy_expr\n\n    @property\n    def is_nan(self):\n        return self.root is None\n\n    @property\n    def value_samples_as_df(self):\n        if self.evaluation is None:\n            warnings.warn(\n                \"Tree not yet evaluated. Use method get_evaluation to evaluate the tree\"\n            )\n            return None\n        data = {\"observation\": self.evaluation[:, 0]}\n        for idx, key in enumerate(self.expr):\n            if key in self.variables:\n                data[key] = self.evaluation[:, idx]\n            if key in self.non_numeric_constants:\n                data[key] = self.evaluation[:, idx]\n        return pd.DataFrame(data)\n\n    @property\n    def has_valid_value(self):\n        if self.evaluation is None:\n            warnings.warn(\n                \"Tree not yet evaluated. Use method get_evaluation to evaluate the tree\"\n            )\n            return False\n        ev = self.evaluation[0, :]\n        return np.any(np.isfinite(ev) &amp; ~np.isnan(ev))\n\n    @property\n    def info(self):\n        \"\"\"\n        Get al information as dictionary\n        \"\"\"\n        info = {}\n        info[\"max_depth\"] = len(self.structure)\n        info[\"depth\"] = max(self.structure)\n        info[\"structures\"] = self.structure\n        info[\"features\"] = {\n            \"constants\": self.n_constants,\n            \"variables\": self.n_variables,\n        }\n        functions = {}\n        function_conditionals = {key: {} for key in self.functions_unique}\n        for f in self.functions_unique:\n            functions[f] = len([_f for _f in self.functions if _f == f])\n            p_functions, p_operators, p_features = self._get_conditionals(f)\n            function_conditionals[f][\"functions\"] = p_functions\n            function_conditionals[f][\"operators\"] = p_operators\n            function_conditionals[f][\"features\"] = p_features\n        operators = {}\n        operator_conditionals = {key: {} for key in self.operators_unique}\n        for o in self.operators_unique:\n            operators[o] = len([_o for _o in self.operators if _o == o])\n            p_functions, p_operators, p_features = self._get_conditionals(o)\n            operator_conditionals[o][\"functions\"] = p_functions\n            operator_conditionals[o][\"operators\"] = p_operators\n            operator_conditionals[o][\"features\"] = p_features\n        info[\"functions\"] = functions\n        info[\"function_conditionals\"] = function_conditionals\n        info[\"operators\"] = operators\n        info[\"operator_conditionals\"] = operator_conditionals\n        return info\n\n    def evaluate(self, variables: Union[dict, pd.DataFrame]):\n        \"\"\"\n        Examples:\n            &gt;&gt;&gt; expr = sympify('x_a + 3 * y')\n            &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*']\n            &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ... )\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            x_1 + 3*x_2\n\n            # We can use dicts:\n            &gt;&gt;&gt; equation_tree.evaluate({'x_1': np.array([2, 3]), 'x_2': np.array([1, 1])})\n            array([5, 6])\n\n            # Or pandas dataframe:\n            &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': np.array([2, 3]), 'x_2': np.array([1, 1])})\n            &gt;&gt;&gt; dataFrame\n               x_1  x_2\n            0    2    1\n            1    3    1\n            &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n            array([5, 6])\n\n            # Or pandas dataframe:\n            &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [2, 3], 'x_2': [1, 1]})\n            &gt;&gt;&gt; dataFrame\n               x_1  x_2\n            0    2    1\n            1    3    1\n            &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n            array([5, 6])\n\n            &gt;&gt;&gt; expr = sympify('min(x_1,x_2)')\n            &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', 'min']\n            &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1', 'x_2']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ... )\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            Min(x_1, x_2)\n\n            &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [1, 2, 3, 4], 'x_2': [2, 1, 4, 3]})\n            &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n            array([1, 1, 3, 3])\n\n            &gt;&gt;&gt; expr = sympify('max(3, x_1)')\n            &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', 'min', 'max']\n            &gt;&gt;&gt; is_function = lambda x : x in ['sqrt', 'log', 'abs']\n            &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1', 'x_2']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     function_test=is_function,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable)\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            Max(3, x_1)\n            &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [1, 2, 3, 4]})\n            &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n            array([3, 3, 3, 4])\n\n            &gt;&gt;&gt; expr = sympify('x_1 + sqrt(x_1)')\n            &gt;&gt;&gt; is_operator = lambda x : x in ['+']\n            &gt;&gt;&gt; is_function = lambda x: x in ['sqrt']\n            &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     function_test=is_function,\n            ...     variable_test=is_variable,\n            ... )\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            sqrt(x_1) + x_1\n\n            &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [4, 9, 16]})\n            &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n            array([ 6., 12., 20.])\n        \"\"\"\n\n        df = pd.DataFrame(variables)\n        symbol_list = list(self.sympy_expr.free_symbols)\n\n        if set(list(df.columns)).issubset(set(symbol_list)):\n            raise Exception(\n                f\"Variables in expression {self.sympy_expr} \"\n                f\"do not match the given ones: {df.columns}\"\n            )\n\n        symbol_names = [str(s) for s in symbol_list]\n\n        f = sympy.lambdify(symbol_list, self.sympy_expr, \"numpy\")\n        try:\n            res = np.array(f(*[df[name] for name in symbol_names]))\n        except ValueError:  # Workaround till sympy gets updated\n            lst = [df[name] for name in symbol_names]\n            res = []\n            for i in range(len(lst[0])):\n                args = []\n                for j in range(len(lst)):\n                    args.append(lst[j].iloc[i])\n                res.append(f(*args))\n        return np.array(res)\n\n    def save_samples(\n        self,\n        path,\n        num_samples,\n        ranges: Optional[Dict] = None,\n        default_range: float = 10,\n        dv_name: str = \"y\",\n        random_state: Optional[int] = None,\n        compression: str = \"gzip\",\n    ):\n        \"\"\"\n        Creates a file with samples of ivs and dvs\n        Args:\n            path: The path were to store the file\n            num_samples: The number of samples\n            ranges: A dictionary with the ranges for the variables in form of a dict\n            default_range: Default range to fall back to if no range for a\n                specific variable is given\n            dv_name: The name to give to the observation\n            random_state: The random seed to be used\n            compression: Compression method\n        \"\"\"\n        if not path.endswith(\"gz\") and compression == \"gzip\":\n            warnings.warn(\n                f\"Compression is gzip but file {path} does not have the ending .gz\"\n            )\n        _ranges = {\n            key: (-default_range, default_range) for key in self.variables_unique\n        }\n        if ranges is not None:\n            for key in ranges.keys():\n                if key in _ranges.keys():\n                    _ranges[key] = ranges[key]\n\n        rng = np.random.default_rng(random_state)\n\n        def _get_conditions_once():\n            raw_conditions = {}\n            for key in _ranges.keys():\n                raw_conditions[key] = rng.uniform(*_ranges[key], size=num_samples)\n            return pd.DataFrame(raw_conditions)\n\n        conditions_ = pd.DataFrame(columns=self.variables_unique + [dv_name])\n        i = 0\n        while i &lt; 1_000_000 and len(conditions_.index) &lt; num_samples:\n            _sample = _get_conditions_once()\n            evaluation = self.evaluate(_sample)\n            _sample[dv_name] = evaluation\n            bad_indices = np.where(np.isnan(evaluation) | np.isinf(evaluation))[0]\n            _sample = _sample.drop(bad_indices)\n            conditions_ = pd.concat([conditions_, _sample], ignore_index=True)\n            i += 1\n            if i &gt;= 1_000_000:\n                break\n        conditions_ = conditions_.head(num_samples)\n        conditions_.to_csv(path, compression=compression, index=False, sep=\"\\t\")\n\n    def save_samples_srbench(\n        self,\n        path,\n        num_samples,\n        ranges: Optional[Dict] = None,\n        default_range: float = 10,\n        random_state: Optional[int] = None,\n    ):\n        self.save_samples(\n            path, num_samples, ranges, default_range, \"target\", random_state\n        )\n\n    def save_meta_srbench(self, path, name_dataset, name_target=\"y\"):\n        info = {}\n        info[\"dataset\"] = name_dataset\n        info[\"description\"] = name_target + \" = \" + str(self.sympy_expr)\n        info[\"source\"] = \"https://github.com/AutoResearch/equation-tree\"\n        info[\"publication\"] = \"Not yet implemented\"\n        info[\"task\"] = \"regression\"\n        info[\"keywords\"] = [\"abstract\", \"math\", \"symbolic regression\"]\n        info[\"target\"] = {\n            \"type\": \"continuous\",\n            \"description\": \"abstract dependent variable\",\n        }\n        info[\"features\"] = [\n            {\n                \"name\": v,\n                \"type\": \"continuous\",\n                \"description\": \"abstract independent variable\",\n            }\n            for v in self.variables_unique\n        ]\n\n        with open(path, \"w\") as f:\n            yaml.dump(info, f, sort_keys=False)\n\n    def export_to_srbench(\n        self,\n        folder: str,\n        data_file_name: Optional[str] = None,\n        num_samples: int = 1000,\n        name_target: str = \"y\",\n        ranges: Optional[Dict] = None,\n        default_range: float = 10,\n        random_state: Optional[int] = None,\n    ):\n        \"\"\"\n        Creates a folder and adds data and metadata to the folder that can be used with sr bench:\n        https://cavalab.org/srbench/\n        Args:\n            folder: Name of the folder\n            data_file_name: Name of the datafile (if none same as folder name)\n            num_samples: Number of samples\n            name_target: Name of the tartget\n            ranges: A dictionary with the ranges for the variables in form of a dict\n            default_range: Default range to fall back to if no range for a\n                specific variable is given\n            random_state: The random seed to be used\n        \"\"\"\n        if data_file_name is None:\n            data_file_name = folder\n        os.mkdir(folder)\n        path_data = f\"{folder}/{data_file_name}.tsv.gz\"\n        path_meta = f\"{folder}/metadata.yaml\"\n        self.save_samples_srbench(\n            path_data, num_samples, ranges, default_range, random_state\n        )\n        self.save_meta_srbench(path_meta, \"data\", name_target)\n\n    def check_validity(\n        self,\n        zero_representations=[\"0\"],\n        log_representations=[\"log\", \"Log\"],\n        division_representations=[\"/\", \":\"],\n        verbose=False,\n    ):\n        \"\"\"\n        Check if the tree is valid:\n            - Check if log(0) or x / 0 exists\n            - Check if function(constant) or operator(constant_1, constant_2) exists\n                    -&gt; unnecessary complexity\n            - Check if each function has exactly one child\n            - Check if each operator has exactly two children\n\n        Args:\n            zero_representations: A list of attributes that represent zero\n            log_representations: A list of attributes that represent log\n            division_representations: A list of attributes that represent division\n            verbose: If set true, print out the reason for the invalid tree\n\n        Example:\n            &gt;&gt;&gt; is_variable = lambda x : x == 'x'\n            &gt;&gt;&gt; is_constant = lambda x : x == 'c' or x == '0'\n            &gt;&gt;&gt; is_operator = lambda x : x == '/'\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     ['/', 'x', '0'],\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     operator_test=is_operator,\n            ... )\n            &gt;&gt;&gt; equation_tree.check_validity()\n            False\n            &gt;&gt;&gt; equation_tree.check_validity(verbose=True)\n            division by 0 is not allowed.\n            False\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     ['/', 'x', 'c'],\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     operator_test=is_operator,\n            ... )\n            &gt;&gt;&gt; equation_tree.check_validity()\n            True\n\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     ['/', '0', 'c'],\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     operator_test=is_operator,\n            ... )\n            &gt;&gt;&gt; equation_tree.check_validity(verbose=True)\n            0 and c are constants applied to the operator /\n            False\n        \"\"\"\n        return self.root.check_validity(\n            zero_representations, log_representations, division_representations, verbose\n        )\n\n    def draw_tree(self, out):\n        try:\n            from graphviz import Source\n        except ImportError:\n            print(\n                \"drawing uses requires `graphviz` to be installed: `pip install graphviz`\"\n            )\n        src = Source(dotprint(self.sympy_expr))\n        src.render(out, view=False)\n\n    def check_possible(\n        self,\n        feature_priors: Dict,\n        function_priors: Dict,\n        operator_priors: Dict,\n        structure_priors: Dict,\n    ):\n        \"\"\"\n        Check weather a tree is a possible tree given the priors\n        Attention:\n            If no prior is given, interpreted as all possibilities are allowed\n        \"\"\"\n        if feature_priors != {}:\n            for c in self.constants:\n                if c not in feature_priors.keys() or feature_priors[c] &lt;= 0:\n                    return False\n            for v in self.variables:\n                if v not in feature_priors.keys() or feature_priors[v] &lt;= 0:\n                    return False\n        if function_priors != {}:\n            for fun in self.functions:\n                if fun not in function_priors.keys() or function_priors[fun] &lt;= 0:\n                    return False\n        if operator_priors != {}:\n            for op in self.operators:\n                if op not in operator_priors.keys() or operator_priors[op] &lt;= 0:\n                    return False\n        if structure_priors != {}:\n            if (\n                str(self.structure) not in structure_priors.keys()\n                or structure_priors[str(self.structure)] &lt;= 0\n            ):\n                return False\n        return True\n\n    def check_possible_from_prior(self, prior: Dict):\n        structure_priors = prior[\"structures\"] if \"structures\" in prior.keys() else {}\n        feature_priors = prior[\"features\"] if \"features\" in prior.keys() else {}\n        function_priors = prior[\"functions\"] if \"functions\" in prior.keys() else {}\n        operator_priors = prior[\"operators\"] if \"operators\" in prior.keys() else {}\n        function_conditionals = (\n            prior[\"function_conditionals\"]\n            if \"function_conditionals\" in prior.keys()\n            else {}\n        )\n        operator_conditionals = (\n            prior[\"operator_conditionals\"]\n            if \"operator_conditionals\" in prior.keys()\n            else {}\n        )\n        if structure_priors:\n            if (\n                str(self.structure) not in structure_priors.keys()\n                or structure_priors[str(self.structure)] &lt;= 0\n            ):\n                return False\n        if feature_priors:\n            if (\n                self.n_variables &gt; 0\n                and (\n                    \"variables\" not in feature_priors.keys()\n                    or feature_priors[\"variables\"] &lt;= 0\n                )\n            ) or (\n                self.n_constants &gt; 0\n                and (\n                    \"constants\" not in feature_priors.keys()\n                    or feature_priors[\"constants\"] &lt;= 0\n                )\n            ):\n                return False\n        if function_priors:\n            for fun in self.functions_unique:\n                if fun not in function_priors.keys() or function_priors[fun] &lt;= 0:\n                    return False\n\n        if operator_priors:\n            for op in self.operators_unique:\n                if op not in operator_priors.keys() or operator_priors[op] &lt;= 0:\n                    return False\n\n        test_lst = []\n\n        def test_node(child):\n            nonlocal test_lst\n            if child is None or child.parent is None:\n                test_lst.append(True)\n                return\n            node = child.parent\n            _prior = {}\n            if (\n                node.kind == NodeKind.FUNCTION\n                and node.attribute in function_conditionals.keys()\n            ):\n                _prior = function_conditionals[node.attribute]\n            elif (\n                node.kind == NodeKind.OPERATOR\n                and node.attribute in operator_conditionals.keys()\n            ):\n                _prior = operator_conditionals[node.attribute]\n            if child.kind == NodeKind.FUNCTION:\n                _p = _prior[node.attribute][\"functions\"]\n                if (\n                    _p != {}\n                    and node.attribute not in _p.keys()\n                    or _p[node.attribute] &lt;= 0\n                ):\n                    test_lst.append(False)\n            elif child.kind == NodeKind.OPERATOR:\n                _p = _prior[node.attribute][\"operators\"]\n                if (\n                    _p != {}\n                    and node.attribute not in _p.keys()\n                    or _p[node.attribute] &lt;= 0\n                ):\n                    test_lst.append(False)\n            else:\n                _p = _prior[\"features\"] if \"features\" in _prior else {}\n                if child.kind == NodeKind.VARIABLE:\n                    if (\n                        _p != {}\n                        and \"variables\" not in _p.keys()\n                        or _p[\"variables\"] &lt;= 0\n                    ):\n                        test_lst.append(False)\n                if child.kind == NodeKind.CONSTANT:\n                    if (\n                        _p != {}\n                        and \"constants\" not in _p.keys()\n                        or _p[\"constants\"] &lt;= 0\n                    ):\n                        test_lst.append(False)\n            for c in child.children:\n                test_node(c)\n\n        conditionals = not any(item is False for item in test_lst)\n        if not conditionals:\n            return False\n        return True\n\n    def standardize(self):\n        \"\"\"\n        Standardize variable and constant names\n\n        Example:\n            &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n            &gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n            &gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n            &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n            &gt;&gt;&gt; prefix = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n\n            # then we create the node root\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     prefix_notation=prefix,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     function_test=is_function,\n            ...     operator_test=is_operator\n            ...     )\n\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            x + sin(y)*cos(z) - 1\n\n            &gt;&gt;&gt; equation_tree.standardize()\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            x_1 + sin(x_2)*cos(x_3) - 1\n\n        \"\"\"\n        variable_count = 0\n        constant_count = 0\n        variables = {}\n        constants = {}\n\n        def rec_stand(node):\n            if node is None:\n                return\n            nonlocal variable_count, constant_count\n            nonlocal variables, constants\n            if node.kind == NodeKind.VARIABLE:\n                if node.attribute not in variables.keys():\n                    variable_count += 1\n                    variables[node.attribute] = f\"x_{variable_count}\"\n                node.attribute = variables[node.attribute]\n            if node.kind == NodeKind.CONSTANT and not is_numeric(node.attribute):\n                if node.attribute not in constants.keys():\n                    constant_count += 1\n                    constants[node.attribute] = f\"c_{constant_count}\"\n                node.attribute = constants[node.attribute]\n            else:\n                rec_stand(node.left)\n                rec_stand(node.right)\n            return node\n\n        self.root = rec_stand(self.root)\n        self._build()\n\n    def simplify(\n        self,\n        function_test: Union[Callable, None] = None,\n        operator_test: Union[Callable, None] = None,\n        is_binary_minus_only: bool = True,\n        is_power_caret: bool = True,\n        verbose: bool = False,\n    ):\n        \"\"\"\n        Simplify equation if the simplified equation has a shorter prefix\n        Args:\n            function_test: A function that tests weather an attribute is a function\n                Attention: simplifying may lead to new functions that were not in the equation\n                    before. If so, add this to the test here.\n            operator_test: A function that tests weather an attribute is an operator\n                Attention: simplifying may lead to new operators that were not in the equation\n                    before. If so, add this to the test here.\n            is_binary_minus_only: Convert all unary minus to binary after simplification\n            is_power_caret: Represent power as a caret after simplification\n            verbose: Show messages if simplification results in errors\n\n        Examples:\n            &gt;&gt;&gt; is_variable = lambda x: 'x_' in x\n            &gt;&gt;&gt; is_constant = lambda x: 'c_' in x or is_numeric(x) or is_known_constant(x)\n            &gt;&gt;&gt; is_operator = lambda x: x in ['+', '*', '/', '^', '-']\n            &gt;&gt;&gt; is_function = lambda x: x.lower() in ['sqrt', 'abs']\n            &gt;&gt;&gt; prefix_notation = ['+', 'x_1', 'x_1' ]\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     prefix_notation=prefix_notation,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     operator_test=is_operator,\n            ...     function_test=is_function)\n            &gt;&gt;&gt; equation_tree.expr\n            ['+', 'x_1', 'x_1']\n\n            # it takes care of multiplication:\n            &gt;&gt;&gt; equation_tree.simplify(function_test=is_function,operator_test=is_operator)\n            &gt;&gt;&gt; equation_tree.expr\n            ['*', '2', 'x_1']\n\n            &gt;&gt;&gt; prefix_notation = ['sqrt', '*', 'x_1', 'x_1']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     prefix_notation=prefix_notation,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     operator_test=is_operator,\n            ...     function_test=is_function)\n            &gt;&gt;&gt; equation_tree.expr\n            ['sqrt', '*', 'x_1', 'x_1']\n\n            # it is good practice to define tests at the begining of a script and use them\n            # throughout the project\n            &gt;&gt;&gt; equation_tree.simplify(\n            ...     operator_test=is_operator,\n            ...     function_test=is_function\n            ... )\n            &gt;&gt;&gt; equation_tree.expr\n            ['abs', 'x_1']\n\n            &gt;&gt;&gt; prefix_notation = ['*', '-', 'c_1', 'x_1', '-', 'x_1', 'c_1']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     prefix_notation=prefix_notation,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     operator_test=is_operator,\n            ...     function_test=is_function)\n            &gt;&gt;&gt; equation_tree.expr\n            ['*', '-', 'c_1', 'x_1', '-', 'x_1', 'c_1']\n\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            (-c_1 + x_1)*(c_1 - x_1)\n\n            # it is good practice to define tests at the begining of a script and use them\n            # throughout the project\n            &gt;&gt;&gt; equation_tree.simplify(\n            ...     operator_test=is_operator,\n            ...     function_test=is_function\n            ... )\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            (-c_1 + x_1)**2\n\n            # &gt;&gt;&gt; equation_tree.expr\n            # ['^', '-', 'x_1', 'c_1', '2']\n        \"\"\"\n\n        if function_test is None:\n\n            def function_test(x):\n                return x in self.functions\n\n        else:\n            tmp_f = function_test\n\n            def function_test(x):\n                return tmp_f(x) or x in self.functions\n\n        if operator_test is None:\n\n            def operator_test(x):\n                return x in self.operators\n\n        else:\n            tmp_o = operator_test\n\n            def operator_test(x):\n                return tmp_o(x) or x in self.operators\n\n        class TimeoutError(Exception):\n            pass\n\n        def timeout_handler(signum, frame):\n            raise TimeoutError(\"Function call timed out\")\n\n        signal.signal(signal.SIGALRM, timeout_handler)\n        signal.alarm(SIMPLIFY_TIMEOUT)\n        try:\n            simplified_equation = simplify(self.sympy_expr)\n            signal.alarm(0)\n        except TimeoutError:\n            simplified_equation = self.sympy_expr\n        if not check_functions(simplified_equation, function_test):\n            warnings.warn(\n                f\"{simplified_equation} has functions that are not in function_test type\"\n            )\n            self.root = None\n            self._build()\n            return\n        if (\n            \"I\" in str(simplified_equation)\n            or \"accumbounds\" in str(simplified_equation).lower()\n        ):\n            if verbose:\n                print(f\"Simplify {str(self.sympy_expr)} results in complex values\")\n            self.root = None\n            self._build()\n            return\n        if is_power_caret:\n            simplified_equation = str(simplified_equation).replace(\"**\", \"^\")\n        simplified_equation = simplified_equation.replace(\"re\", \"\")\n        if is_binary_minus_only:\n            simplified_equation = unary_minus_to_binary(\n                simplified_equation, operator_test\n            )\n        simplified_equation = simplified_equation.replace(\" \", \"\")\n\n        prefix = infix_to_prefix(simplified_equation, function_test, operator_test)\n        if verbose:\n            print(\"prefix\", simplified_equation)\n            print(\"prefix tree\", prefix)\n        if \"re\" in prefix:\n            prefix.remove(\"re\")\n        if len(prefix) &gt; len(self.expr):\n            prefix = self.expr\n        if \"zoo\" in prefix or \"oo\" in prefix:\n            if verbose:\n                print(f\"Simplify {str(self.sympy_expr)} results in None\")\n            self.root = None\n            self._build()\n            return\n        self.root = node_from_prefix(\n            prefix,\n            function_test,\n            operator_test,\n            lambda x: x in self.variables,\n            lambda x: x in self.constants or is_numeric(x) or is_known_constant(x),\n        )\n        self._build()\n\n    def get_evaluation(\n        self, min_val: int = -1, max_val: int = 1, num_samples: int = 100\n    ):\n        \"\"\"\n        Evaluate the nodes with random samples for variables and constants.\n        \"\"\"\n\n        crossings = self._create_crossing(min_val, max_val, num_samples)\n        evaluation = np.zeros((len(crossings), len(self.expr)))\n\n        for i, crossing in enumerate(crossings):\n            eqn_input = dict()\n            k = 0\n            for c in self.constants_unique:\n                if is_numeric(c):\n                    eqn_input[c] = float(c)\n                elif c == \"e\":\n                    eqn_input[c] = 2.71828182846\n                elif c == \"pi\":\n                    eqn_input[c] = 3.14159265359\n                else:\n                    eqn_input[c] = crossing[self.n_variables_unique + k]\n                    k += 1\n            for idx, x in enumerate(self.variables_unique):\n                eqn_input[x] = crossing[idx]\n            evaluation[i, :] = self._evaluate(eqn_input)\n\n        self.evaluation = evaluation\n        return evaluation\n\n    def _evaluate(self, features: Dict):\n        values: List[float] = list()\n\n        if self.root is not None:\n            self._evaluate_node(features, self.root)\n            values = self._get_full_evaluation(self.root)\n\n        return values\n\n    def _evaluate_node(self, features: Dict, node: TreeNode):\n        if node.kind == NodeKind.FUNCTION:\n            if node.left is None:\n                raise Exception(\"Invalid tree: %s\" % self.expr)\n            value = FUNCTIONS[node.attribute](self._evaluate_node(features, node.left))\n\n        elif node.kind == NodeKind.OPERATOR:\n            if node.left is None or node.right is None:\n                raise Exception(\"Invalid tree: %s\" % self.expr)\n            value = OPERATORS[node.attribute](\n                self._evaluate_node(features, node.left),\n                self._evaluate_node(features, node.right),\n            )\n\n        elif node.kind == NodeKind.CONSTANT or node.kind == NodeKind.VARIABLE:\n            value = features[node.attribute]\n        else:\n            raise Exception(\"Invalid attribute %s\" % node.attribute)\n        node.evaluation = value\n        return value\n\n    def _get_full_evaluation(self, node: TreeNode):\n        values = list()\n        values.append(node.evaluation)\n\n        if node.kind == NodeKind.FUNCTION:\n            if node.left is None:\n                raise Exception(\"Invalid tree: %s\" % self.expr)\n            eval_add = self._get_full_evaluation(node.left)\n            for eval_element in eval_add:\n                values.append(eval_element)\n\n        if node.kind == NodeKind.OPERATOR:\n            if node.left is None or node.right is None:\n                raise Exception(\"Invalid tree: %s\" % self.expr)\n            eval_add = self._get_full_evaluation(node.left)\n            for eval_element in eval_add:\n                values.append(eval_element)\n            eval_add = self._get_full_evaluation(node.right)\n            for eval_element in eval_add:\n                values.append(eval_element)\n\n        return values\n\n    def _create_crossing(\n        self, min_val: float = -1, max_val: float = 1, num_samples: int = 100\n    ):\n        crossings = []\n\n        total_unique = self.n_variables_unique + self.n_non_numeric_constants_unique\n\n        for _ in range(num_samples):\n            sample = []\n            for _ in range(total_unique):\n                value = np.random.uniform(min_val, max_val)\n                sample.append(value)\n            crossings.append(sample)\n\n        return np.array(crossings)\n\n    def _build(self):\n        self.structure: List[int] = []\n\n        # make function to get this here\n        self.expr: List[str] = list()\n\n        self.variables: List[str] = list()\n        self.functions: List[str] = list()\n        self.operators: List[str] = list()\n        self.constants: List[str] = list()\n\n        self.evaluation = None\n\n        self._collect_structure(self.structure, 0, self.root)\n\n        self._collect_attributes(\n            lambda node: node.kind == NodeKind.VARIABLE, self.variables, self.root\n        )\n        self._collect_attributes(\n            lambda node: node.kind == NodeKind.FUNCTION, self.functions, self.root\n        )\n        self._collect_attributes(\n            lambda node: node.kind == NodeKind.CONSTANT, self.constants, self.root\n        )\n        self._collect_attributes(\n            lambda node: node.kind == NodeKind.OPERATOR, self.operators, self.root\n        )\n        self._collect_expr(self.expr, self.root)\n\n    def _collect_structure(self, structure=[], level=0, node=None):\n        if node is None:\n            return\n        structure.append(level)\n        self._collect_structure(structure, level + 1, node.left)\n        self._collect_structure(structure, level + 1, node.right)\n        return\n\n    def _collect_expr(self, expression=[], node=None):\n        if node is None:\n            return\n        expression.append(node.attribute)\n        self._collect_expr(expression, node.left)\n        self._collect_expr(expression, node.right)\n\n    def _collect_attributes(\n        self, attribute_identifier: Callable = lambda _: True, attributes=[], node=None\n    ):\n        if node is None:\n            return list()\n        if attribute_identifier(node):\n            attributes.append(node.attribute)\n        if node.left is not None:\n            self._collect_attributes(attribute_identifier, attributes, node.left)\n        if node.right is not None:\n            self._collect_attributes(attribute_identifier, attributes, node.right)\n        return attributes\n\n    def _get_conditionals(self, attribute):\n        functions = {}\n        operators = {}\n        features = {\"constants\": 0, \"variables\": 0}\n\n        def get_child(node):\n            nonlocal functions, operators, features\n            if node is None:\n                return\n            if node.attribute == attribute:\n                if node.kind == NodeKind.FUNCTION or NodeKind.OPERATOR:\n                    if node.left.kind == NodeKind.FUNCTION:\n                        if node.left.attribute in functions.keys():\n                            functions[node.left.attribute] += 1\n                        else:\n                            functions[node.left.attribute] = 1\n                    if node.left.kind == NodeKind.OPERATOR:\n                        if node.left.attribute in operators.keys():\n                            operators[node.left.attribute] += 1\n                        else:\n                            operators[node.left.attribute] = 1\n                    if node.left.kind == NodeKind.CONSTANT:\n                        features[\"constants\"] += 1\n                    if node.left.kind == NodeKind.VARIABLE:\n                        features[\"variables\"] += 1\n                if node.kind == NodeKind.OPERATOR:\n                    if node.right.kind == NodeKind.FUNCTION:\n                        if node.right.attribute in functions.keys():\n                            functions[node.right.attribute] += 1\n                        else:\n                            functions[node.right.attribute] = 1\n                    if node.right.kind == NodeKind.OPERATOR:\n                        if node.right.attribute in operators.keys():\n                            operators[node.right.attribute] += 1\n                        else:\n                            operators[node.right.attribute] = 1\n                    if node.right.kind == NodeKind.CONSTANT:\n                        features[\"constants\"] += 1\n                    if node.right.kind == NodeKind.VARIABLE:\n                        features[\"variables\"] += 1\n            get_child(node.left)\n            get_child(node.right)\n\n        get_child(self.root)\n\n        return functions, operators, features\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.info","title":"<code>info</code>  <code>property</code>","text":"<p>Get al information as dictionary</p>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__","title":"<code>__init__(node)</code>","text":"<p>Initializes a tree from a TreeNode</p> <p>Examples:</p>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--we-can-inititlize-from-a-single-node","title":"We can inititlize from a single node","text":"<pre><code>&gt;&gt;&gt; node_root = TreeNode(kind=NodeKind.VARIABLE, attribute=\"x\")\n&gt;&gt;&gt; equation_tree = EquationTree(node_root)\n&gt;&gt;&gt; equation_tree.expr\n['x']\n&gt;&gt;&gt; equation_tree.structure\n[0]\n&gt;&gt;&gt; equation_tree.variables\n['x']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--or-from-a-node-with-children","title":"Or from a node with children","text":"<pre><code>&gt;&gt;&gt; node_left = TreeNode(kind=NodeKind.VARIABLE, attribute=\"x\")\n&gt;&gt;&gt; node_right = TreeNode(kind=NodeKind.CONSTANT, attribute=\"c\")\n&gt;&gt;&gt; node_root = TreeNode(kind=NodeKind.OPERATOR, attribute=\"+\",                             left=node_left, right=node_right)\n&gt;&gt;&gt; equation_tree = EquationTree(node_root)\n&gt;&gt;&gt; equation_tree.expr\n['+', 'x', 'c']\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 1]\n&gt;&gt;&gt; equation_tree.variables\n['x']\n&gt;&gt;&gt; equation_tree.constants\n['c']\n&gt;&gt;&gt; equation_tree.operators\n['+']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--we-can-first-sample-a-node-and-children-and-initialize-from-that","title":"We can first sample a node and children and initialize from that","text":"<pre><code>&gt;&gt;&gt; np.random.seed(42)\n&gt;&gt;&gt; max_depth = 12\n&gt;&gt;&gt; structure_priors = {'[0, 1, 2, 1, 2, 3]': .5, '[0, 1, 2, 2, 1, 2, 3]': .5}\n&gt;&gt;&gt; feature_priors = {\"x_1\": 0.5, \"c_1\": 0.5}\n&gt;&gt;&gt; function_priors = {\"sin\": 0.5, \"cos\": 0.5}\n&gt;&gt;&gt; operator_priors = {\"+\": 0.5, \"-\": 0.5}\n&gt;&gt;&gt; node_root = sample_tree(feature_priors, function_priors,\n...     operator_priors, structure_priors)\n&gt;&gt;&gt; equation_tree = EquationTree(node_root)\n&gt;&gt;&gt; equation_tree.expr\n['-', 'cos', 'c_1', 'sin', 'sin', 'x_1']\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 2, 1, 2, 3]\n&gt;&gt;&gt; equation_tree.variables\n['x_1']\n&gt;&gt;&gt; equation_tree.n_variables\n1\n&gt;&gt;&gt; equation_tree.n_variables_unique\n1\n&gt;&gt;&gt; equation_tree.constants\n['c_1']\n&gt;&gt;&gt; equation_tree.n_constants\n1\n&gt;&gt;&gt; equation_tree.n_constants_unique\n1\n&gt;&gt;&gt; equation_tree.n_leafs\n2\n&gt;&gt;&gt; equation_tree.operators\n['-']\n&gt;&gt;&gt; equation_tree.functions\n['cos', 'sin', 'sin']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--first-we-create-test-functions-that-test-weather-an-attribute-is-a-variable","title":"First we create test functions that test weather an attribute is a variable,","text":""},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--a-constant-a-function-or-an-operater","title":"a constant, a function, or an operater","text":"<pre><code>&gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n&gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n&gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n&gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--here-we-use-the-prefix-notation","title":"here we use the prefix notation","text":"<pre><code>&gt;&gt;&gt; prefix_notation = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--then-we-create-the-node-root","title":"then we create the node root","text":"<pre><code>&gt;&gt;&gt; node_root = node_from_prefix(\n...     prefix_notation=prefix_notation,\n...     variable_test=is_variable,\n...     constant_test=is_constant,\n...     function_test=is_function,\n...     operator_test=is_operator\n...     )\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--and-initialize-the-tree","title":"and initialize the tree","text":"<pre><code>&gt;&gt;&gt; equation_tree = EquationTree(node_root)\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 2, 2, 1, 2, 3, 2, 3]\n&gt;&gt;&gt; equation_tree.variables\n['x', 'y', 'z']\n&gt;&gt;&gt; equation_tree.constants\n['1']\n&gt;&gt;&gt; equation_tree.operators\n['+', '-', '*']\n&gt;&gt;&gt; equation_tree.functions\n['sin', 'cos']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--the-tree-expression-is-the-same-as-the-prefix-notation","title":"The tree expression is the same as the prefix notation","text":"<pre><code>&gt;&gt;&gt; equation_tree.expr == prefix_notation\nTrue\n</code></pre> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def __init__(self, node: TreeNode):\n    \"\"\"\n    Initializes a tree from a TreeNode\n\n    Examples:\n        # We can inititlize from a single node\n        &gt;&gt;&gt; node_root = TreeNode(kind=NodeKind.VARIABLE, attribute=\"x\")\n        &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n        &gt;&gt;&gt; equation_tree.expr\n        ['x']\n        &gt;&gt;&gt; equation_tree.structure\n        [0]\n        &gt;&gt;&gt; equation_tree.variables\n        ['x']\n\n        # Or from a node with children\n        &gt;&gt;&gt; node_left = TreeNode(kind=NodeKind.VARIABLE, attribute=\"x\")\n        &gt;&gt;&gt; node_right = TreeNode(kind=NodeKind.CONSTANT, attribute=\"c\")\n        &gt;&gt;&gt; node_root = TreeNode(kind=NodeKind.OPERATOR, attribute=\"+\", \\\n                        left=node_left, right=node_right)\n        &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n        &gt;&gt;&gt; equation_tree.expr\n        ['+', 'x', 'c']\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 1]\n        &gt;&gt;&gt; equation_tree.variables\n        ['x']\n        &gt;&gt;&gt; equation_tree.constants\n        ['c']\n        &gt;&gt;&gt; equation_tree.operators\n        ['+']\n\n        # We can first sample a node and children and initialize from that\n        &gt;&gt;&gt; np.random.seed(42)\n        &gt;&gt;&gt; max_depth = 12\n        &gt;&gt;&gt; structure_priors = {'[0, 1, 2, 1, 2, 3]': .5, '[0, 1, 2, 2, 1, 2, 3]': .5}\n        &gt;&gt;&gt; feature_priors = {\"x_1\": 0.5, \"c_1\": 0.5}\n        &gt;&gt;&gt; function_priors = {\"sin\": 0.5, \"cos\": 0.5}\n        &gt;&gt;&gt; operator_priors = {\"+\": 0.5, \"-\": 0.5}\n        &gt;&gt;&gt; node_root = sample_tree(feature_priors, function_priors,\n        ...     operator_priors, structure_priors)\n        &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n        &gt;&gt;&gt; equation_tree.expr\n        ['-', 'cos', 'c_1', 'sin', 'sin', 'x_1']\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2, 1, 2, 3]\n        &gt;&gt;&gt; equation_tree.variables\n        ['x_1']\n        &gt;&gt;&gt; equation_tree.n_variables\n        1\n        &gt;&gt;&gt; equation_tree.n_variables_unique\n        1\n        &gt;&gt;&gt; equation_tree.constants\n        ['c_1']\n        &gt;&gt;&gt; equation_tree.n_constants\n        1\n        &gt;&gt;&gt; equation_tree.n_constants_unique\n        1\n        &gt;&gt;&gt; equation_tree.n_leafs\n        2\n        &gt;&gt;&gt; equation_tree.operators\n        ['-']\n        &gt;&gt;&gt; equation_tree.functions\n        ['cos', 'sin', 'sin']\n\n        # First we create test functions that test weather an attribute is a variable,\n        # a constant, a function, or an operater\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n        &gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n        &gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n        &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n\n        # here we use the prefix notation\n        &gt;&gt;&gt; prefix_notation = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n\n        # then we create the node root\n        &gt;&gt;&gt; node_root = node_from_prefix(\n        ...     prefix_notation=prefix_notation,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     function_test=is_function,\n        ...     operator_test=is_operator\n        ...     )\n\n        # and initialize the tree\n        &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2, 2, 1, 2, 3, 2, 3]\n        &gt;&gt;&gt; equation_tree.variables\n        ['x', 'y', 'z']\n        &gt;&gt;&gt; equation_tree.constants\n        ['1']\n        &gt;&gt;&gt; equation_tree.operators\n        ['+', '-', '*']\n        &gt;&gt;&gt; equation_tree.functions\n        ['sin', 'cos']\n\n        # The tree expression is the same as the prefix notation\n        &gt;&gt;&gt; equation_tree.expr == prefix_notation\n        True\n    \"\"\"\n\n    self.root: Union[TreeNode, None] = node\n\n    self.structure: List[int] = []\n\n    self.expr: List[str] = list()\n\n    self.variables: List[str] = list()\n    self.functions: List[str] = list()\n    self.operators: List[str] = list()\n    self.constants: List[str] = list()\n\n    self.evaluation = None\n\n    self._build()\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.check_possible","title":"<code>check_possible(feature_priors, function_priors, operator_priors, structure_priors)</code>","text":"<p>Check weather a tree is a possible tree given the priors Attention:     If no prior is given, interpreted as all possibilities are allowed</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def check_possible(\n    self,\n    feature_priors: Dict,\n    function_priors: Dict,\n    operator_priors: Dict,\n    structure_priors: Dict,\n):\n    \"\"\"\n    Check weather a tree is a possible tree given the priors\n    Attention:\n        If no prior is given, interpreted as all possibilities are allowed\n    \"\"\"\n    if feature_priors != {}:\n        for c in self.constants:\n            if c not in feature_priors.keys() or feature_priors[c] &lt;= 0:\n                return False\n        for v in self.variables:\n            if v not in feature_priors.keys() or feature_priors[v] &lt;= 0:\n                return False\n    if function_priors != {}:\n        for fun in self.functions:\n            if fun not in function_priors.keys() or function_priors[fun] &lt;= 0:\n                return False\n    if operator_priors != {}:\n        for op in self.operators:\n            if op not in operator_priors.keys() or operator_priors[op] &lt;= 0:\n                return False\n    if structure_priors != {}:\n        if (\n            str(self.structure) not in structure_priors.keys()\n            or structure_priors[str(self.structure)] &lt;= 0\n        ):\n            return False\n    return True\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.check_validity","title":"<code>check_validity(zero_representations=['0'], log_representations=['log', 'Log'], division_representations=['/', ':'], verbose=False)</code>","text":"Check if the tree is valid <ul> <li>Check if log(0) or x / 0 exists</li> <li>Check if function(constant) or operator(constant_1, constant_2) exists         -&gt; unnecessary complexity</li> <li>Check if each function has exactly one child</li> <li>Check if each operator has exactly two children</li> </ul> <p>Parameters:</p> Name Type Description Default <code>zero_representations</code> <p>A list of attributes that represent zero</p> <code>['0']</code> <code>log_representations</code> <p>A list of attributes that represent log</p> <code>['log', 'Log']</code> <code>division_representations</code> <p>A list of attributes that represent division</p> <code>['/', ':']</code> <code>verbose</code> <p>If set true, print out the reason for the invalid tree</p> <code>False</code> Example <p>is_variable = lambda x : x == 'x' is_constant = lambda x : x == 'c' or x == '0' is_operator = lambda x : x == '/' equation_tree = EquationTree.from_prefix( ...     ['/', 'x', '0'], ...     variable_test=is_variable, ...     constant_test=is_constant, ...     operator_test=is_operator, ... ) equation_tree.check_validity() False equation_tree.check_validity(verbose=True) division by 0 is not allowed. False equation_tree = EquationTree.from_prefix( ...     ['/', 'x', 'c'], ...     variable_test=is_variable, ...     constant_test=is_constant, ...     operator_test=is_operator, ... ) equation_tree.check_validity() True</p> <p>equation_tree = EquationTree.from_prefix( ...     ['/', '0', 'c'], ...     variable_test=is_variable, ...     constant_test=is_constant, ...     operator_test=is_operator, ... ) equation_tree.check_validity(verbose=True) 0 and c are constants applied to the operator / False</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def check_validity(\n    self,\n    zero_representations=[\"0\"],\n    log_representations=[\"log\", \"Log\"],\n    division_representations=[\"/\", \":\"],\n    verbose=False,\n):\n    \"\"\"\n    Check if the tree is valid:\n        - Check if log(0) or x / 0 exists\n        - Check if function(constant) or operator(constant_1, constant_2) exists\n                -&gt; unnecessary complexity\n        - Check if each function has exactly one child\n        - Check if each operator has exactly two children\n\n    Args:\n        zero_representations: A list of attributes that represent zero\n        log_representations: A list of attributes that represent log\n        division_representations: A list of attributes that represent division\n        verbose: If set true, print out the reason for the invalid tree\n\n    Example:\n        &gt;&gt;&gt; is_variable = lambda x : x == 'x'\n        &gt;&gt;&gt; is_constant = lambda x : x == 'c' or x == '0'\n        &gt;&gt;&gt; is_operator = lambda x : x == '/'\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     ['/', 'x', '0'],\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     operator_test=is_operator,\n        ... )\n        &gt;&gt;&gt; equation_tree.check_validity()\n        False\n        &gt;&gt;&gt; equation_tree.check_validity(verbose=True)\n        division by 0 is not allowed.\n        False\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     ['/', 'x', 'c'],\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     operator_test=is_operator,\n        ... )\n        &gt;&gt;&gt; equation_tree.check_validity()\n        True\n\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     ['/', '0', 'c'],\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     operator_test=is_operator,\n        ... )\n        &gt;&gt;&gt; equation_tree.check_validity(verbose=True)\n        0 and c are constants applied to the operator /\n        False\n    \"\"\"\n    return self.root.check_validity(\n        zero_representations, log_representations, division_representations, verbose\n    )\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.evaluate","title":"<code>evaluate(variables)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; expr = sympify('x_a + 3 * y')\n&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*']\n&gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; equation_tree.sympy_expr\nx_1 + 3*x_2\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.evaluate--we-can-use-dicts","title":"We can use dicts:","text":"<pre><code>&gt;&gt;&gt; equation_tree.evaluate({'x_1': np.array([2, 3]), 'x_2': np.array([1, 1])})\narray([5, 6])\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.evaluate--or-pandas-dataframe","title":"Or pandas dataframe:","text":"<pre><code>&gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': np.array([2, 3]), 'x_2': np.array([1, 1])})\n&gt;&gt;&gt; dataFrame\n   x_1  x_2\n0    2    1\n1    3    1\n&gt;&gt;&gt; equation_tree.evaluate(dataFrame)\narray([5, 6])\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.evaluate--or-pandas-dataframe","title":"Or pandas dataframe:","text":"<pre><code>&gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [2, 3], 'x_2': [1, 1]})\n&gt;&gt;&gt; dataFrame\n   x_1  x_2\n0    2    1\n1    3    1\n&gt;&gt;&gt; equation_tree.evaluate(dataFrame)\narray([5, 6])\n</code></pre> <pre><code>&gt;&gt;&gt; expr = sympify('min(x_1,x_2)')\n&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', 'min']\n&gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1', 'x_2']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; equation_tree.sympy_expr\nMin(x_1, x_2)\n</code></pre> <pre><code>&gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [1, 2, 3, 4], 'x_2': [2, 1, 4, 3]})\n&gt;&gt;&gt; equation_tree.evaluate(dataFrame)\narray([1, 1, 3, 3])\n</code></pre> <pre><code>&gt;&gt;&gt; expr = sympify('max(3, x_1)')\n&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', 'min', 'max']\n&gt;&gt;&gt; is_function = lambda x : x in ['sqrt', 'log', 'abs']\n&gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1', 'x_2']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     function_test=is_function,\n...     operator_test=is_operator,\n...     variable_test=is_variable)\n&gt;&gt;&gt; equation_tree.sympy_expr\nMax(3, x_1)\n&gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [1, 2, 3, 4]})\n&gt;&gt;&gt; equation_tree.evaluate(dataFrame)\narray([3, 3, 3, 4])\n</code></pre> <pre><code>&gt;&gt;&gt; expr = sympify('x_1 + sqrt(x_1)')\n&gt;&gt;&gt; is_operator = lambda x : x in ['+']\n&gt;&gt;&gt; is_function = lambda x: x in ['sqrt']\n&gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     function_test=is_function,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; equation_tree.sympy_expr\nsqrt(x_1) + x_1\n</code></pre> <pre><code>&gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [4, 9, 16]})\n&gt;&gt;&gt; equation_tree.evaluate(dataFrame)\narray([ 6., 12., 20.])\n</code></pre> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def evaluate(self, variables: Union[dict, pd.DataFrame]):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; expr = sympify('x_a + 3 * y')\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*']\n        &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        x_1 + 3*x_2\n\n        # We can use dicts:\n        &gt;&gt;&gt; equation_tree.evaluate({'x_1': np.array([2, 3]), 'x_2': np.array([1, 1])})\n        array([5, 6])\n\n        # Or pandas dataframe:\n        &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': np.array([2, 3]), 'x_2': np.array([1, 1])})\n        &gt;&gt;&gt; dataFrame\n           x_1  x_2\n        0    2    1\n        1    3    1\n        &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n        array([5, 6])\n\n        # Or pandas dataframe:\n        &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [2, 3], 'x_2': [1, 1]})\n        &gt;&gt;&gt; dataFrame\n           x_1  x_2\n        0    2    1\n        1    3    1\n        &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n        array([5, 6])\n\n        &gt;&gt;&gt; expr = sympify('min(x_1,x_2)')\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', 'min']\n        &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1', 'x_2']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        Min(x_1, x_2)\n\n        &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [1, 2, 3, 4], 'x_2': [2, 1, 4, 3]})\n        &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n        array([1, 1, 3, 3])\n\n        &gt;&gt;&gt; expr = sympify('max(3, x_1)')\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', 'min', 'max']\n        &gt;&gt;&gt; is_function = lambda x : x in ['sqrt', 'log', 'abs']\n        &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1', 'x_2']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     function_test=is_function,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable)\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        Max(3, x_1)\n        &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [1, 2, 3, 4]})\n        &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n        array([3, 3, 3, 4])\n\n        &gt;&gt;&gt; expr = sympify('x_1 + sqrt(x_1)')\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+']\n        &gt;&gt;&gt; is_function = lambda x: x in ['sqrt']\n        &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     function_test=is_function,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        sqrt(x_1) + x_1\n\n        &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [4, 9, 16]})\n        &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n        array([ 6., 12., 20.])\n    \"\"\"\n\n    df = pd.DataFrame(variables)\n    symbol_list = list(self.sympy_expr.free_symbols)\n\n    if set(list(df.columns)).issubset(set(symbol_list)):\n        raise Exception(\n            f\"Variables in expression {self.sympy_expr} \"\n            f\"do not match the given ones: {df.columns}\"\n        )\n\n    symbol_names = [str(s) for s in symbol_list]\n\n    f = sympy.lambdify(symbol_list, self.sympy_expr, \"numpy\")\n    try:\n        res = np.array(f(*[df[name] for name in symbol_names]))\n    except ValueError:  # Workaround till sympy gets updated\n        lst = [df[name] for name in symbol_names]\n        res = []\n        for i in range(len(lst[0])):\n            args = []\n            for j in range(len(lst)):\n                args.append(lst[j].iloc[i])\n            res.append(f(*args))\n    return np.array(res)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.export_to_srbench","title":"<code>export_to_srbench(folder, data_file_name=None, num_samples=1000, name_target='y', ranges=None, default_range=10, random_state=None)</code>","text":"<p>Creates a folder and adds data and metadata to the folder that can be used with sr bench: https://cavalab.org/srbench/ Args:     folder: Name of the folder     data_file_name: Name of the datafile (if none same as folder name)     num_samples: Number of samples     name_target: Name of the tartget     ranges: A dictionary with the ranges for the variables in form of a dict     default_range: Default range to fall back to if no range for a         specific variable is given     random_state: The random seed to be used</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def export_to_srbench(\n    self,\n    folder: str,\n    data_file_name: Optional[str] = None,\n    num_samples: int = 1000,\n    name_target: str = \"y\",\n    ranges: Optional[Dict] = None,\n    default_range: float = 10,\n    random_state: Optional[int] = None,\n):\n    \"\"\"\n    Creates a folder and adds data and metadata to the folder that can be used with sr bench:\n    https://cavalab.org/srbench/\n    Args:\n        folder: Name of the folder\n        data_file_name: Name of the datafile (if none same as folder name)\n        num_samples: Number of samples\n        name_target: Name of the tartget\n        ranges: A dictionary with the ranges for the variables in form of a dict\n        default_range: Default range to fall back to if no range for a\n            specific variable is given\n        random_state: The random seed to be used\n    \"\"\"\n    if data_file_name is None:\n        data_file_name = folder\n    os.mkdir(folder)\n    path_data = f\"{folder}/{data_file_name}.tsv.gz\"\n    path_meta = f\"{folder}/metadata.yaml\"\n    self.save_samples_srbench(\n        path_data, num_samples, ranges, default_range, random_state\n    )\n    self.save_meta_srbench(path_meta, \"data\", name_target)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prefix","title":"<code>from_prefix(prefix_notation, function_test=lambda : False, operator_test=lambda : False, variable_test=lambda : False, constant_test=lambda : False)</code>  <code>classmethod</code>","text":"<p>Instantiate a tree from prefix notation</p> <p>Parameters:</p> Name Type Description Default <code>prefix_notation</code> <code>List[str]</code> <p>The equation in prefix notation</p> required <code>function_test</code> <code>Callable</code> <p>A function that tests if the attribute is a function</p> <code>lambda : False</code> <code>operator_test</code> <code>Callable</code> <p>A function that tests if the attribute is an operator</p> <code>lambda : False</code> <code>variable_test</code> <code>Callable</code> <p>A function that tests if the attribute is a variable</p> <code>lambda : False</code> <code>constant_test</code> <code>Callable</code> <p>A function that tests if the attribute is a constant</p> <code>lambda : False</code> Example <p>is_variable = lambda x : x in ['x', 'y', 'z'] is_constant = lambda x : x in ['0', '1', '2'] is_function = lambda x : x in ['sin', 'cos'] is_operator = lambda x: x in ['+', '-', '', '/'] prefix = ['+', '-', 'x', '1', '', 'sin', 'y', 'cos', 'z']</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>@classmethod\ndef from_prefix(\n    cls,\n    prefix_notation: List[str],\n    function_test: Callable = lambda _: False,\n    operator_test: Callable = lambda _: False,\n    variable_test: Callable = lambda _: False,\n    constant_test: Callable = lambda _: False,\n):\n    \"\"\"\n    Instantiate a tree from prefix notation\n\n    Args:\n        prefix_notation: The equation in prefix notation\n        function_test: A function that tests if the attribute is a function\n        operator_test: A function that tests if the attribute is an operator\n        variable_test: A function that tests if the attribute is a variable\n        constant_test: A function that tests if the attribute is a constant\n\n    Example:\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n        &gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n        &gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n        &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n        &gt;&gt;&gt; prefix = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n\n        # then we create the node root\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     prefix_notation=prefix,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     function_test=is_function,\n        ...     operator_test=is_operator\n        ...     )\n\n        # and initialize the tree\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2, 2, 1, 2, 3, 2, 3]\n        &gt;&gt;&gt; equation_tree.variables\n        ['x', 'y', 'z']\n        &gt;&gt;&gt; equation_tree.constants\n        ['1']\n        &gt;&gt;&gt; equation_tree.operators\n        ['+', '-', '*']\n        &gt;&gt;&gt; equation_tree.functions\n        ['sin', 'cos']\n\n        # The tree expression is the same as the prefix notation\n        &gt;&gt;&gt; equation_tree.expr == prefix\n        True\n\n\n    \"\"\"\n    root = node_from_prefix(\n        prefix_notation, function_test, operator_test, variable_test, constant_test\n    )\n    return cls(root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prefix--then-we-create-the-node-root","title":"then we create the node root","text":"<p>equation_tree = EquationTree.from_prefix( ...     prefix_notation=prefix, ...     variable_test=is_variable, ...     constant_test=is_constant, ...     function_test=is_function, ...     operator_test=is_operator ...     )</p>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prefix--and-initialize-the-tree","title":"and initialize the tree","text":"<p>equation_tree.structure [0, 1, 2, 2, 1, 2, 3, 2, 3] equation_tree.variables ['x', 'y', 'z'] equation_tree.constants ['1'] equation_tree.operators ['+', '-', '*'] equation_tree.functions ['sin', 'cos']</p>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prefix--the-tree-expression-is-the-same-as-the-prefix-notation","title":"The tree expression is the same as the prefix notation","text":"<p>equation_tree.expr == prefix True</p>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prior","title":"<code>from_prior(prior, max_variables_unique)</code>  <code>classmethod</code>","text":"<p>Initiate a tree from a prior</p> <p>Parameters:</p> Name Type Description Default <code>prior</code> <code>Dict</code> <p>The priors in dictionary form</p> required <code>max_variables_unique</code> <code>int</code> <p>The maximum number of unique variables (a tree can have less then this number)</p> required <p>Examples:</p> <pre><code>&gt;&gt;&gt; np.random.seed(42)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prior--we-can-set-priors-for-features-functions-operators","title":"We can set priors for features, functions, operators","text":""},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prior--and-also-conditionals-based-the-parent","title":"and also conditionals based the parent","text":"<pre><code>&gt;&gt;&gt; p = {\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .2, 'variables': .8},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': 1., '-': .0},\n...     'function_conditionals': {\n...                             'sin': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': 0., 'cos': 1.},\n...                                 'operators': {'+': 0., '-': 1.}\n...                             },\n...                             'cos': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'cos': 1., 'sin': 0.},\n...                                 'operators': {'+': 0., '-': 1.}\n...                             }\n...                         },\n...     'operator_conditionals': {\n...                             '+': {\n...                                 'features': {'constants': .5, 'variables': .5},\n...                                 'functions': {'sin': 1., 'cos': 0.},\n...                                 'operators': {'+': 1., '-': 0.}\n...                             },\n...                             '-': {\n...                                 'features': {'constants': .3, 'variables': .7},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .9, '-': .1}\n...                             }\n...                         },\n... }\n&gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 2]\n&gt;&gt;&gt; equation_tree.expr\n['cos', 'cos', 'x_1']\n&gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 2]\n&gt;&gt;&gt; equation_tree.expr\n['sin', 'cos', 'x_1']\n&gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 1]\n&gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 2, 3, 2, 3, 1]\n&gt;&gt;&gt; equation_tree.expr\n['+', '+', 'sin', 'x_1', 'sin', 'x_2', 'x_2']\n&gt;&gt;&gt; equation_tree.sympy_expr\nx_2 + sin(x_1) + sin(x_2)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prior--without-conditionals-the-unconditioned-priors-are-the-fallback-option","title":"Without conditionals, the unconditioned priors are the fallback option","text":"<pre><code>&gt;&gt;&gt; p = {\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .2, 'variables': .8},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': .5, '-': .5},\n... }\n&gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 2, 3, 2, 3, 1]\n&gt;&gt;&gt; equation_tree.expr\n['+', '-', 'cos', 'c_1', 'cos', 'c_2', 'c_3']\n&gt;&gt;&gt; equation_tree.sympy_expr\nc_3 + cos(c_1) - cos(c_2)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prior--note-this-would-be-discarded-in-a-future-step-as-unnecesarry-complex","title":"Note: this would be discarded in a future step as unnecesarry complex","text":"Source code in <code>src/equation_tree/tree.py</code> <pre><code>@classmethod\ndef from_prior(cls, prior: Dict, max_variables_unique: int):\n    \"\"\"\n    Initiate a tree from a prior\n\n    Args:\n        prior: The priors in dictionary form\n        max_variables_unique: The maximum number of unique variables (a tree can have less then\n            this number)\n\n    Examples:\n        &gt;&gt;&gt; np.random.seed(42)\n\n        # We can set priors for features, functions, operators\n        # and also conditionals based the parent\n        &gt;&gt;&gt; p = {\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .2, 'variables': .8},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': 1., '-': .0},\n        ...     'function_conditionals': {\n        ...                             'sin': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': 0., 'cos': 1.},\n        ...                                 'operators': {'+': 0., '-': 1.}\n        ...                             },\n        ...                             'cos': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'cos': 1., 'sin': 0.},\n        ...                                 'operators': {'+': 0., '-': 1.}\n        ...                             }\n        ...                         },\n        ...     'operator_conditionals': {\n        ...                             '+': {\n        ...                                 'features': {'constants': .5, 'variables': .5},\n        ...                                 'functions': {'sin': 1., 'cos': 0.},\n        ...                                 'operators': {'+': 1., '-': 0.}\n        ...                             },\n        ...                             '-': {\n        ...                                 'features': {'constants': .3, 'variables': .7},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .9, '-': .1}\n        ...                             }\n        ...                         },\n        ... }\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2]\n        &gt;&gt;&gt; equation_tree.expr\n        ['cos', 'cos', 'x_1']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2]\n        &gt;&gt;&gt; equation_tree.expr\n        ['sin', 'cos', 'x_1']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 1]\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2, 3, 2, 3, 1]\n        &gt;&gt;&gt; equation_tree.expr\n        ['+', '+', 'sin', 'x_1', 'sin', 'x_2', 'x_2']\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        x_2 + sin(x_1) + sin(x_2)\n\n        # Without conditionals, the unconditioned priors are the fallback option\n        &gt;&gt;&gt; p = {\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .2, 'variables': .8},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': .5, '-': .5},\n        ... }\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2, 3, 2, 3, 1]\n        &gt;&gt;&gt; equation_tree.expr\n        ['+', '-', 'cos', 'c_1', 'cos', 'c_2', 'c_3']\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        c_3 + cos(c_1) - cos(c_2)\n\n        # Note: this would be discarded in a future step as unnecesarry complex\n    \"\"\"\n    root = sample_tree_full(prior, max_variables_unique)\n    return cls(root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prior_fast","title":"<code>from_prior_fast(prior, tree_depth, max_variables_unique)</code>  <code>classmethod</code>","text":"<p>Initiate a tree from a prior with fast sampling Attention: structure prior is not supported</p> <p>Parameters:</p> Name Type Description Default <code>prior</code> <code>Dict</code> <p>The priors in dictionary form (structure priors are not needed)</p> required <code>tree_depth</code> <p>depth of the tree</p> required <code>max_variables_unique</code> <code>int</code> <p>The maximum number of unique variables (a tree can have less then this number)</p> required Source code in <code>src/equation_tree/tree.py</code> <pre><code>@classmethod\ndef from_prior_fast(cls, prior: Dict, tree_depth, max_variables_unique: int):\n    \"\"\"\n    Initiate a tree from a prior with fast sampling\n    Attention: structure prior is not supported\n\n    Args:\n        prior: The priors in dictionary form (structure priors are not needed)\n        tree_depth: depth of the tree\n        max_variables_unique: The maximum number of unique variables (a tree can have less then\n            this number)\n    \"\"\"\n    root = sample_tree_full_fast(prior, tree_depth, max_variables_unique)\n    return cls(root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_priors","title":"<code>from_priors(feature_priors={}, function_priors={}, operator_priors={}, structure_priors={})</code>  <code>classmethod</code>","text":"<p>Instantiate a tree from priors</p> <p>Attention     - use standard notation here:   variables should be in form x_{number}                                     constants should be in form c_{number}</p> <p>Parameters:</p> Name Type Description Default <code>max_depth</code> <p>Maximum depth of the tree</p> required <code>feature_priors</code> <p>The priors for the features (variables + constants)</p> <code>{}</code> <code>function_priors</code> <p>The priors for the functions</p> <code>{}</code> <code>operator_priors</code> <p>The priors for the operators</p> <code>{}</code> <code>structure_priors</code> <p>The priors for the tree structures</p> <code>{}</code> Example <p>np.random.seed(42) max_depth = 12 feature_priors = {\"x_1\": 0.5, \"c_1\": 0.5} function_priors = {\"sin\": 0.5, \"cos\": 0.5} operator_priors = {\"+\": 0.5, \"-\": 0.5} structure_priors = {'[0, 1, 2, 3, 4, 5, 5, 2, 3, 4, 4]': 1} equation_tree = EquationTree.from_priors( ...     feature_priors, function_priors, operator_priors, structure_priors) equation_tree.expr ['cos', '-', 'cos', 'sin', '+', 'x_1', 'c_1', 'cos', '-', 'x_1', 'c_1'] equation_tree.structure [0, 1, 2, 3, 4, 5, 5, 2, 3, 4, 4] equation_tree.variables ['x_1', 'x_1'] equation_tree.n_variables 2 equation_tree.n_variables_unique 1 equation_tree.constants ['c_1', 'c_1'] equation_tree.n_constants 2 equation_tree.n_constants_unique 1 equation_tree.n_leafs 4 equation_tree.operators ['-', '+', '-'] equation_tree.functions ['cos', 'cos', 'sin', 'cos']</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>@classmethod\ndef from_priors(\n    cls,\n    feature_priors={},\n    function_priors={},\n    operator_priors={},\n    structure_priors={},\n):\n    \"\"\"\n    Instantiate a tree from priors\n\n    Attention\n        - use standard notation here:   variables should be in form x_{number}\n                                        constants should be in form c_{number}\n\n    Args:\n        max_depth: Maximum depth of the tree\n        feature_priors: The priors for the features (variables + constants)\n        function_priors: The priors for the functions\n        operator_priors: The priors for the operators\n        structure_priors: The priors for the tree structures\n\n    Example:\n        &gt;&gt;&gt; np.random.seed(42)\n        &gt;&gt;&gt; max_depth = 12\n        &gt;&gt;&gt; feature_priors = {\"x_1\": 0.5, \"c_1\": 0.5}\n        &gt;&gt;&gt; function_priors = {\"sin\": 0.5, \"cos\": 0.5}\n        &gt;&gt;&gt; operator_priors = {\"+\": 0.5, \"-\": 0.5}\n        &gt;&gt;&gt; structure_priors = {'[0, 1, 2, 3, 4, 5, 5, 2, 3, 4, 4]': 1}\n        &gt;&gt;&gt; equation_tree = EquationTree.from_priors(\n        ...     feature_priors, function_priors, operator_priors, structure_priors)\n        &gt;&gt;&gt; equation_tree.expr\n        ['cos', '-', 'cos', 'sin', '+', 'x_1', 'c_1', 'cos', '-', 'x_1', 'c_1']\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2, 3, 4, 5, 5, 2, 3, 4, 4]\n        &gt;&gt;&gt; equation_tree.variables\n        ['x_1', 'x_1']\n        &gt;&gt;&gt; equation_tree.n_variables\n        2\n        &gt;&gt;&gt; equation_tree.n_variables_unique\n        1\n        &gt;&gt;&gt; equation_tree.constants\n        ['c_1', 'c_1']\n        &gt;&gt;&gt; equation_tree.n_constants\n        2\n        &gt;&gt;&gt; equation_tree.n_constants_unique\n        1\n        &gt;&gt;&gt; equation_tree.n_leafs\n        4\n        &gt;&gt;&gt; equation_tree.operators\n        ['-', '+', '-']\n        &gt;&gt;&gt; equation_tree.functions\n        ['cos', 'cos', 'sin', 'cos']\n    \"\"\"\n    root = sample_tree(\n        feature_priors,\n        function_priors,\n        operator_priors,\n        structure_priors,\n    )\n    return cls(root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_sympy","title":"<code>from_sympy(expression, function_test=lambda : False, operator_test=lambda : False, variable_test=lambda : False, constant_test=lambda : False)</code>  <code>classmethod</code>","text":"<p>Instantiate a tree from a sympy function</p> Attention <ul> <li>constant and variable names get standardized</li> <li>unary minus get converted to binary minus</li> </ul> <p>Examples:</p> <pre><code>&gt;&gt;&gt; expr = sympify('x_a + B * y')\n&gt;&gt;&gt; expr\nB*y + x_a\n&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*']\n&gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n&gt;&gt;&gt; is_constant = lambda x : x == 'B'\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n...     constant_test=is_constant\n... )\n&gt;&gt;&gt; equation_tree.expr\n['+', '*', 'c_1', 'x_2', 'x_1']\n&gt;&gt;&gt; equation_tree.sympy_expr\nc_1*x_2 + x_1\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_sympy--numbers-dont-get-standardized-but-are-constants","title":"Numbers don't get standardized but are constants","text":"<pre><code>&gt;&gt;&gt; expr = sympify('x_a + 2 * y')\n&gt;&gt;&gt; expr\nx_a + 2*y\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n...     constant_test=is_constant\n... )\n&gt;&gt;&gt; equation_tree.expr\n['+', 'x_1', '*', '2', 'x_2']\n&gt;&gt;&gt; equation_tree.sympy_expr\nx_1 + 2*x_2\n&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**']\n&gt;&gt;&gt; is_variable = lambda x: '_' in x\n&gt;&gt;&gt; is_constant = lambda x: x == 'B'\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     sympify('B*x_1**2'),\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n...     constant_test=is_constant\n... )\n</code></pre> <pre><code>&gt;&gt;&gt; expr = sympify('min(x_1, x_2)')\n&gt;&gt;&gt; expr\nMin(x_1, x_2)\n&gt;&gt;&gt; is_operator = lambda x : x in ['min']\n&gt;&gt;&gt; is_variable = lambda x : x in ['x_1', 'x_2']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; equation_tree.expr\n['min', 'x_1', 'x_2']\n</code></pre> <pre><code>&gt;&gt;&gt; expr = sympify('x_1**2')\n&gt;&gt;&gt; expr\nx_1**2\n&gt;&gt;&gt; is_operator = lambda x : x in ['*', '/', '**', '+']\n&gt;&gt;&gt; is_variable = lambda x : x in ['x_1']\n&gt;&gt;&gt; is_function = lambda x : x in ['squared']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n...     function_test=is_function\n... )\n&gt;&gt;&gt; equation_tree.expr\n['squared', 'x_1']\n</code></pre> Source code in <code>src/equation_tree/tree.py</code> <pre><code>@classmethod\ndef from_sympy(\n    cls,\n    expression,\n    function_test: Callable = lambda _: False,\n    operator_test: Callable = lambda _: False,\n    variable_test: Callable = lambda _: False,\n    constant_test: Callable = lambda _: False,\n):\n    \"\"\"\n    Instantiate a tree from a sympy function\n\n    Attention:\n        - constant and variable names get standardized\n        - unary minus get converted to binary minus\n\n    Examples:\n        &gt;&gt;&gt; expr = sympify('x_a + B * y')\n        &gt;&gt;&gt; expr\n        B*y + x_a\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*']\n        &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n        &gt;&gt;&gt; is_constant = lambda x : x == 'B'\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant\n        ... )\n        &gt;&gt;&gt; equation_tree.expr\n        ['+', '*', 'c_1', 'x_2', 'x_1']\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        c_1*x_2 + x_1\n\n        # Numbers don't get standardized but are constants\n        &gt;&gt;&gt; expr = sympify('x_a + 2 * y')\n        &gt;&gt;&gt; expr\n        x_a + 2*y\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant\n        ... )\n        &gt;&gt;&gt; equation_tree.expr\n        ['+', 'x_1', '*', '2', 'x_2']\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        x_1 + 2*x_2\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**']\n        &gt;&gt;&gt; is_variable = lambda x: '_' in x\n        &gt;&gt;&gt; is_constant = lambda x: x == 'B'\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     sympify('B*x_1**2'),\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant\n        ... )\n\n        &gt;&gt;&gt; expr = sympify('min(x_1, x_2)')\n        &gt;&gt;&gt; expr\n        Min(x_1, x_2)\n        &gt;&gt;&gt; is_operator = lambda x : x in ['min']\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x_1', 'x_2']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; equation_tree.expr\n        ['min', 'x_1', 'x_2']\n\n        &gt;&gt;&gt; expr = sympify('x_1**2')\n        &gt;&gt;&gt; expr\n        x_1**2\n        &gt;&gt;&gt; is_operator = lambda x : x in ['*', '/', '**', '+']\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x_1']\n        &gt;&gt;&gt; is_function = lambda x : x in ['squared']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ...     function_test=is_function\n        ... )\n        &gt;&gt;&gt; equation_tree.expr\n        ['squared', 'x_1']\n\n    \"\"\"\n    standard = standardize_sympy(expression, variable_test, constant_test)\n    standard = unary_minus_to_binary(standard, operator_test)\n    standard = op_const_to_func(standard)\n    prefix = infix_to_prefix(str(standard), function_test, operator_test)\n    root = node_from_prefix(\n        prefix,\n        function_test,\n        operator_test,\n        lambda x: \"x_\" in x,\n        lambda x: \"c_\" in x,\n    )\n    return cls(root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.get_evaluation","title":"<code>get_evaluation(min_val=-1, max_val=1, num_samples=100)</code>","text":"<p>Evaluate the nodes with random samples for variables and constants.</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def get_evaluation(\n    self, min_val: int = -1, max_val: int = 1, num_samples: int = 100\n):\n    \"\"\"\n    Evaluate the nodes with random samples for variables and constants.\n    \"\"\"\n\n    crossings = self._create_crossing(min_val, max_val, num_samples)\n    evaluation = np.zeros((len(crossings), len(self.expr)))\n\n    for i, crossing in enumerate(crossings):\n        eqn_input = dict()\n        k = 0\n        for c in self.constants_unique:\n            if is_numeric(c):\n                eqn_input[c] = float(c)\n            elif c == \"e\":\n                eqn_input[c] = 2.71828182846\n            elif c == \"pi\":\n                eqn_input[c] = 3.14159265359\n            else:\n                eqn_input[c] = crossing[self.n_variables_unique + k]\n                k += 1\n        for idx, x in enumerate(self.variables_unique):\n            eqn_input[x] = crossing[idx]\n        evaluation[i, :] = self._evaluate(eqn_input)\n\n    self.evaluation = evaluation\n    return evaluation\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.save_samples","title":"<code>save_samples(path, num_samples, ranges=None, default_range=10, dv_name='y', random_state=None, compression='gzip')</code>","text":"<p>Creates a file with samples of ivs and dvs Args:     path: The path were to store the file     num_samples: The number of samples     ranges: A dictionary with the ranges for the variables in form of a dict     default_range: Default range to fall back to if no range for a         specific variable is given     dv_name: The name to give to the observation     random_state: The random seed to be used     compression: Compression method</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def save_samples(\n    self,\n    path,\n    num_samples,\n    ranges: Optional[Dict] = None,\n    default_range: float = 10,\n    dv_name: str = \"y\",\n    random_state: Optional[int] = None,\n    compression: str = \"gzip\",\n):\n    \"\"\"\n    Creates a file with samples of ivs and dvs\n    Args:\n        path: The path were to store the file\n        num_samples: The number of samples\n        ranges: A dictionary with the ranges for the variables in form of a dict\n        default_range: Default range to fall back to if no range for a\n            specific variable is given\n        dv_name: The name to give to the observation\n        random_state: The random seed to be used\n        compression: Compression method\n    \"\"\"\n    if not path.endswith(\"gz\") and compression == \"gzip\":\n        warnings.warn(\n            f\"Compression is gzip but file {path} does not have the ending .gz\"\n        )\n    _ranges = {\n        key: (-default_range, default_range) for key in self.variables_unique\n    }\n    if ranges is not None:\n        for key in ranges.keys():\n            if key in _ranges.keys():\n                _ranges[key] = ranges[key]\n\n    rng = np.random.default_rng(random_state)\n\n    def _get_conditions_once():\n        raw_conditions = {}\n        for key in _ranges.keys():\n            raw_conditions[key] = rng.uniform(*_ranges[key], size=num_samples)\n        return pd.DataFrame(raw_conditions)\n\n    conditions_ = pd.DataFrame(columns=self.variables_unique + [dv_name])\n    i = 0\n    while i &lt; 1_000_000 and len(conditions_.index) &lt; num_samples:\n        _sample = _get_conditions_once()\n        evaluation = self.evaluate(_sample)\n        _sample[dv_name] = evaluation\n        bad_indices = np.where(np.isnan(evaluation) | np.isinf(evaluation))[0]\n        _sample = _sample.drop(bad_indices)\n        conditions_ = pd.concat([conditions_, _sample], ignore_index=True)\n        i += 1\n        if i &gt;= 1_000_000:\n            break\n    conditions_ = conditions_.head(num_samples)\n    conditions_.to_csv(path, compression=compression, index=False, sep=\"\\t\")\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify","title":"<code>simplify(function_test=None, operator_test=None, is_binary_minus_only=True, is_power_caret=True, verbose=False)</code>","text":"<p>Simplify equation if the simplified equation has a shorter prefix Args:     function_test: A function that tests weather an attribute is a function         Attention: simplifying may lead to new functions that were not in the equation             before. If so, add this to the test here.     operator_test: A function that tests weather an attribute is an operator         Attention: simplifying may lead to new operators that were not in the equation             before. If so, add this to the test here.     is_binary_minus_only: Convert all unary minus to binary after simplification     is_power_caret: Represent power as a caret after simplification     verbose: Show messages if simplification results in errors</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; is_variable = lambda x: 'x_' in x\n&gt;&gt;&gt; is_constant = lambda x: 'c_' in x or is_numeric(x) or is_known_constant(x)\n&gt;&gt;&gt; is_operator = lambda x: x in ['+', '*', '/', '^', '-']\n&gt;&gt;&gt; is_function = lambda x: x.lower() in ['sqrt', 'abs']\n&gt;&gt;&gt; prefix_notation = ['+', 'x_1', 'x_1' ]\n&gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n...     prefix_notation=prefix_notation,\n...     variable_test=is_variable,\n...     constant_test=is_constant,\n...     operator_test=is_operator,\n...     function_test=is_function)\n&gt;&gt;&gt; equation_tree.expr\n['+', 'x_1', 'x_1']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify--it-takes-care-of-multiplication","title":"it takes care of multiplication:","text":"<pre><code>&gt;&gt;&gt; equation_tree.simplify(function_test=is_function,operator_test=is_operator)\n&gt;&gt;&gt; equation_tree.expr\n['*', '2', 'x_1']\n</code></pre> <pre><code>&gt;&gt;&gt; prefix_notation = ['sqrt', '*', 'x_1', 'x_1']\n&gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n...     prefix_notation=prefix_notation,\n...     variable_test=is_variable,\n...     constant_test=is_constant,\n...     operator_test=is_operator,\n...     function_test=is_function)\n&gt;&gt;&gt; equation_tree.expr\n['sqrt', '*', 'x_1', 'x_1']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify--it-is-good-practice-to-define-tests-at-the-begining-of-a-script-and-use-them","title":"it is good practice to define tests at the begining of a script and use them","text":""},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify--throughout-the-project","title":"throughout the project","text":"<pre><code>&gt;&gt;&gt; equation_tree.simplify(\n...     operator_test=is_operator,\n...     function_test=is_function\n... )\n&gt;&gt;&gt; equation_tree.expr\n['abs', 'x_1']\n</code></pre> <pre><code>&gt;&gt;&gt; prefix_notation = ['*', '-', 'c_1', 'x_1', '-', 'x_1', 'c_1']\n&gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n...     prefix_notation=prefix_notation,\n...     variable_test=is_variable,\n...     constant_test=is_constant,\n...     operator_test=is_operator,\n...     function_test=is_function)\n&gt;&gt;&gt; equation_tree.expr\n['*', '-', 'c_1', 'x_1', '-', 'x_1', 'c_1']\n</code></pre> <pre><code>&gt;&gt;&gt; equation_tree.sympy_expr\n(-c_1 + x_1)*(c_1 - x_1)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify--it-is-good-practice-to-define-tests-at-the-begining-of-a-script-and-use-them","title":"it is good practice to define tests at the begining of a script and use them","text":""},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify--throughout-the-project","title":"throughout the project","text":"<pre><code>&gt;&gt;&gt; equation_tree.simplify(\n...     operator_test=is_operator,\n...     function_test=is_function\n... )\n&gt;&gt;&gt; equation_tree.sympy_expr\n(-c_1 + x_1)**2\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify--equation_treeexpr","title":"&gt;&gt;&gt; equation_tree.expr","text":""},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify---x_1-c_1-2","title":"['^', '-', 'x_1', 'c_1', '2']","text":"Source code in <code>src/equation_tree/tree.py</code> <pre><code>def simplify(\n    self,\n    function_test: Union[Callable, None] = None,\n    operator_test: Union[Callable, None] = None,\n    is_binary_minus_only: bool = True,\n    is_power_caret: bool = True,\n    verbose: bool = False,\n):\n    \"\"\"\n    Simplify equation if the simplified equation has a shorter prefix\n    Args:\n        function_test: A function that tests weather an attribute is a function\n            Attention: simplifying may lead to new functions that were not in the equation\n                before. If so, add this to the test here.\n        operator_test: A function that tests weather an attribute is an operator\n            Attention: simplifying may lead to new operators that were not in the equation\n                before. If so, add this to the test here.\n        is_binary_minus_only: Convert all unary minus to binary after simplification\n        is_power_caret: Represent power as a caret after simplification\n        verbose: Show messages if simplification results in errors\n\n    Examples:\n        &gt;&gt;&gt; is_variable = lambda x: 'x_' in x\n        &gt;&gt;&gt; is_constant = lambda x: 'c_' in x or is_numeric(x) or is_known_constant(x)\n        &gt;&gt;&gt; is_operator = lambda x: x in ['+', '*', '/', '^', '-']\n        &gt;&gt;&gt; is_function = lambda x: x.lower() in ['sqrt', 'abs']\n        &gt;&gt;&gt; prefix_notation = ['+', 'x_1', 'x_1' ]\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     prefix_notation=prefix_notation,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     operator_test=is_operator,\n        ...     function_test=is_function)\n        &gt;&gt;&gt; equation_tree.expr\n        ['+', 'x_1', 'x_1']\n\n        # it takes care of multiplication:\n        &gt;&gt;&gt; equation_tree.simplify(function_test=is_function,operator_test=is_operator)\n        &gt;&gt;&gt; equation_tree.expr\n        ['*', '2', 'x_1']\n\n        &gt;&gt;&gt; prefix_notation = ['sqrt', '*', 'x_1', 'x_1']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     prefix_notation=prefix_notation,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     operator_test=is_operator,\n        ...     function_test=is_function)\n        &gt;&gt;&gt; equation_tree.expr\n        ['sqrt', '*', 'x_1', 'x_1']\n\n        # it is good practice to define tests at the begining of a script and use them\n        # throughout the project\n        &gt;&gt;&gt; equation_tree.simplify(\n        ...     operator_test=is_operator,\n        ...     function_test=is_function\n        ... )\n        &gt;&gt;&gt; equation_tree.expr\n        ['abs', 'x_1']\n\n        &gt;&gt;&gt; prefix_notation = ['*', '-', 'c_1', 'x_1', '-', 'x_1', 'c_1']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     prefix_notation=prefix_notation,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     operator_test=is_operator,\n        ...     function_test=is_function)\n        &gt;&gt;&gt; equation_tree.expr\n        ['*', '-', 'c_1', 'x_1', '-', 'x_1', 'c_1']\n\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        (-c_1 + x_1)*(c_1 - x_1)\n\n        # it is good practice to define tests at the begining of a script and use them\n        # throughout the project\n        &gt;&gt;&gt; equation_tree.simplify(\n        ...     operator_test=is_operator,\n        ...     function_test=is_function\n        ... )\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        (-c_1 + x_1)**2\n\n        # &gt;&gt;&gt; equation_tree.expr\n        # ['^', '-', 'x_1', 'c_1', '2']\n    \"\"\"\n\n    if function_test is None:\n\n        def function_test(x):\n            return x in self.functions\n\n    else:\n        tmp_f = function_test\n\n        def function_test(x):\n            return tmp_f(x) or x in self.functions\n\n    if operator_test is None:\n\n        def operator_test(x):\n            return x in self.operators\n\n    else:\n        tmp_o = operator_test\n\n        def operator_test(x):\n            return tmp_o(x) or x in self.operators\n\n    class TimeoutError(Exception):\n        pass\n\n    def timeout_handler(signum, frame):\n        raise TimeoutError(\"Function call timed out\")\n\n    signal.signal(signal.SIGALRM, timeout_handler)\n    signal.alarm(SIMPLIFY_TIMEOUT)\n    try:\n        simplified_equation = simplify(self.sympy_expr)\n        signal.alarm(0)\n    except TimeoutError:\n        simplified_equation = self.sympy_expr\n    if not check_functions(simplified_equation, function_test):\n        warnings.warn(\n            f\"{simplified_equation} has functions that are not in function_test type\"\n        )\n        self.root = None\n        self._build()\n        return\n    if (\n        \"I\" in str(simplified_equation)\n        or \"accumbounds\" in str(simplified_equation).lower()\n    ):\n        if verbose:\n            print(f\"Simplify {str(self.sympy_expr)} results in complex values\")\n        self.root = None\n        self._build()\n        return\n    if is_power_caret:\n        simplified_equation = str(simplified_equation).replace(\"**\", \"^\")\n    simplified_equation = simplified_equation.replace(\"re\", \"\")\n    if is_binary_minus_only:\n        simplified_equation = unary_minus_to_binary(\n            simplified_equation, operator_test\n        )\n    simplified_equation = simplified_equation.replace(\" \", \"\")\n\n    prefix = infix_to_prefix(simplified_equation, function_test, operator_test)\n    if verbose:\n        print(\"prefix\", simplified_equation)\n        print(\"prefix tree\", prefix)\n    if \"re\" in prefix:\n        prefix.remove(\"re\")\n    if len(prefix) &gt; len(self.expr):\n        prefix = self.expr\n    if \"zoo\" in prefix or \"oo\" in prefix:\n        if verbose:\n            print(f\"Simplify {str(self.sympy_expr)} results in None\")\n        self.root = None\n        self._build()\n        return\n    self.root = node_from_prefix(\n        prefix,\n        function_test,\n        operator_test,\n        lambda x: x in self.variables,\n        lambda x: x in self.constants or is_numeric(x) or is_known_constant(x),\n    )\n    self._build()\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.standardize","title":"<code>standardize()</code>","text":"<p>Standardize variable and constant names</p> Example <p>is_variable = lambda x : x in ['x', 'y', 'z'] is_constant = lambda x : x in ['0', '1', '2'] is_function = lambda x : x in ['sin', 'cos'] is_operator = lambda x: x in ['+', '-', '', '/'] prefix = ['+', '-', 'x', '1', '', 'sin', 'y', 'cos', 'z']</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def standardize(self):\n    \"\"\"\n    Standardize variable and constant names\n\n    Example:\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n        &gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n        &gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n        &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n        &gt;&gt;&gt; prefix = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n\n        # then we create the node root\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     prefix_notation=prefix,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     function_test=is_function,\n        ...     operator_test=is_operator\n        ...     )\n\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        x + sin(y)*cos(z) - 1\n\n        &gt;&gt;&gt; equation_tree.standardize()\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        x_1 + sin(x_2)*cos(x_3) - 1\n\n    \"\"\"\n    variable_count = 0\n    constant_count = 0\n    variables = {}\n    constants = {}\n\n    def rec_stand(node):\n        if node is None:\n            return\n        nonlocal variable_count, constant_count\n        nonlocal variables, constants\n        if node.kind == NodeKind.VARIABLE:\n            if node.attribute not in variables.keys():\n                variable_count += 1\n                variables[node.attribute] = f\"x_{variable_count}\"\n            node.attribute = variables[node.attribute]\n        if node.kind == NodeKind.CONSTANT and not is_numeric(node.attribute):\n            if node.attribute not in constants.keys():\n                constant_count += 1\n                constants[node.attribute] = f\"c_{constant_count}\"\n            node.attribute = constants[node.attribute]\n        else:\n            rec_stand(node.left)\n            rec_stand(node.right)\n        return node\n\n    self.root = rec_stand(self.root)\n    self._build()\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.standardize--then-we-create-the-node-root","title":"then we create the node root","text":"<p>equation_tree = EquationTree.from_prefix( ...     prefix_notation=prefix, ...     variable_test=is_variable, ...     constant_test=is_constant, ...     function_test=is_function, ...     operator_test=is_operator ...     )</p> <p>equation_tree.sympy_expr x + sin(y)*cos(z) - 1</p> <p>equation_tree.standardize() equation_tree.sympy_expr x_1 + sin(x_2)*cos(x_3) - 1</p>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.instantiate_constants","title":"<code>instantiate_constants(tree, fct)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; expr = sympify('e ** (- e **( x + y))')\n&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**', '-']\n&gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']\n&gt;&gt;&gt; is_constant = lambda x : x in ['e']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; equation_tree.sympy_expr\ne**((-e)**(x_1 + x_2))\n&gt;&gt;&gt; instantiated = instantiate_constants(equation_tree, lambda: 2)\n&gt;&gt;&gt; instantiated.sympy_expr\ne**((-e)**(x_1 + x_2))\n&gt;&gt;&gt; expr_2 = sympify('c_1 ** (- e **( x + y))')\n&gt;&gt;&gt; equation_tree_2 = EquationTree.from_sympy(\n...     expr_2,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; instantiated = instantiate_constants(equation_tree_2, lambda: 2)\n&gt;&gt;&gt; instantiated.sympy_expr\n2**((-e)**(x_1 + x_2))\n</code></pre> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def instantiate_constants(tree, fct: Callable):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; expr = sympify('e ** (- e **( x + y))')\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**', '-']\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']\n        &gt;&gt;&gt; is_constant = lambda x : x in ['e']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        e**((-e)**(x_1 + x_2))\n        &gt;&gt;&gt; instantiated = instantiate_constants(equation_tree, lambda: 2)\n        &gt;&gt;&gt; instantiated.sympy_expr\n        e**((-e)**(x_1 + x_2))\n        &gt;&gt;&gt; expr_2 = sympify('c_1 ** (- e **( x + y))')\n        &gt;&gt;&gt; equation_tree_2 = EquationTree.from_sympy(\n        ...     expr_2,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; instantiated = instantiate_constants(equation_tree_2, lambda: 2)\n        &gt;&gt;&gt; instantiated.sympy_expr\n        2**((-e)**(x_1 + x_2))\n\n\n\n    \"\"\"\n    root = copy.deepcopy(tree.root)\n\n    def _rec_apply(node):\n        if (\n            node.kind == NodeKind.CONSTANT\n            and not is_known_constant(node.attribute)\n            and not is_numeric(node.attribute)\n        ):\n            node.attribute = str(fct())\n        for c in node.children:\n            _rec_apply(c)\n\n    _rec_apply(root)\n    return EquationTree(root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.normalized_tree_distance","title":"<code>normalized_tree_distance(e_a, e_b)</code>","text":"<p>Normalized edit distance between two trees according to <code>Li, Y., &amp; Chenguang, Z. (2011). A metric normalization of tree edit distance. Frontiers of Computer Science in China, 5, 119-125.</code></p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def normalized_tree_distance(e_a: EquationTree, e_b: EquationTree):\n    \"\"\"\n    Normalized edit distance between two trees according to\n    `Li, Y., &amp; Chenguang, Z. (2011). A metric normalization of tree edit distance.\n    Frontiers of Computer Science in China, 5, 119-125.`\n\n    \"\"\"\n    if e_a.root is None or e_b.root is None:\n        return 1\n    return ned(e_a.root, e_b.root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.prediction_distance","title":"<code>prediction_distance(e_a, e_b, X)</code>","text":"<p>Mean squared difference between the prediction of two equations on X</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**', '-']\n&gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']\n&gt;&gt;&gt; expr_1 = sympify('x + y')\n&gt;&gt;&gt; expr_2 = sympify('x')\n&gt;&gt;&gt; et_1 = EquationTree.from_sympy(\n...     expr_1,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; et_1.sympy_expr\nx_1 + x_2\n&gt;&gt;&gt; et_2 = EquationTree.from_sympy(\n...     expr_2,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; et_2.sympy_expr\nx_1\n&gt;&gt;&gt; prediction_distance(et_1, et_2, {'x_1': [1], 'x_2': [1]})\n1.0\n&gt;&gt;&gt; prediction_distance(et_1, et_2, {'x_1': [1, 2, 3], 'x_2': [0, 0, 0]})\n0.0\n&gt;&gt;&gt; prediction_distance(et_1, et_2, {'x_1': [1, 2], 'x_2': [1, 2]})\n2.5\n</code></pre> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def prediction_distance(\n    e_a: EquationTree, e_b: EquationTree, X: Union[dict, pd.DataFrame]\n):\n    \"\"\"\n    Mean squared difference between the prediction of two equations on X\n\n    Examples:\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**', '-']\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']\n        &gt;&gt;&gt; expr_1 = sympify('x + y')\n        &gt;&gt;&gt; expr_2 = sympify('x')\n        &gt;&gt;&gt; et_1 = EquationTree.from_sympy(\n        ...     expr_1,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; et_1.sympy_expr\n        x_1 + x_2\n        &gt;&gt;&gt; et_2 = EquationTree.from_sympy(\n        ...     expr_2,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; et_2.sympy_expr\n        x_1\n        &gt;&gt;&gt; prediction_distance(et_1, et_2, {'x_1': [1], 'x_2': [1]})\n        1.0\n        &gt;&gt;&gt; prediction_distance(et_1, et_2, {'x_1': [1, 2, 3], 'x_2': [0, 0, 0]})\n        0.0\n        &gt;&gt;&gt; prediction_distance(et_1, et_2, {'x_1': [1, 2], 'x_2': [1, 2]})\n        2.5\n\n    \"\"\"\n    predict_a = e_a.evaluate(X)\n    predict_b = e_b.evaluate(X)\n    squared_diff = (predict_a - predict_b) ** 2\n    return squared_diff.mean()\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.symbolic_solution_diff","title":"<code>symbolic_solution_diff(e_a, e_b)</code>","text":"<p>Symbolic solution with difference constant based on <code>La Cava, W. et al (2021). Contemporary symbolic regression methods and their relative performance.</code> Examples:     &gt;&gt;&gt; is_operator = lambda x : x in ['+', '', '*', '-']     &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']     &gt;&gt;&gt; is_constant = lambda x: is_numeric(x)     &gt;&gt;&gt; expr_1 = sympify('x + .1')     &gt;&gt;&gt; expr_2 = sympify('x')     &gt;&gt;&gt; et_1 = EquationTree.from_sympy(     ...     expr_1,     ...     operator_test=is_operator,     ...     variable_test=is_variable,     ...     constant_test=is_constant     ... )     &gt;&gt;&gt; et_1.sympy_expr     x_1 + 0.1     &gt;&gt;&gt; et_2 = EquationTree.from_sympy(     ...     expr_2,     ...     operator_test=is_operator,     ...     variable_test=is_variable,     ... )     &gt;&gt;&gt; et_2.sympy_expr     x_1     &gt;&gt;&gt; symbolic_solution_diff(et_1, et_2)     0.1</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def symbolic_solution_diff(e_a: EquationTree, e_b: EquationTree):\n    \"\"\"\n    Symbolic solution with difference constant based on\n    `La Cava, W. et al (2021).\n    Contemporary symbolic regression methods and their relative performance.`\n    Examples:\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**', '-']\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']\n        &gt;&gt;&gt; is_constant = lambda x: is_numeric(x)\n        &gt;&gt;&gt; expr_1 = sympify('x + .1')\n        &gt;&gt;&gt; expr_2 = sympify('x')\n        &gt;&gt;&gt; et_1 = EquationTree.from_sympy(\n        ...     expr_1,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant\n        ... )\n        &gt;&gt;&gt; et_1.sympy_expr\n        x_1 + 0.1\n        &gt;&gt;&gt; et_2 = EquationTree.from_sympy(\n        ...     expr_2,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; et_2.sympy_expr\n        x_1\n        &gt;&gt;&gt; symbolic_solution_diff(et_1, et_2)\n        0.1\n    \"\"\"\n    diff = simplify(e_a.sympy_expr - e_b.sympy_expr)\n    if diff.is_constant():\n        return float(diff)\n    else:\n        return np.infty\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.symbolic_solution_quot","title":"<code>symbolic_solution_quot(e_a, e_b)</code>","text":"<p>Symbolic solution with quotient constant based on <code>La Cava, W. et al (2021). Contemporary symbolic regression methods and their relative performance.</code> Examples:     &gt;&gt;&gt; is_operator = lambda x : x in ['+', '', '', '-']     &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']     &gt;&gt;&gt; is_constant = lambda x: is_numeric(x)     &gt;&gt;&gt; expr_1 = sympify('x * .1')     &gt;&gt;&gt; expr_2 = sympify('x')     &gt;&gt;&gt; et_1 = EquationTree.from_sympy(     ...     expr_1,     ...     operator_test=is_operator,     ...     variable_test=is_variable,     ...     constant_test=is_constant     ... )     &gt;&gt;&gt; et_1.sympy_expr     0.1x_1     &gt;&gt;&gt; et_2 = EquationTree.from_sympy(     ...     expr_2,     ...     operator_test=is_operator,     ...     variable_test=is_variable,     ... )     &gt;&gt;&gt; et_2.sympy_expr     x_1     &gt;&gt;&gt; symbolic_solution_quot(et_1, et_2)     0.1</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def symbolic_solution_quot(e_a: EquationTree, e_b: EquationTree):\n    \"\"\"\n    Symbolic solution with quotient constant based on\n    `La Cava, W. et al (2021).\n    Contemporary symbolic regression methods and their relative performance.`\n    Examples:\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**', '-']\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']\n        &gt;&gt;&gt; is_constant = lambda x: is_numeric(x)\n        &gt;&gt;&gt; expr_1 = sympify('x * .1')\n        &gt;&gt;&gt; expr_2 = sympify('x')\n        &gt;&gt;&gt; et_1 = EquationTree.from_sympy(\n        ...     expr_1,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant\n        ... )\n        &gt;&gt;&gt; et_1.sympy_expr\n        0.1*x_1\n        &gt;&gt;&gt; et_2 = EquationTree.from_sympy(\n        ...     expr_2,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; et_2.sympy_expr\n        x_1\n        &gt;&gt;&gt; symbolic_solution_quot(et_1, et_2)\n        0.1\n    \"\"\"\n    quot_1 = simplify(e_a.sympy_expr / e_b.sympy_expr)\n    quot_2 = simplify(e_a.sympy_expr / e_b.sympy_expr)\n    if quot_1.is_constant():\n        return min(float(quot_1), float(quot_2))\n    else:\n        return np.infty\n</code></pre>"},{"location":"reference/src/equation_tree/src/","title":"Src","text":""},{"location":"reference/src/equation_tree/src/sample_tree_structure/","title":"Sample tree structure","text":""},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure","title":"<code>sample_tree_structure(prior={})</code>","text":"<p>Sample a tree structure.</p> <p>Parameters:</p> Name Type Description Default <code>prior</code> <code>Dict</code> <p>priors in form of a dictionary. The keys are the tree structures as strings</p> <code>{}</code> <p>Examples:</p>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure--set-seed-for-reproducibility","title":"Set seed for reproducibility","text":"<pre><code>&gt;&gt;&gt; np.random.seed(42)\n</code></pre> <pre><code>&gt;&gt;&gt; [sample_tree_structure({'[0, 1, 1]': 1}) for _ in range(4)]\n[[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 1]]\n</code></pre> <pre><code>&gt;&gt;&gt; [sample_tree_structure({'[0, 1, 1]': .5, '[0, 1, 2]': .5}) for _ in range(4)]\n[[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 2]]\n</code></pre> <pre><code>&gt;&gt;&gt; sample_tree_structure({'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 1, 2': .4})\n[0, 1, 2, 3, 1]\n</code></pre> Source code in <code>src/equation_tree/src/sample_tree_structure.py</code> <pre><code>def sample_tree_structure(prior: Dict = {}):\n    \"\"\"\n    Sample a tree structure.\n\n    Args:\n        prior: priors in form of a dictionary. The keys are the tree structures as strings\n\n    Examples:\n        # Set seed for reproducibility\n        &gt;&gt;&gt; np.random.seed(42)\n\n        &gt;&gt;&gt; [sample_tree_structure({'[0, 1, 1]': 1}) for _ in range(4)]\n        [[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 1]]\n\n        &gt;&gt;&gt; [sample_tree_structure({'[0, 1, 1]': .5, '[0, 1, 2]': .5}) for _ in range(4)]\n        [[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 2]]\n\n        &gt;&gt;&gt; sample_tree_structure({'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 1, 2': .4})\n        [0, 1, 2, 3, 1]\n\n    \"\"\"\n    tree_structures = [parse_string_list_int(str(key)) for key in prior.keys()]\n    probabilities = [prior[key] for key in prior.keys()]\n\n    for _ in range(MAX_ITER):\n        sample_index = np.random.choice(len(tree_structures), p=probabilities)\n        tree_structure = tree_structures[sample_index]\n        if not _is_binary_tree(tree_structure):\n            warnings.warn(\n                \"Found a non binary tree structure, \"\n                \"this might lead to discrepancies between set priors and sample frequencies.\"\n            )\n            continue\n        return tree_structure\n    raise Exception(f\"Could not generate tree structure with prior: {prior}\")\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso","title":"<code>sample_tree_structure_non_iso(max_depth, priors={})</code>","text":"<p>Sample a tree structure.</p> <p>Parameters:</p> Name Type Description Default <code>max_depth</code> <code>int</code> <p>the maximum depth of a tree</p> required <code>priors</code> <code>Dict</code> <p>priors in form of a dictionary. The keys are the tree structures as strings</p> <code>{}</code> <p>Examples:</p>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--set-seed-for-reproducibility","title":"Set seed for reproducibility","text":"<pre><code>&gt;&gt;&gt; np.random.seed(42)\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--sample-a-single-structure","title":"Sample a single structure","text":"<pre><code>&gt;&gt;&gt; sample_tree_structure_non_iso(7)\n[0, 1, 2, 3, 3, 2]\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--get-a-list-of-4-samples-with-max_depth-4","title":"Get a list of 4 samples with max_depth = 4","text":"<pre><code>&gt;&gt;&gt; [sample_tree_structure_non_iso(5) for _ in range(4)]\n[[0, 1, 2, 1, 2], [0, 1, 2, 3, 1], [0, 1, 2, 3, 3], [0, 1, 1]]\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--set-a-prior","title":"Set a prior","text":"<pre><code>&gt;&gt;&gt; [sample_tree_structure_non_iso(5, {'[0, 1, 1]': 1}) for _ in range(4)]\n[[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 1]]\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--set-a-different-prior","title":"Set a different prior","text":"<pre><code>&gt;&gt;&gt; [sample_tree_structure_non_iso(5, {'[0, 1, 1]': .5, '[0, 1, 2]': .5}) for _ in range(4)]\n[[0, 1, 1], [0, 1, 2], [0, 1, 1], [0, 1, 1]]\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--we-can-also-set-a-full-prior-here-the-max_depth-for-the-structure-is-3-which-only-allows","title":"We can also set a full prior( here the max_depth for the structure is 3 which only allows","text":""},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--for-two-structures-0-1-1-and-0-1-2","title":"for two structures: [0, 1, 1] and [0, 1, 2]","text":"<pre><code>&gt;&gt;&gt; [sample_tree_structure_non_iso(3, {'[0, 1, 1]': .3, '[0, 1, 2]': .7}) for _ in range(4)]\n[[0, 1, 2], [0, 1, 2], [0, 1, 2], [0, 1, 2]]\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--if-we-set-an-invalid-prior-an-exeption-is-raised-doctest-ellipsis","title":"If we set an invalid prior, an Exeption is raised  # doctest: +ELLIPSIS","text":"<pre><code>&gt;&gt;&gt; [sample_tree_structure_non_iso(3, {'[0, 1, 3]': .5}) for _ in range(4)]\nTraceback (most recent call last):\n...\nException: Priors {'[0, 1, 3]': 0.5} are not subset of space ['[0, 1, 2]', '[0, 1, 1]']\n</code></pre> Source code in <code>src/equation_tree/src/sample_tree_structure.py</code> <pre><code>def sample_tree_structure_non_iso(max_depth: int, priors: Dict = {}):\n    \"\"\"\n    Sample a tree structure.\n\n    Args:\n        max_depth: the maximum depth of a tree\n        priors: priors in form of a dictionary. The keys are the tree structures as strings\n\n    Examples:\n        # Set seed for reproducibility\n        &gt;&gt;&gt; np.random.seed(42)\n\n        # Sample a single structure\n        &gt;&gt;&gt; sample_tree_structure_non_iso(7)\n        [0, 1, 2, 3, 3, 2]\n\n        # Get a list of 4 samples with max_depth = 4\n        &gt;&gt;&gt; [sample_tree_structure_non_iso(5) for _ in range(4)]\n        [[0, 1, 2, 1, 2], [0, 1, 2, 3, 1], [0, 1, 2, 3, 3], [0, 1, 1]]\n\n        # Set a prior\n        &gt;&gt;&gt; [sample_tree_structure_non_iso(5, {'[0, 1, 1]': 1}) for _ in range(4)]\n        [[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 1]]\n\n        # Set a different prior\n        &gt;&gt;&gt; [sample_tree_structure_non_iso(5, {'[0, 1, 1]': .5, '[0, 1, 2]': .5}) for _ in range(4)]\n        [[0, 1, 1], [0, 1, 2], [0, 1, 1], [0, 1, 1]]\n\n        # We can also set a full prior( here the max_depth for the structure is 3 which only allows\n        # for two structures: [0, 1, 1] and [0, 1, 2]\n        &gt;&gt;&gt; [sample_tree_structure_non_iso(3, {'[0, 1, 1]': .3, '[0, 1, 2]': .7}) for _ in range(4)]\n        [[0, 1, 2], [0, 1, 2], [0, 1, 2], [0, 1, 2]]\n\n        # If we set an invalid prior, an Exeption is raised  # doctest: +ELLIPSIS\n        &gt;&gt;&gt; [sample_tree_structure_non_iso(3, {'[0, 1, 3]': .5}) for _ in range(4)]\n        Traceback (most recent call last):\n        ...\n        Exception: Priors {'[0, 1, 3]': 0.5} are not subset of space ['[0, 1, 2]', '[0, 1, 1]']\n\n    \"\"\"\n    tree_structures = _gen_all_tree_structures_non_iso(max_depth)\n\n    priors = set_priors(priors, [str(structure) for structure in tree_structures])\n    probabilities = [priors[key] for key in priors.keys()]\n\n    for _ in range(MAX_ITER):\n        sample_index = np.random.choice(len(tree_structures), p=probabilities)\n        tree_structure = tree_structures[sample_index]\n        if not _is_binary_tree(tree_structure):\n            warnings.warn(\n                \"Found a non binary tree structure, \"\n                \"this might lead to discrepancies between set priors and sample frequencies.\"\n            )\n            continue\n        return tree_structure\n    raise Exception(f\"Could not generate tree structure with max depth {max_depth}\")\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/","title":"Tree node","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.TreeNode","title":"<code>TreeNode</code>","text":"Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>class TreeNode:\n    def __init__(\n        self,\n        left=None,\n        right=None,\n        kind=NodeKind.NONE,\n        attribute=\"\",\n    ):\n        \"\"\"\n        Examples:\n            &gt;&gt;&gt; gc_1 = TreeNode(attribute='grand_child_1')\n            &gt;&gt;&gt; gc_1.size\n            1\n            &gt;&gt;&gt; child_1 = TreeNode(attribute='child_1', left=gc_1)\n            &gt;&gt;&gt; child_1.size\n            2\n            &gt;&gt;&gt; child_2 = TreeNode(attribute='child_2')\n            &gt;&gt;&gt; child_2.size\n            1\n            &gt;&gt;&gt; root = TreeNode(left=child_1,right=child_2,attribute='root')\n            &gt;&gt;&gt; root.size\n            4\n        \"\"\"\n\n        self.attribute = attribute\n        self.kind = kind\n        self.parent = None\n        self.left = left\n        self.right = right\n        self.evaluation = 0\n\n        self.children = []\n        if left is not None:\n            self.children.append(left)\n            left.parent = self\n        if right is not None:\n            self.children.append(right)\n            right.parent = self\n        self.is_leaf = self.children == []\n\n    def check_validity(\n        self,\n        zero_representations=[\"0\"],\n        log_representations=[\"log\", \"Log\"],\n        division_representations=[\"/\", \":\"],\n        verbose=False,\n    ):\n        return check_node_validity(\n            self,\n            zero_representations,\n            log_representations,\n            division_representations,\n            verbose,\n        )\n\n    @property\n    def size(self):\n        s_ = 1\n        for c in self.children:\n            s_ += c.size\n        return s_\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.TreeNode.__init__","title":"<code>__init__(left=None, right=None, kind=NodeKind.NONE, attribute='')</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; gc_1 = TreeNode(attribute='grand_child_1')\n&gt;&gt;&gt; gc_1.size\n1\n&gt;&gt;&gt; child_1 = TreeNode(attribute='child_1', left=gc_1)\n&gt;&gt;&gt; child_1.size\n2\n&gt;&gt;&gt; child_2 = TreeNode(attribute='child_2')\n&gt;&gt;&gt; child_2.size\n1\n&gt;&gt;&gt; root = TreeNode(left=child_1,right=child_2,attribute='root')\n&gt;&gt;&gt; root.size\n4\n</code></pre> Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>def __init__(\n    self,\n    left=None,\n    right=None,\n    kind=NodeKind.NONE,\n    attribute=\"\",\n):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; gc_1 = TreeNode(attribute='grand_child_1')\n        &gt;&gt;&gt; gc_1.size\n        1\n        &gt;&gt;&gt; child_1 = TreeNode(attribute='child_1', left=gc_1)\n        &gt;&gt;&gt; child_1.size\n        2\n        &gt;&gt;&gt; child_2 = TreeNode(attribute='child_2')\n        &gt;&gt;&gt; child_2.size\n        1\n        &gt;&gt;&gt; root = TreeNode(left=child_1,right=child_2,attribute='root')\n        &gt;&gt;&gt; root.size\n        4\n    \"\"\"\n\n    self.attribute = attribute\n    self.kind = kind\n    self.parent = None\n    self.left = left\n    self.right = right\n    self.evaluation = 0\n\n    self.children = []\n    if left is not None:\n        self.children.append(left)\n        left.parent = self\n    if right is not None:\n        self.children.append(right)\n        right.parent = self\n    self.is_leaf = self.children == []\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.edit_distance","title":"<code>edit_distance(tree_a, tree_b)</code>","text":"<p>Computes the tree edit distance between trees A and B</p> Implements the algorithm described here <p><code>Zhang, K., &amp; Shasha, D. (1989). Simple fast algorithms for the editing distance between trees and related problems. SIAM journal on computing, 18(6), 1245-1262.</code></p> <p>Inspired and adjusted(simplified) for the purpose of this repository from:     <code>https://github.com/timtadh/zhang-shasha</code></p> <p>Parameters:</p> Name Type Description Default <code>tree_a</code> <code>TreeNode</code> <p>Root of tree A</p> required <code>tree_b</code> <code>TreeNode</code> <p>Root of tree B</p> required Return <p>An integer distance [0, inf+)</p> <p>Examples:     &gt;&gt;&gt; gc_1_a = TreeNode(attribute='grand_child_1')     &gt;&gt;&gt; gc_1_b = TreeNode(attribute='grand_child_1')     &gt;&gt;&gt; edit_distance(gc_1_a, gc_1_b)     0     &gt;&gt;&gt; child_1_a = TreeNode(attribute='child_1', left=gc_1_a)     &gt;&gt;&gt; child_1_b = TreeNode(attribute='child_1_', left=gc_1_b)     &gt;&gt;&gt; edit_distance(child_1_a, child_1_b)     1     &gt;&gt;&gt; child_2_a = TreeNode(attribute='child_2')     &gt;&gt;&gt; child_2_b = TreeNode(attribute='child_2')     &gt;&gt;&gt; edit_distance(child_2_a, child_2_b)     0     &gt;&gt;&gt; root_a = TreeNode(attribute='root', left=child_1_a, right=child_2_a)     &gt;&gt;&gt; root_b = TreeNode(attribute='root', left=child_1_b, right=child_2_b)     &gt;&gt;&gt; edit_distance(root_a, root_b)     1     &gt;&gt;&gt; root_a_ = TreeNode(attribute='root', left=child_2_a, right=child_1_a)     &gt;&gt;&gt; edit_distance(root_a, root_a_)     2     &gt;&gt;&gt; edit_distance(root_a_, root_b)     3</p> Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>def edit_distance(tree_a: TreeNode, tree_b: TreeNode):\n    \"\"\"\n    Computes the tree edit distance between trees A and B\n\n    Implements the algorithm described here:\n        `Zhang, K., &amp; Shasha, D. (1989).\n        Simple fast algorithms for the editing distance between trees and related problems.\n        SIAM journal on computing, 18(6), 1245-1262.`\n    Inspired and adjusted(simplified) for the purpose of this repository from:\n        `https://github.com/timtadh/zhang-shasha`\n\n    Args:\n        tree_a: Root of tree A\n        tree_b: Root of tree B\n\n    Return:\n        An integer distance [0, inf+)\n    Examples:\n        &gt;&gt;&gt; gc_1_a = TreeNode(attribute='grand_child_1')\n        &gt;&gt;&gt; gc_1_b = TreeNode(attribute='grand_child_1')\n        &gt;&gt;&gt; edit_distance(gc_1_a, gc_1_b)\n        0\n        &gt;&gt;&gt; child_1_a = TreeNode(attribute='child_1', left=gc_1_a)\n        &gt;&gt;&gt; child_1_b = TreeNode(attribute='child_1_', left=gc_1_b)\n        &gt;&gt;&gt; edit_distance(child_1_a, child_1_b)\n        1\n        &gt;&gt;&gt; child_2_a = TreeNode(attribute='child_2')\n        &gt;&gt;&gt; child_2_b = TreeNode(attribute='child_2')\n        &gt;&gt;&gt; edit_distance(child_2_a, child_2_b)\n        0\n        &gt;&gt;&gt; root_a = TreeNode(attribute='root', left=child_1_a, right=child_2_a)\n        &gt;&gt;&gt; root_b = TreeNode(attribute='root', left=child_1_b, right=child_2_b)\n        &gt;&gt;&gt; edit_distance(root_a, root_b)\n        1\n        &gt;&gt;&gt; root_a_ = TreeNode(attribute='root', left=child_2_a, right=child_1_a)\n        &gt;&gt;&gt; edit_distance(root_a, root_a_)\n        2\n        &gt;&gt;&gt; edit_distance(root_a_, root_b)\n        3\n\n    \"\"\"\n    tree_a_helper = _HelperTree(tree_a)\n    tree_b_helper = _HelperTree(tree_b)\n\n    treedists = np.zeros((tree_a.size, tree_b.size), float)\n\n    def update_cost(node_a, node_b):\n        return int(node_a.attribute != node_b.attribute)\n\n    def treedist(i, j):\n        al = tree_a_helper.lmds\n        bl = tree_b_helper.lmds\n\n        an = tree_a_helper.nodes\n        bn = tree_b_helper.nodes\n\n        m = i - al[i] + 2\n        n = j - bl[j] + 2\n\n        ioff = al[i] - 1\n        joff = bl[j] - 1\n\n        # Initialize the fd array\n        fd = np.zeros((m, n), float)\n        fd[1:, 0] = np.arange(1, m)\n        fd[0, 1:] = np.arange(1, n)\n\n        partial_ops = [[([1] if x == 0 else []) for x in range(n)] for _ in range(m)]\n\n        for x in range(1, m):\n            for y in range(1, n):\n                if al[i] == al[x + ioff] and bl[j] == bl[y + joff]:\n                    costs = [\n                        fd[x - 1][y] + 1,\n                        fd[x][y - 1] + 1,\n                        fd[x - 1][y - 1] + update_cost(an[x + ioff], bn[y + joff]),\n                    ]\n                    fd[x][y] = min(costs)\n                    min_index = costs.index(fd[x][y])\n                    if min_index == 0:\n                        partial_ops[x][y] = partial_ops[x - 1][y] + [1]\n                    elif min_index == 1:\n                        partial_ops[x][y] = partial_ops[x][y - 1] + [1]\n                    else:\n                        partial_ops[x][y] = partial_ops[x - 1][y - 1] + [1]\n\n                    treedists[x + ioff][y + joff] = fd[x][y]\n                else:\n                    p = al[x + ioff] - 1 - ioff\n                    q = bl[y + joff] - 1 - joff\n                    costs = [\n                        fd[x - 1][y] + 1,\n                        fd[x][y - 1] + 1,\n                        fd[p][q] + treedists[x + ioff][y + joff],\n                    ]\n                    fd[x][y] = min(costs)\n                    min_index = costs.index(fd[x][y])\n                    if min_index == 0:\n                        partial_ops[x][y] = partial_ops[x - 1][y] + [1]\n                    elif min_index == 1:\n                        partial_ops[x][y] = partial_ops[x][y - 1] + [1]\n                    else:\n                        partial_ops[x][y] = partial_ops[p][q] + [1]\n\n    for i in tree_a_helper.keyroots:\n        for j in tree_b_helper.keyroots:\n            treedist(i, j)\n    return int(treedists[-1][-1])\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.ned","title":"<code>ned(tree_a, tree_b)</code>","text":"<p>Normalized tree edit distance according to: <code>Li, Y., &amp; Chenguang, Z. (2011). A metric normalization of tree edit distance. Frontiers of Computer Science in China, 5, 119-125.</code> Examples:     &gt;&gt;&gt; gc_1_a = TreeNode(attribute='grand_child_1')     &gt;&gt;&gt; gc_1_b = TreeNode(attribute='grand_child_1')     &gt;&gt;&gt; ned(gc_1_a, gc_1_b)     0.0     &gt;&gt;&gt; child_1_a = TreeNode(attribute='child_1', left=gc_1_a)     &gt;&gt;&gt; child_1_b = TreeNode(attribute='child_1_', left=gc_1_b)     &gt;&gt;&gt; ned(child_1_a, child_1_b)     0.4     &gt;&gt;&gt; child_2_a = TreeNode(attribute='child_2')     &gt;&gt;&gt; child_2_b = TreeNode(attribute='child_2')     &gt;&gt;&gt; ned(child_2_a, child_2_b)     0.0     &gt;&gt;&gt; root_a = TreeNode(attribute='root', left=child_1_a, right=child_2_a)     &gt;&gt;&gt; root_b = TreeNode(attribute='root', left=child_1_b, right=child_2_b)     &gt;&gt;&gt; ned(root_a, root_b)     0.2222222222222222     &gt;&gt;&gt; root_a_ = TreeNode(attribute='root', left=child_2_a, right=child_1_a)     &gt;&gt;&gt; ned(root_a, root_a_)     0.4     &gt;&gt;&gt; ned(root_a_, root_b)     0.5454545454545454</p> Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>def ned(tree_a: TreeNode, tree_b: TreeNode):\n    \"\"\"\n    Normalized tree edit distance according to:\n    `Li, Y., &amp; Chenguang, Z. (2011). A metric normalization of tree edit distance.\n    Frontiers of Computer Science in China, 5, 119-125.`\n    Examples:\n        &gt;&gt;&gt; gc_1_a = TreeNode(attribute='grand_child_1')\n        &gt;&gt;&gt; gc_1_b = TreeNode(attribute='grand_child_1')\n        &gt;&gt;&gt; ned(gc_1_a, gc_1_b)\n        0.0\n        &gt;&gt;&gt; child_1_a = TreeNode(attribute='child_1', left=gc_1_a)\n        &gt;&gt;&gt; child_1_b = TreeNode(attribute='child_1_', left=gc_1_b)\n        &gt;&gt;&gt; ned(child_1_a, child_1_b)\n        0.4\n        &gt;&gt;&gt; child_2_a = TreeNode(attribute='child_2')\n        &gt;&gt;&gt; child_2_b = TreeNode(attribute='child_2')\n        &gt;&gt;&gt; ned(child_2_a, child_2_b)\n        0.0\n        &gt;&gt;&gt; root_a = TreeNode(attribute='root', left=child_1_a, right=child_2_a)\n        &gt;&gt;&gt; root_b = TreeNode(attribute='root', left=child_1_b, right=child_2_b)\n        &gt;&gt;&gt; ned(root_a, root_b)\n        0.2222222222222222\n        &gt;&gt;&gt; root_a_ = TreeNode(attribute='root', left=child_2_a, right=child_1_a)\n        &gt;&gt;&gt; ned(root_a, root_a_)\n        0.4\n        &gt;&gt;&gt; ned(root_a_, root_b)\n        0.5454545454545454\n    \"\"\"\n    ed = edit_distance(tree_a, tree_b)\n    return 2 * ed / (tree_a.size + tree_b.size + ed)\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.node_from_prefix","title":"<code>node_from_prefix(prefix_notation, function_test=lambda : False, operator_test=lambda : False, variable_test=lambda : False, constant_test=lambda : False)</code>","text":"<p>Create a tree from a prefix notation</p> <p>Parameters:</p> Name Type Description Default <code>prefix_notation</code> <code>List[str]</code> <p>The equation in prefix notation</p> required <code>function_test</code> <code>Callable</code> <p>A function that tests if the attribute is a function</p> <code>lambda : False</code> <code>operator_test</code> <code>Callable</code> <p>A function that tests if the attribute is an operator</p> <code>lambda : False</code> <code>variable_test</code> <code>Callable</code> <p>A function that tests if the attribute is a variable</p> <code>lambda : False</code> <code>constant_test</code> <code>Callable</code> <p>A function that tests if the attribute is a constant</p> <code>lambda : False</code> <p>Examples:</p>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.node_from_prefix--the-equation-is-a-single-variable-the-test-for-variables-is-a-check-in-a-hard","title":"The equation is a single variable. The test for variables is a check in a hard","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.node_from_prefix--coded-list","title":"coded list","text":"<pre><code>&gt;&gt;&gt; tree = node_from_prefix(['x'], variable_test=lambda x: 'x' in ['x', 'y', 'z'])\n&gt;&gt;&gt; tree.kind == NodeKind.VARIABLE\nTrue\n&gt;&gt;&gt; tree.attribute\n'x'\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.node_from_prefix--we-can-also-use-more-elaborate-tests-depending-for-example-checking-weather-the","title":"We can also use more elaborate tests depending. For example checking, weather the","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.node_from_prefix--attribute-contains-an-underscore","title":"attribute contains an underscore","text":"<pre><code>&gt;&gt;&gt; tree = node_from_prefix(\n...     prefix_notation=['sin', 'x_1'],\n...     function_test=lambda x: x in ['sin', 'cos'],\n...     variable_test=lambda x: '_' in x)\n&gt;&gt;&gt; tree.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; tree.attribute\n'sin'\n&gt;&gt;&gt; tree.left.kind == NodeKind.VARIABLE\nTrue\n&gt;&gt;&gt; tree.left.attribute\n'x_1'\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.node_from_prefix--we-can-also-pass-other-functions","title":"We can also pass other functions","text":"<pre><code>&gt;&gt;&gt; def is_variable(x):\n...     return x == 'x' or x == 'y'\n&gt;&gt;&gt; def is_operator(x):\n...     return not is_variable(x) and len(x) == 1\n&gt;&gt;&gt; def is_function(x):\n...     return not is_variable(x) and not is_operator(x)\n&gt;&gt;&gt; tree = node_from_prefix(\n...     prefix_notation=['+', 'sin', 'x', 'cos', 'y'],\n...     variable_test=is_variable,\n...     operator_test=is_operator,\n...     function_test=is_function\n...     )\n&gt;&gt;&gt; tree.kind == NodeKind.OPERATOR\nTrue\n&gt;&gt;&gt; tree.attribute\n'+'\n&gt;&gt;&gt; tree.left.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; tree.left.attribute\n'sin'\n&gt;&gt;&gt; tree.left.left.kind == NodeKind.VARIABLE\nTrue\n&gt;&gt;&gt; tree.left.left.attribute\n'x'\n&gt;&gt;&gt; tree.right.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; tree.right.attribute\n'cos'\n&gt;&gt;&gt; tree.right.left.kind == NodeKind.VARIABLE\nTrue\n&gt;&gt;&gt; tree.right.left.attribute\n'y'\n</code></pre> Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>def node_from_prefix(\n    prefix_notation: List[str],\n    function_test: Callable = lambda _: False,\n    operator_test: Callable = lambda _: False,\n    variable_test: Callable = lambda _: False,\n    constant_test: Callable = lambda _: False,\n):\n    \"\"\"\n    Create a tree from a prefix notation\n\n    Args:\n        prefix_notation: The equation in prefix notation\n        function_test: A function that tests if the attribute is a function\n        operator_test: A function that tests if the attribute is an operator\n        variable_test: A function that tests if the attribute is a variable\n        constant_test: A function that tests if the attribute is a constant\n\n    Examples:\n        # The equation is a single variable. The test for variables is a check in a hard\n        # coded list\n        &gt;&gt;&gt; tree = node_from_prefix(['x'], variable_test=lambda x: 'x' in ['x', 'y', 'z'])\n        &gt;&gt;&gt; tree.kind == NodeKind.VARIABLE\n        True\n        &gt;&gt;&gt; tree.attribute\n        'x'\n\n        # We can also use more elaborate tests depending. For example checking, weather the\n        # attribute contains an underscore\n        &gt;&gt;&gt; tree = node_from_prefix(\n        ...     prefix_notation=['sin', 'x_1'],\n        ...     function_test=lambda x: x in ['sin', 'cos'],\n        ...     variable_test=lambda x: '_' in x)\n        &gt;&gt;&gt; tree.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; tree.attribute\n        'sin'\n        &gt;&gt;&gt; tree.left.kind == NodeKind.VARIABLE\n        True\n        &gt;&gt;&gt; tree.left.attribute\n        'x_1'\n\n        # We can also pass other functions\n        &gt;&gt;&gt; def is_variable(x):\n        ...     return x == 'x' or x == 'y'\n        &gt;&gt;&gt; def is_operator(x):\n        ...     return not is_variable(x) and len(x) == 1\n        &gt;&gt;&gt; def is_function(x):\n        ...     return not is_variable(x) and not is_operator(x)\n        &gt;&gt;&gt; tree = node_from_prefix(\n        ...     prefix_notation=['+', 'sin', 'x', 'cos', 'y'],\n        ...     variable_test=is_variable,\n        ...     operator_test=is_operator,\n        ...     function_test=is_function\n        ...     )\n        &gt;&gt;&gt; tree.kind == NodeKind.OPERATOR\n        True\n        &gt;&gt;&gt; tree.attribute\n        '+'\n        &gt;&gt;&gt; tree.left.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; tree.left.attribute\n        'sin'\n        &gt;&gt;&gt; tree.left.left.kind == NodeKind.VARIABLE\n        True\n        &gt;&gt;&gt; tree.left.left.attribute\n        'x'\n        &gt;&gt;&gt; tree.right.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; tree.right.attribute\n        'cos'\n        &gt;&gt;&gt; tree.right.left.kind == NodeKind.VARIABLE\n        True\n        &gt;&gt;&gt; tree.right.left.attribute\n        'y'\n\n    \"\"\"\n    node, _ = _from_prefix_recursion(\n        prefix_notation, function_test, operator_test, variable_test, constant_test\n    )\n\n    return node\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full","title":"<code>sample_tree_full(prior, max_var_unique)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; np.random.seed(42)\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full--we-can-set-priors-for-features-functions-operators","title":"We can set priors for features, functions, operators","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full--and-also-conditionals-based-the-parent","title":"and also conditionals based the parent","text":"<pre><code>&gt;&gt;&gt; p = {\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .2, 'variables': .8},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': 1., '-': .0},\n...     'function_conditionals': {\n...                             'sin': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': 0., 'cos': 1.},\n...                                 'operators': {'+': 0., '-': 1.}\n...                             },\n...                             'cos': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'cos': 1., 'sin': 0.},\n...                                 'operators': {'+': 0., '-': 1.}\n...                             }\n...                         },\n...     'operator_conditionals': {\n...                             '+': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': 1., 'cos': 0.},\n...                                 'operators': {'+': 1., '-': 0.}\n...                             },\n...                             '-': {\n...                                 'features': {'constants': .3, 'variables': .7},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .9, '-': .1}\n...                             }\n...                         },\n... }\n&gt;&gt;&gt; sample = sample_tree_full(p, 3)\n&gt;&gt;&gt; sample.attribute\n'cos'\n&gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.left.attribute\n'cos'\n&gt;&gt;&gt; sample.left.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.right is None\nTrue\n&gt;&gt;&gt; sample = sample_tree_full(p, 3)\n&gt;&gt;&gt; sample.attribute\n'sin'\n&gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.left.attribute\n'cos'\n&gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.left.left.attribute\n'x_1'\n&gt;&gt;&gt; sample.left.left.kind == NodeKind.VARIABLE\nTrue\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full--if-we-dont-provide-priors-for-the-conditionals","title":"If we don't provide priors for the conditionals,","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full--the-fallback-is-the-unconditioned-priors","title":"the fallback is the unconditioned priors","text":"<pre><code>&gt;&gt;&gt; p = {'max_depth': 8,\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .2, 'variables': .8},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': .5, '-': .5},\n... }\n&gt;&gt;&gt; sample = sample_tree_full(p, 3)\n&gt;&gt;&gt; sample.attribute\n'-'\n&gt;&gt;&gt; sample.kind == NodeKind.OPERATOR\nTrue\n&gt;&gt;&gt; sample.right.attribute\n'x_1'\n&gt;&gt;&gt; sample.left.attribute\n'x_1'\n&gt;&gt;&gt; sample.left.kind == NodeKind.VARIABLE\nTrue\n</code></pre> Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>def sample_tree_full(prior, max_var_unique):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; np.random.seed(42)\n\n        # We can set priors for features, functions, operators\n        # and also conditionals based the parent\n        &gt;&gt;&gt; p = {\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .2, 'variables': .8},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': 1., '-': .0},\n        ...     'function_conditionals': {\n        ...                             'sin': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': 0., 'cos': 1.},\n        ...                                 'operators': {'+': 0., '-': 1.}\n        ...                             },\n        ...                             'cos': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'cos': 1., 'sin': 0.},\n        ...                                 'operators': {'+': 0., '-': 1.}\n        ...                             }\n        ...                         },\n        ...     'operator_conditionals': {\n        ...                             '+': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': 1., 'cos': 0.},\n        ...                                 'operators': {'+': 1., '-': 0.}\n        ...                             },\n        ...                             '-': {\n        ...                                 'features': {'constants': .3, 'variables': .7},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .9, '-': .1}\n        ...                             }\n        ...                         },\n        ... }\n        &gt;&gt;&gt; sample = sample_tree_full(p, 3)\n        &gt;&gt;&gt; sample.attribute\n        'cos'\n        &gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.left.attribute\n        'cos'\n        &gt;&gt;&gt; sample.left.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.right is None\n        True\n        &gt;&gt;&gt; sample = sample_tree_full(p, 3)\n        &gt;&gt;&gt; sample.attribute\n        'sin'\n        &gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.left.attribute\n        'cos'\n        &gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.left.left.attribute\n        'x_1'\n        &gt;&gt;&gt; sample.left.left.kind == NodeKind.VARIABLE\n        True\n\n        # If we don't provide priors for the conditionals,\n        # the fallback is the unconditioned priors\n        &gt;&gt;&gt; p = {'max_depth': 8,\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .2, 'variables': .8},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': .5, '-': .5},\n        ... }\n        &gt;&gt;&gt; sample = sample_tree_full(p, 3)\n        &gt;&gt;&gt; sample.attribute\n        '-'\n        &gt;&gt;&gt; sample.kind == NodeKind.OPERATOR\n        True\n        &gt;&gt;&gt; sample.right.attribute\n        'x_1'\n        &gt;&gt;&gt; sample.left.attribute\n        'x_1'\n        &gt;&gt;&gt; sample.left.kind == NodeKind.VARIABLE\n        True\n\n    \"\"\"\n    tree_structure = sample_tree_structure(prior[\"structures\"])\n    function_conditionals = None\n    operator_conditionals = None\n    if \"function_conditionals\" in prior.keys():\n        function_conditionals = prior[\"function_conditionals\"]\n    if \"operator_conditionals\" in prior.keys():\n        operator_conditionals = prior[\"operator_conditionals\"]\n\n    tree = sample_equation_tree_from_structure_with_conditionals(\n        tree_structure,\n        0,\n        prior[\"features\"],\n        prior[\"functions\"],\n        function_conditionals,\n        prior[\"operators\"],\n        operator_conditionals,\n    )\n    post(tree, max_var_unique)\n    return tree\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full_fast","title":"<code>sample_tree_full_fast(prior, tree_depth, max_var_unique)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; np.random.seed(42)\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full_fast--we-can-set-priors-for-features-functions-operators","title":"We can set priors for features, functions, operators","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full_fast--and-also-conditionals-based-the-parent","title":"and also conditionals based the parent","text":"<pre><code>&gt;&gt;&gt; p = {\n...     'features': {'constants': .2, 'variables': .8},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': 1., '-': .0},\n...     'function_conditionals': {\n...                             'sin': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': 0., 'cos': 1.},\n...                                 'operators': {'+': 0., '-': 1.}\n...                             },\n...                             'cos': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'cos': 1., 'sin': 0.},\n...                                 'operators': {'+': 0., '-': 1.}\n...                             }\n...                         },\n...     'operator_conditionals': {\n...                             '+': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': 1., 'cos': 0.},\n...                                 'operators': {'+': 1., '-': 0.}\n...                             },\n...                             '-': {\n...                                 'features': {'constants': .3, 'variables': .7},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .9, '-': .1}\n...                             }\n...                         },\n... }\n&gt;&gt;&gt; sample = sample_tree_full_fast(p, 3, 2)\n&gt;&gt;&gt; sample.attribute\n'cos'\n&gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.left.attribute\n'cos'\n&gt;&gt;&gt; sample.left.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.right is None\nTrue\n&gt;&gt;&gt; sample = sample_tree_full_fast(p, 4, 3)\n&gt;&gt;&gt; sample.attribute\n'sin'\n&gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.left.attribute\n'-'\n&gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.left.left.attribute\n'x_1'\n&gt;&gt;&gt; sample.left.left.kind == NodeKind.VARIABLE\nTrue\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full_fast--if-we-dont-provide-priors-for-the-conditionals","title":"If we don't provide priors for the conditionals,","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full_fast--the-fallback-is-the-unconditioned-priors","title":"the fallback is the unconditioned priors","text":"<pre><code>&gt;&gt;&gt; p = {'max_depth': 8,\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .2, 'variables': .8},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': .5, '-': .5},\n... }\n&gt;&gt;&gt; sample = sample_tree_full_fast(p, 5, 3)\n&gt;&gt;&gt; sample.attribute\n'-'\n&gt;&gt;&gt; sample.kind == NodeKind.OPERATOR\nTrue\n&gt;&gt;&gt; sample.right.attribute\n'cos'\n&gt;&gt;&gt; sample.left.attribute\n'sin'\n&gt;&gt;&gt; sample.left.kind == NodeKind.FUNCTION\nTrue\n</code></pre> Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>def sample_tree_full_fast(prior, tree_depth, max_var_unique):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; np.random.seed(42)\n\n        # We can set priors for features, functions, operators\n        # and also conditionals based the parent\n        &gt;&gt;&gt; p = {\n        ...     'features': {'constants': .2, 'variables': .8},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': 1., '-': .0},\n        ...     'function_conditionals': {\n        ...                             'sin': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': 0., 'cos': 1.},\n        ...                                 'operators': {'+': 0., '-': 1.}\n        ...                             },\n        ...                             'cos': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'cos': 1., 'sin': 0.},\n        ...                                 'operators': {'+': 0., '-': 1.}\n        ...                             }\n        ...                         },\n        ...     'operator_conditionals': {\n        ...                             '+': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': 1., 'cos': 0.},\n        ...                                 'operators': {'+': 1., '-': 0.}\n        ...                             },\n        ...                             '-': {\n        ...                                 'features': {'constants': .3, 'variables': .7},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .9, '-': .1}\n        ...                             }\n        ...                         },\n        ... }\n        &gt;&gt;&gt; sample = sample_tree_full_fast(p, 3, 2)\n        &gt;&gt;&gt; sample.attribute\n        'cos'\n        &gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.left.attribute\n        'cos'\n        &gt;&gt;&gt; sample.left.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.right is None\n        True\n        &gt;&gt;&gt; sample = sample_tree_full_fast(p, 4, 3)\n        &gt;&gt;&gt; sample.attribute\n        'sin'\n        &gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.left.attribute\n        '-'\n        &gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.left.left.attribute\n        'x_1'\n        &gt;&gt;&gt; sample.left.left.kind == NodeKind.VARIABLE\n        True\n\n        # If we don't provide priors for the conditionals,\n        # the fallback is the unconditioned priors\n        &gt;&gt;&gt; p = {'max_depth': 8,\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .2, 'variables': .8},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': .5, '-': .5},\n        ... }\n        &gt;&gt;&gt; sample = sample_tree_full_fast(p, 5, 3)\n        &gt;&gt;&gt; sample.attribute\n        '-'\n        &gt;&gt;&gt; sample.kind == NodeKind.OPERATOR\n        True\n        &gt;&gt;&gt; sample.right.attribute\n        'cos'\n        &gt;&gt;&gt; sample.left.attribute\n        'sin'\n        &gt;&gt;&gt; sample.left.kind == NodeKind.FUNCTION\n        True\n\n    \"\"\"\n    tree_structure = sample_tree_structure_fast(tree_depth)\n    function_conditionals = None\n    operator_conditionals = None\n    if \"function_conditionals\" in prior.keys():\n        function_conditionals = prior[\"function_conditionals\"]\n    if \"operator_conditionals\" in prior.keys():\n        operator_conditionals = prior[\"operator_conditionals\"]\n\n    tree = sample_equation_tree_from_structure_with_conditionals(\n        tree_structure,\n        0,\n        prior[\"features\"],\n        prior[\"functions\"],\n        function_conditionals,\n        prior[\"operators\"],\n        operator_conditionals,\n    )\n    post(tree, max_var_unique)\n    return tree\n</code></pre>"},{"location":"reference/src/equation_tree/util/","title":"Util","text":""},{"location":"reference/src/equation_tree/util/conversions/","title":"Conversions","text":""},{"location":"reference/src/equation_tree/util/conversions/#src.equation_tree.util.conversions.func_to_op_const","title":"<code>func_to_op_const(expr)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; e_1 = 'x_1*cubed(x_1*3-squared(c_1/x_1*2)-x_3)-squared(x)'\n&gt;&gt;&gt; func_to_op_const(e_1)\n'x_1*(x_1*3-(c_1/x_1*2)**2-x_3)**3-(x)**2'\n&gt;&gt;&gt; func_to_op_const('cubed(x_1)')\n'(x_1)**3'\n</code></pre> Source code in <code>src/equation_tree/util/conversions.py</code> <pre><code>def func_to_op_const(expr):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; e_1 = 'x_1*cubed(x_1*3-squared(c_1/x_1*2)-x_3)-squared(x)'\n        &gt;&gt;&gt; func_to_op_const(e_1)\n        'x_1*(x_1*3-(c_1/x_1*2)**2-x_3)**3-(x)**2'\n        &gt;&gt;&gt; func_to_op_const('cubed(x_1)')\n        '(x_1)**3'\n    \"\"\"\n    for key, el in CONVERSIONS_FUNC_OP_CONST.items():\n        expr = _func_op_const_rec(expr, key, el)\n    return expr\n</code></pre>"},{"location":"reference/src/equation_tree/util/conversions/#src.equation_tree.util.conversions.infix_to_prefix","title":"<code>infix_to_prefix(infix, function_test, operator_test)</code>","text":"<p>Transforms prefix notation to infix notation</p> Example <p>is_function = lambda x: x in ['sin', 'cos'] is_operator = lambda x : x in ['+', '-', '*', '/'] infix_to_prefix('x_2-x_1', is_function, is_operator) ['-', 'x_2', 'x_1']</p> <p>infix_to_prefix('x_1-(x_2+x_4)', is_function, is_operator) ['-', 'x_1', '+', 'x_2', 'x_4']</p> <p>infix_to_prefix('x_1cos(c_1+x_2)', is_function, is_operator) ['', 'x_1', 'cos', '+', 'c_1', 'x_2']</p> <p>is_function = lambda x: x in ['sin', 'cos', 'e'] is_operator = lambda x: x in ['+', '-', '', '^', 'max', '*', '/'] infix_to_prefix('x_1 + max(x_2, x_3)', is_function, is_operator) ['+', 'x_1', 'max', 'x_2', 'x_3']</p> <p>infix_to_prefix('x_1-(x_2/(x_3-x_4))',is_function, is_operator) ['-', 'x_1', '/', 'x_2', '-', 'x_3', 'x_4']</p> <p>infix_to_prefix('x_1^(sin(x_2)/x_3)', is_function, is_operator) ['^', 'x_1', '/', 'sin', 'x_2', 'x_3']</p> <p>infix_to_prefix('sin(x_1)-x_2', is_function, is_operator) ['-', 'sin', 'x_1', 'x_2']</p> Source code in <code>src/equation_tree/util/conversions.py</code> <pre><code>def infix_to_prefix(infix, function_test, operator_test):\n    \"\"\"\n    Transforms prefix notation to infix notation\n\n    Example:\n        &gt;&gt;&gt; is_function = lambda x: x in ['sin', 'cos']\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '-', '*', '/']\n        &gt;&gt;&gt; infix_to_prefix('x_2-x_1', is_function, is_operator)\n        ['-', 'x_2', 'x_1']\n\n        &gt;&gt;&gt; infix_to_prefix('x_1-(x_2+x_4)', is_function, is_operator)\n        ['-', 'x_1', '+', 'x_2', 'x_4']\n\n        &gt;&gt;&gt; infix_to_prefix('x_1*cos(c_1+x_2)', is_function, is_operator)\n        ['*', 'x_1', 'cos', '+', 'c_1', 'x_2']\n\n        &gt;&gt;&gt; is_function = lambda x: x in ['sin', 'cos', 'e']\n        &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '^', 'max', '**', '/']\n        &gt;&gt;&gt; infix_to_prefix('x_1 + max(x_2, x_3)', is_function, is_operator)\n        ['+', 'x_1', 'max', 'x_2', 'x_3']\n\n        &gt;&gt;&gt; infix_to_prefix('x_1-(x_2/(x_3-x_4))',is_function, is_operator)\n        ['-', 'x_1', '/', 'x_2', '-', 'x_3', 'x_4']\n\n        &gt;&gt;&gt; infix_to_prefix('x_1^(sin(x_2)/x_3)', is_function, is_operator)\n        ['^', 'x_1', '/', 'sin', 'x_2', 'x_3']\n\n        &gt;&gt;&gt; infix_to_prefix('sin(x_1)-x_2', is_function, is_operator)\n        ['-', 'sin', 'x_1', 'x_2']\n    \"\"\"\n\n    # n = len(infix)\n\n    # infix = list(infix[::-1].lower())\n    #\n    # for i in range(n):\n    #     if infix[i] == \"(\":\n    #         infix[i] = \")\"\n    #     elif infix[i] == \")\":\n    #         infix[i] = \"(\"\n    #\n    # infix = \"\".join(infix)\n    postfix = _infix_to_postfix(infix, function_test, operator_test)\n    prefix = postfix[::-1]\n\n    return prefix\n</code></pre>"},{"location":"reference/src/equation_tree/util/conversions/#src.equation_tree.util.conversions.op_const_to_func","title":"<code>op_const_to_func(expr)</code>","text":"<p>Known operators with constants to functions. For exampl, e2-&gt;squared Examples:     &gt;&gt;&gt; op_const_to_func('x_1(x_13-(c_1/x_1*2)2-x_3)3-(x)2')     'x_1cubed(x_13-squared(c_1/x_12)-x_3)-squared(x)'     &gt;&gt;&gt; op_const_to_func('(x_1)3')     'cubed(x_1)'     &gt;&gt;&gt; op_const_to_func('x2')     'squared(x)'     &gt;&gt;&gt; op_const_to_func('c_13')     'cubed(c_1)'     &gt;&gt;&gt; op_const_to_func('(x_2*2)')     'squared(x_2)'</p> Source code in <code>src/equation_tree/util/conversions.py</code> <pre><code>def op_const_to_func(expr):\n    \"\"\"\n    Known operators with constants to functions. For exampl, e**2-&gt;squared\n    Examples:\n        &gt;&gt;&gt; op_const_to_func('x_1*(x_1*3-(c_1/x_1*2)**2-x_3)**3-(x)**2')\n        'x_1*cubed(x_1*3-squared(c_1/x_1*2)-x_3)-squared(x)'\n        &gt;&gt;&gt; op_const_to_func('(x_1)**3')\n        'cubed(x_1)'\n        &gt;&gt;&gt; op_const_to_func('x**2')\n        'squared(x)'\n        &gt;&gt;&gt; op_const_to_func('c_1**3')\n        'cubed(c_1)'\n        &gt;&gt;&gt; op_const_to_func('(x_2**2)')\n        'squared(x_2)'\n    \"\"\"\n\n    for key, el in CONVERSION_OP_CONST_FUNC.items():\n        expr = _op_const_func_rec(expr, key, el)\n    expr = _remove_unnecessary_parentheses(expr)\n\n    return expr\n</code></pre>"},{"location":"reference/src/equation_tree/util/conversions/#src.equation_tree.util.conversions.prefix_to_infix","title":"<code>prefix_to_infix(prefix, function_test=lambda : False, operator_test=lambda : False)</code>","text":"<p>Transforms prefix notation to infix notation</p> Example <p>is_function = lambda x: x in ['sin', 'cos'] is_operator = lambda x : x in ['+', '-', '', 'max', '*'] prefix_to_infix(['-', 'x_1', 'x_2'], is_function, is_operator) '(x_1-x_2)'</p> <p>prefix_to_infix( ...     ['', 'x', 'cos', '+', 'y', 'z'], is_function, is_operator) '(xcos((y+z)))'</p> <p>prefix_to_infix(['max', 'x_1', 'x_2'], is_function, is_operator) 'max(x_1,x_2)'</p> <p>prefix_to_infix(['', 'x_1', 'x_2'], is_function, is_operator) '(x_1x_2)'</p> Source code in <code>src/equation_tree/util/conversions.py</code> <pre><code>def prefix_to_infix(\n    prefix, function_test=lambda _: False, operator_test=lambda _: False\n):\n    \"\"\"\n    Transforms prefix notation to infix notation\n\n    Example:\n        &gt;&gt;&gt; is_function = lambda x: x in ['sin', 'cos']\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '-', '*', 'max', '**']\n        &gt;&gt;&gt; prefix_to_infix(['-', 'x_1', 'x_2'], is_function, is_operator)\n        '(x_1-x_2)'\n\n        &gt;&gt;&gt; prefix_to_infix(\n        ...     ['*', 'x', 'cos', '+', 'y', 'z'], is_function, is_operator)\n        '(x*cos((y+z)))'\n\n        &gt;&gt;&gt; prefix_to_infix(['max', 'x_1', 'x_2'], is_function, is_operator)\n        'max(x_1,x_2)'\n\n        &gt;&gt;&gt; prefix_to_infix(['**', 'x_1', 'x_2'], is_function, is_operator)\n        '(x_1**x_2)'\n\n    \"\"\"\n    stack = []\n    for i in range(len(prefix) - 1, -1, -1):\n        if function_test(prefix[i]):\n            # symbol in unary operator\n            stack.append(prefix[i] + \"(\" + stack.pop() + \")\")\n        elif (operator_test(prefix[i]) or prefix[i] == \"**\") and prefix[i] in [\n            \"+\",\n            \"-\",\n            \"/\",\n            \"^\",\n            \"*\",\n            \"**\",\n        ]:\n            # symbol is binary operator\n            str = \"(\" + stack.pop() + prefix[i] + stack.pop() + \")\"\n            stack.append(str)\n        elif operator_test(prefix[i]):\n            str = prefix[i] + \"(\" + stack.pop() + \",\" + stack.pop() + \")\"\n            stack.append(str)\n        else:\n            # symbol is operand\n            stack.append(prefix[i])\n    return stack.pop()\n</code></pre>"},{"location":"reference/src/equation_tree/util/conversions/#src.equation_tree.util.conversions.standardize_sympy","title":"<code>standardize_sympy(sympy_expr, variable_test=lambda : False, constant_test=lambda : False)</code>","text":"<p>replace all variables and constants with standards</p> Example <p>from sympy import sympify expr = sympify('x + A * cos(z+y)') expr A*cos(y + z) + x</p> <p>is_variable = lambda x : x in ['x', 'y', 'z'] is_constant = lambda x : x in ['A'] standardize_sympy(expr, is_variable, is_constant) c_1*cos(x_2 + x_3) + x_1</p> <p>expr = sympify('x_a+By') expr By + x_a is_variable = lambda x : '_' in x or x in ['y'] is_constant = lambda x : x == 'B' standardize_sympy(expr, is_variable, is_constant) c_1*x_2 + x_1</p> <p>expr = sympify('x ** x') expr xx is_variable = lambda x: x in ['x'] standardize_sympy(expr, is_variable) x_1x_1</p> <p>expr = sympify('sin(Cx) + cos(Cx)') expr sin(Cx) + cos(Cx)</p> <p>is_variable = lambda x: x == 'x' is_constant = lambda x: x == 'C' standardize_sympy(expr, is_variable, is_constant) sin(c_1x_1) + cos(c_1x_1)</p> Source code in <code>src/equation_tree/util/conversions.py</code> <pre><code>def standardize_sympy(\n    sympy_expr, variable_test=lambda _: False, constant_test=lambda _: False\n):\n    \"\"\"\n    replace all variables and constants with standards\n\n    Example:\n        &gt;&gt;&gt; from sympy import sympify\n        &gt;&gt;&gt; expr = sympify('x + A * cos(z+y)')\n        &gt;&gt;&gt; expr\n        A*cos(y + z) + x\n\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n        &gt;&gt;&gt; is_constant = lambda x : x in ['A']\n        &gt;&gt;&gt; standardize_sympy(expr, is_variable, is_constant)\n        c_1*cos(x_2 + x_3) + x_1\n\n        &gt;&gt;&gt; expr = sympify('x_a+B*y')\n        &gt;&gt;&gt; expr\n        B*y + x_a\n        &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n        &gt;&gt;&gt; is_constant = lambda x : x == 'B'\n        &gt;&gt;&gt; standardize_sympy(expr, is_variable, is_constant)\n        c_1*x_2 + x_1\n\n        &gt;&gt;&gt; expr = sympify('x ** x')\n        &gt;&gt;&gt; expr\n        x**x\n        &gt;&gt;&gt; is_variable = lambda x: x in ['x']\n        &gt;&gt;&gt; standardize_sympy(expr, is_variable)\n        x_1**x_1\n\n        &gt;&gt;&gt; expr = sympify('sin(C*x) + cos(C*x)')\n        &gt;&gt;&gt; expr\n        sin(C*x) + cos(C*x)\n\n        &gt;&gt;&gt; is_variable = lambda x: x == 'x'\n        &gt;&gt;&gt; is_constant = lambda x: x == 'C'\n        &gt;&gt;&gt; standardize_sympy(expr, is_variable, is_constant)\n        sin(c_1*x_1) + cos(c_1*x_1)\n    \"\"\"\n    variable_count = 0\n    constant_count = 0\n    variables = {}\n    constants = {}\n\n    def replace_symbols(node):\n        nonlocal variable_count, constant_count, variables, constants\n        if variable_test(str(node)):\n            if not str(node) in variables.keys():\n                variable_count += 1\n                new_symbol = symbols(f\"x_{variable_count}\")\n                variables[str(node)] = new_symbol\n            else:\n                new_symbol = variables[str(node)]\n            return new_symbol\n        elif constant_test(str(node)) and not is_numeric(str(node)):\n            if not str(node) in constants.keys():\n                constant_count += 1\n                new_symbol = symbols(f\"c_{constant_count}\")\n                constants[str(node)] = new_symbol\n            else:\n                new_symbol = constants[str(node)]\n            return new_symbol\n        else:\n            return node\n\n    def recursive_replace(node):\n        if node.is_Function or node.is_Add or node.is_Mul or node.is_Pow:\n            return node.func(*[recursive_replace(arg) for arg in node.args])\n        return replace_symbols(node)\n\n    new_expression = recursive_replace(sympy_expr)\n    return new_expression\n</code></pre>"},{"location":"reference/src/equation_tree/util/conversions/#src.equation_tree.util.conversions.unary_minus_to_binary","title":"<code>unary_minus_to_binary(expr, operator_test)</code>","text":"<p>replace unary minus with binary</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; o = lambda x: x in ['+', '-', '*', '/', '^']\n&gt;&gt;&gt; unary_minus_to_binary('-x_1+x_2', o)\n'x_2-x_1'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('x_1-x_2', o)\n'x_1-x_2'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('x_1+(-x_2+x_3)', o)\n'x_1+(x_3-x_2)'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('-tan(x_1-exp(x_2))', o)\n'(0-tan(x_1-exp(x_2)))'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('-x_2', o)\n'(0-x_2)'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('exp(-x_1)*log(x_2)', o)\n'exp((0-x_1))*log(x_2)'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('(c_1 + x_2)*(-c_2 + x_3)', o)\n'(c_1+x_2)*(x_3-c_2)'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('-(c_1 - x_1)^2', o)\n'(0-(c_1-x_1))^2'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('-(c_1 - x_2)*(x_1 + x_2)', o)\n'(0-(c_1-x_2))*(x_1+x_2)'\n</code></pre> Source code in <code>src/equation_tree/util/conversions.py</code> <pre><code>def unary_minus_to_binary(expr, operator_test):\n    \"\"\"\n    replace unary minus with binary\n\n    Examples:\n        &gt;&gt;&gt; o = lambda x: x in ['+', '-', '*', '/', '^']\n        &gt;&gt;&gt; unary_minus_to_binary('-x_1+x_2', o)\n        'x_2-x_1'\n\n        &gt;&gt;&gt; unary_minus_to_binary('x_1-x_2', o)\n        'x_1-x_2'\n\n        &gt;&gt;&gt; unary_minus_to_binary('x_1+(-x_2+x_3)', o)\n        'x_1+(x_3-x_2)'\n\n        &gt;&gt;&gt; unary_minus_to_binary('-tan(x_1-exp(x_2))', o)\n        '(0-tan(x_1-exp(x_2)))'\n\n        &gt;&gt;&gt; unary_minus_to_binary('-x_2', o)\n        '(0-x_2)'\n\n        &gt;&gt;&gt; unary_minus_to_binary('exp(-x_1)*log(x_2)', o)\n        'exp((0-x_1))*log(x_2)'\n\n        &gt;&gt;&gt; unary_minus_to_binary('(c_1 + x_2)*(-c_2 + x_3)', o)\n        '(c_1+x_2)*(x_3-c_2)'\n\n        &gt;&gt;&gt; unary_minus_to_binary('-(c_1 - x_1)^2', o)\n        '(0-(c_1-x_1))^2'\n\n        &gt;&gt;&gt; unary_minus_to_binary('-(c_1 - x_2)*(x_1 + x_2)', o)\n        '(0-(c_1-x_2))*(x_1+x_2)'\n\n    \"\"\"\n    _temp = _find_unary(\"-\", str(expr), operator_test)\n    while \"#\" in _temp:\n        _temp = _move_placeholder(_temp, operator_test)\n    _temp = _find_unary(\"+\", _temp, operator_test)\n    _temp = __remove_character_from_string(_temp, \"#\")\n    _temp = _find_unary(\"-\", _temp, operator_test)\n    while \"#\" in _temp:\n        _temp = _replace_with_zero_minus(_temp, operator_test)\n    return _temp\n</code></pre>"},{"location":"reference/src/equation_tree/util/io/","title":"Io","text":""},{"location":"reference/src/equation_tree/util/priors/","title":"Priors","text":""},{"location":"reference/src/equation_tree/util/priors/#src.equation_tree.util.priors.normalized_dict","title":"<code>normalized_dict(d)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; t_d = {'a': 1, 'b': 3}\n&gt;&gt;&gt; t_d = normalized_dict(t_d)\n&gt;&gt;&gt; t_d\n{'a': 0.25, 'b': 0.75}\n&gt;&gt;&gt; t_d = {'c': 0, 'd': 0}\n&gt;&gt;&gt; t_d = normalized_dict(t_d)\n&gt;&gt;&gt; t_d\n{'c': 0, 'd': 0}\n</code></pre> Source code in <code>src/equation_tree/util/priors.py</code> <pre><code>def normalized_dict(d):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; t_d = {'a': 1, 'b': 3}\n        &gt;&gt;&gt; t_d = normalized_dict(t_d)\n        &gt;&gt;&gt; t_d\n        {'a': 0.25, 'b': 0.75}\n        &gt;&gt;&gt; t_d = {'c': 0, 'd': 0}\n        &gt;&gt;&gt; t_d = normalized_dict(t_d)\n        &gt;&gt;&gt; t_d\n        {'c': 0, 'd': 0}\n    \"\"\"\n    n = sum(d.values())\n    if n == 0:\n        return d\n    else:\n        return {key: value / n for key, value in d.items()}\n</code></pre>"},{"location":"reference/src/equation_tree/util/priors/#src.equation_tree.util.priors.set_priors","title":"<code>set_priors(priors=None, space=None)</code>","text":"<p>Utility function to set priors without setting all probabilities of the space</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; default_priors = set_priors(space=['a', 'b', 'c', 'd'])\n&gt;&gt;&gt; default_priors\n{'a': 0.25, 'b': 0.25, 'c': 0.25, 'd': 0.25}\n</code></pre> <pre><code>&gt;&gt;&gt; custom_priors_full = set_priors({'a' : .3, 'b': .7}, ['a', 'b'])\n&gt;&gt;&gt; custom_priors_full\n{'a': 0.3, 'b': 0.7}\n</code></pre> <pre><code>&gt;&gt;&gt; custom_priors_partial = set_priors({'a' : .5}, ['a', 'b', 'c'])\n&gt;&gt;&gt; custom_priors_partial\n{'a': 0.5, 'b': 0.25, 'c': 0.25}\n</code></pre> Source code in <code>src/equation_tree/util/priors.py</code> <pre><code>def set_priors(priors=None, space=None):\n    \"\"\"\n    Utility function to set priors without setting all probabilities of the space\n\n    Examples:\n        &gt;&gt;&gt; default_priors = set_priors(space=['a', 'b', 'c', 'd'])\n        &gt;&gt;&gt; default_priors\n        {'a': 0.25, 'b': 0.25, 'c': 0.25, 'd': 0.25}\n\n        &gt;&gt;&gt; custom_priors_full = set_priors({'a' : .3, 'b': .7}, ['a', 'b'])\n        &gt;&gt;&gt; custom_priors_full\n        {'a': 0.3, 'b': 0.7}\n\n        &gt;&gt;&gt; custom_priors_partial = set_priors({'a' : .5}, ['a', 'b', 'c'])\n        &gt;&gt;&gt; custom_priors_partial\n        {'a': 0.5, 'b': 0.25, 'c': 0.25}\n    \"\"\"\n    if space is None:\n        space = []\n    if priors is None:\n        priors = {}\n\n    n = len(space)\n    default_prior = 1 / n\n\n    # Set all to default to begin with\n    _priors = {el: default_prior for el in space}\n\n    # If the user provides priors\n    if priors:\n        if not set(priors.keys()).issubset(set(space)):\n            raise Exception(f\"Priors {priors} are not subset of space {space}\")\n        total_custom_prior = sum(math.floor(p * 100) / 100 for p in (priors.values()))\n        if total_custom_prior &gt; 1:\n            raise ValueError(f\"Sum of custom priors {priors} is greater than 1\")\n\n        # Update the priors dict with custom values\n        for key, value in priors.items():\n            _priors[key] = value\n\n        # Adjust the other priors\n        remaining_probability = 1 - total_custom_prior\n        num_unset_possibilities = n - len(priors)\n        for key in _priors:\n            if key not in priors:\n                _priors[key] = remaining_probability / num_unset_possibilities\n    return _normalize(_priors)\n</code></pre>"},{"location":"reference/src/equation_tree/util/type_check/","title":"Type check","text":""},{"location":"reference/src/equation_tree/util/type_check/#src.equation_tree.util.type_check.check_functions","title":"<code>check_functions(expression, function_test)</code>","text":"Example <p>from sympy import sympify expr = sympify('sin(x)') check_functions(expr, lambda x: x in ['sin']) True</p> <p>expr = sympify('x + y') check_functions(expr, lambda x: x in ['sin']) True</p> <p>expr = sympify('sin(x) + cos(y)') check_functions(expr, lambda x: x in ['sin', 'cos']) True</p> <p>check_functions(expr, lambda x: x in ['sin']) False</p> Source code in <code>src/equation_tree/util/type_check.py</code> <pre><code>def check_functions(expression, function_test):\n    \"\"\"\n    Example:\n        &gt;&gt;&gt; from sympy import sympify\n        &gt;&gt;&gt; expr = sympify('sin(x)')\n        &gt;&gt;&gt; check_functions(expr, lambda x: x in ['sin'])\n        True\n\n        &gt;&gt;&gt; expr = sympify('x + y')\n        &gt;&gt;&gt; check_functions(expr, lambda x: x in ['sin'])\n        True\n\n        &gt;&gt;&gt; expr = sympify('sin(x) + cos(y)')\n        &gt;&gt;&gt; check_functions(expr, lambda x: x in ['sin', 'cos'])\n        True\n\n        &gt;&gt;&gt; check_functions(expr, lambda x: x in ['sin'])\n        False\n\n    \"\"\"\n\n    def apply_test(node):\n        if isinstance(node, Function):\n            return function_test(str(node.func).lower()) or str(node.func) == \"re\"\n        elif isinstance(node, (Add, Mul, Pow)):\n            return all(apply_test(arg) or str(node.func) == \"re\" for arg in node.args)\n        return True\n\n    return apply_test(expression)\n</code></pre>"},{"location":"reference/src/equation_tree/util/type_check/#src.equation_tree.util.type_check.is_constant_formatted","title":"<code>is_constant_formatted(s)</code>","text":"<p>Tests weather the input is in standard format for a constant</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; is_constant_formatted('c_4')\nTrue\n&gt;&gt;&gt; is_constant_formatted('c_42')\nTrue\n&gt;&gt;&gt; is_constant_formatted('c_a')\nFalse\n&gt;&gt;&gt; is_constant_formatted('abc')\nFalse\n&gt;&gt;&gt; is_constant_formatted('x_3')\nFalse\n</code></pre> Source code in <code>src/equation_tree/util/type_check.py</code> <pre><code>def is_constant_formatted(s: str):\n    \"\"\"\n    Tests weather the input is in standard format for a constant\n\n    Examples:\n        &gt;&gt;&gt; is_constant_formatted('c_4')\n        True\n        &gt;&gt;&gt; is_constant_formatted('c_42')\n        True\n        &gt;&gt;&gt; is_constant_formatted('c_a')\n        False\n        &gt;&gt;&gt; is_constant_formatted('abc')\n        False\n        &gt;&gt;&gt; is_constant_formatted('x_3')\n        False\n    \"\"\"\n    pattern = r\"^c_\\d+$\"\n    return re.match(pattern, s) is not None\n</code></pre>"},{"location":"reference/src/equation_tree/util/type_check/#src.equation_tree.util.type_check.is_numeric","title":"<code>is_numeric(s)</code>","text":"<p>Tests weather the input is a number</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; is_numeric('0')\nTrue\n&gt;&gt;&gt; is_numeric('10')\nTrue\n&gt;&gt;&gt; is_numeric('hallo')\nFalse\n&gt;&gt;&gt; is_numeric('.1')\nTrue\n&gt;&gt;&gt; is_numeric('+.1')\nFalse\n</code></pre> Source code in <code>src/equation_tree/util/type_check.py</code> <pre><code>def is_numeric(s):\n    \"\"\"\n    Tests weather the input is a number\n\n    Examples:\n        &gt;&gt;&gt; is_numeric('0')\n        True\n        &gt;&gt;&gt; is_numeric('10')\n        True\n        &gt;&gt;&gt; is_numeric('hallo')\n        False\n        &gt;&gt;&gt; is_numeric('.1')\n        True\n        &gt;&gt;&gt; is_numeric('+.1')\n        False\n\n    \"\"\"\n    if isinstance(s, str) and (not s[0].isnumeric() and s[0] != \".\"):\n        return False\n    try:\n        float(s)\n        return True\n    except ValueError:\n        return False\n</code></pre>"},{"location":"reference/src/equation_tree/util/type_check/#src.equation_tree.util.type_check.is_variable_formatted","title":"<code>is_variable_formatted(s)</code>","text":"<p>Tests weather the input is in standard format for a variable</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; is_variable_formatted('x_1')\nTrue\n&gt;&gt;&gt; is_variable_formatted('x_42')\nTrue\n&gt;&gt;&gt; is_variable_formatted('x_a')\nFalse\n&gt;&gt;&gt; is_variable_formatted('abc')\nFalse\n&gt;&gt;&gt; is_variable_formatted('c_3')\nFalse\n</code></pre> Source code in <code>src/equation_tree/util/type_check.py</code> <pre><code>def is_variable_formatted(s: str):\n    \"\"\"\n    Tests weather the input is in standard format for a variable\n\n    Examples:\n        &gt;&gt;&gt; is_variable_formatted('x_1')\n        True\n        &gt;&gt;&gt; is_variable_formatted('x_42')\n        True\n        &gt;&gt;&gt; is_variable_formatted('x_a')\n        False\n        &gt;&gt;&gt; is_variable_formatted('abc')\n        False\n        &gt;&gt;&gt; is_variable_formatted('c_3')\n        False\n    \"\"\"\n    pattern = r\"^x_\\d+$\"\n    return re.match(pattern, s) is not None\n</code></pre>"},{"location":"reference/src/equation_tree/util/type_check/#src.equation_tree.util.type_check.parse_string_list_int","title":"<code>parse_string_list_int(lst)</code>","text":"Example <p>a = '[1, 2, 3, 4]' parse_string_list_int(a) [1, 2, 3, 4] b = '[10, 2, 3]' parse_string_list_int(b) [10, 2, 3]</p> Source code in <code>src/equation_tree/util/type_check.py</code> <pre><code>def parse_string_list_int(lst):\n    \"\"\"\n    Example:\n        &gt;&gt;&gt; a = '[1, 2, 3, 4]'\n        &gt;&gt;&gt; parse_string_list_int(a)\n        [1, 2, 3, 4]\n        &gt;&gt;&gt; b = '[10, 2, 3]'\n        &gt;&gt;&gt; parse_string_list_int(b)\n        [10, 2, 3]\n    \"\"\"\n    res = []\n    i = 0\n    while i &lt; len(lst) - 1:\n        start = i\n        end = i\n        while is_numeric(lst[i]):\n            end += 1\n            i += 1\n        if start != end:\n            i = end\n            res.append(int(lst[start:end]))\n        i += 1\n    return res\n</code></pre>"}]}
\ No newline at end of file
+{"config":{"lang":["en"],"separator":"[\\s\\-]+","pipeline":["stopWordFilter"]},"docs":[{"location":"","title":"Equation Tree","text":"<p>The Equation Tree package is an equation toolbox with symbolic regression in mind. It represents expressions as incomplete binary trees and has various features tailored towards testing symbolic regression algorithms or training models. The most notable features are:</p> <ul> <li>Equation sampling (including priors)</li> <li>Feature Extraction from equation distributions</li> <li>Distance metrics between equations</li> </ul>"},{"location":"#equation-sampling","title":"Equation Sampling","text":"<p>coming soon</p>"},{"location":"#feature-extraction","title":"Feature Extraction","text":"<p>coming soon</p>"},{"location":"#distance-metrics","title":"Distance Metrics","text":"<p>coming soon</p>"},{"location":"#about","title":"About","text":"<p>This project is in active development by the Autonomous Empirical Research Group (package developer: Younes Strittmatter, PI: Sebastian Musslick. This research program is supported by Schmidt Science Fellows, in partnership with the Rhodes Trust, as well as the Carney BRAINSTORM program at Brown University.</p>"},{"location":"Basic%20Usage/","title":"Basic Usage","text":"In\u00a0[1]: Copied! <pre>import random\n!pip install equation_tree\n</pre> import random !pip install equation_tree <pre>Requirement already satisfied: equation_tree in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src (0.0.11.dev27+g1da6b63.d20231102)\r\nRequirement already satisfied: numpy in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (1.25.2)\r\nRequirement already satisfied: sympy in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (1.12)\r\nRequirement already satisfied: importlib_resources in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (6.0.1)\r\nRequirement already satisfied: tqdm in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (4.66.1)\r\nRequirement already satisfied: mpmath&gt;=0.19 in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from sympy-&gt;equation_tree) (1.3.0)\r\n\r\n[notice] A new release of pip is available: 23.1.2 -&gt; 23.3.1\r\n[notice] To update, run: pip install --upgrade pip\r\n</pre> In\u00a0[2]: Copied! <pre>from equation_tree import sample\n\n# To obtain reproducible results, we set a seed for the following section\nimport numpy as np\nnp.random.seed(42)\n# Adjusting the input dimension of the equations\n</pre> from equation_tree import sample  # To obtain reproducible results, we set a seed for the following section import numpy as np np.random.seed(42) # Adjusting the input dimension of the equations <p>We use this to sample an equation:</p> In\u00a0[3]: Copied! <pre>equation = sample()\n</pre> equation = sample() <pre>/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.\n  warnings.warn(\nProcessing: 100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 1/1 [00:00&lt;00:00,  9.77iteration/s]\n</pre> In\u00a0[4]: Copied! <pre>type(equation)\n</pre> type(equation) Out[4]: <pre>list</pre> <p>It is a list! This is because we can sample multiple equations in one go:</p> In\u00a0[5]: Copied! <pre>equations = sample(n = 100)\n</pre> equations = sample(n = 100) <pre>Processing:   0%|          | 0/100 [00:00&lt;?, ?iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:51: RuntimeWarning: invalid value encountered in log\n  \"log\": lambda a: np.log(a),\n/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:55: RuntimeWarning: invalid value encountered in arccos\n  \"acos\": lambda a: np.arccos(a),\nProcessing:   7%|\u258b         | 7/100 [00:00&lt;00:01, 68.58iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:40: RuntimeWarning: invalid value encountered in scalar power\n  \"^\": lambda a, b: a**b,\n/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:52: RuntimeWarning: invalid value encountered in sqrt\n  \"sqrt\": lambda a: np.sqrt(a),\nProcessing:  14%|\u2588\u258d        | 14/100 [00:00&lt;00:01, 68.71iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:56: RuntimeWarning: invalid value encountered in arcsin\n  \"asin\": lambda a: np.arcsin(a),\nProcessing: 100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 100/100 [00:01&lt;00:00, 85.06iteration/s]\n</pre> <p>This returns 100 equations:</p> In\u00a0[6]: Copied! <pre>len(equations)\n</pre> len(equations) Out[6]: <pre>100</pre> In\u00a0[7]: Copied! <pre>equations[0]\n</pre> equations[0] Out[7]: <pre>-sin(x_1 - exp(exp(x_1)))</pre> In\u00a0[8]: Copied! <pre>equations[42]\n</pre> equations[42] Out[8]: <pre>-c_2 + tan(c_1*x_1)</pre> <p>They are represented as strings, but we can look at other representations as well. For example, prefix notation (for more details on different representations of the equations, see the respective section of the documentation):</p> In\u00a0[9]: Copied! <pre>equations[42].prefix\n</pre> equations[42].prefix Out[9]: <pre>['-', 'tan', '*', 'c_1', 'x_1', 'c_2']</pre> <p>We can also look at features of the equation, for example at the number of constants, the tree depth of the underlying tree, the number of nodes or the tree structure (for more details on these features, see the respective section of the documentation):</p> In\u00a0[10]: Copied! <pre>equations[42].n_constants\n</pre> equations[42].n_constants Out[10]: <pre>2</pre> In\u00a0[11]: Copied! <pre>equations[42].depth\n</pre> equations[42].depth Out[11]: <pre>3</pre> In\u00a0[12]: Copied! <pre>equations[42].n_nodes\n</pre> equations[42].n_nodes Out[12]: <pre>6</pre> In\u00a0[13]: Copied! <pre>equations[42].structure\n</pre> equations[42].structure Out[13]: <pre>[0, 1, 2, 3, 3, 1]</pre> In\u00a0[14]: Copied! <pre># first we need to import the functionality\nfrom equation_tree import instantiate_constants\nimport random\n\n# then we can use a function to instantiate the constants. For example for random constants between 0 and 1:\ninstantiated_equation = instantiate_constants(equations[42], lambda : random.random())\nprint(f'abstract: {equations[42]}', f', instantiated: {instantiated_equation}')\n</pre> # first we need to import the functionality from equation_tree import instantiate_constants import random  # then we can use a function to instantiate the constants. For example for random constants between 0 and 1: instantiated_equation = instantiate_constants(equations[42], lambda : random.random()) print(f'abstract: {equations[42]}', f', instantiated: {instantiated_equation}') <pre>abstract: -c_2 + tan(c_1*x_1) , instantiated: tan(0.2720878822071884*x_1) - 0.4936315339297549\n</pre> In\u00a0[15]: Copied! <pre># we can also use other functions (for example all functions to be a constant\ninstantiated_equation_ = instantiate_constants(equations[41], lambda : 1)\nprint(f'abstract: {equations[41]}', f', instantiated: {instantiated_equation_}')\n</pre> # we can also use other functions (for example all functions to be a constant instantiated_equation_ = instantiate_constants(equations[41], lambda : 1) print(f'abstract: {equations[41]}', f', instantiated: {instantiated_equation_}') <pre>abstract: c_2*x_1**c_1 , instantiated: x_1\n</pre> <p>**We can use arbitrary functions to instantiate the constants.</p> In\u00a0[16]: Copied! <pre># import functionality\nvalues = instantiated_equation.evaluate({'x_1': [1, 2, 3, 4]})\nvalues\n</pre> # import functionality values = instantiated_equation.evaluate({'x_1': [1, 2, 3, 4]}) values Out[16]: <pre>array([-0.21462429,  0.11148855,  0.57008635,  1.41577756])</pre> In\u00a0[17]: Copied! <pre># We can also use pandas dataframes as inputs:\n\n# import functionality\nimport pandas as pd\n\n# define the input and get the values\ninput_df = pd.DataFrame({'x_1': [1, 2, 3, 4]})\ninstantiated_equation.evaluate(input_df)\n</pre> # We can also use pandas dataframes as inputs:  # import functionality import pandas as pd  # define the input and get the values input_df = pd.DataFrame({'x_1': [1, 2, 3, 4]}) instantiated_equation.evaluate(input_df) Out[17]: <pre>array([-0.21462429,  0.11148855,  0.57008635,  1.41577756])</pre> In\u00a0[25]: Copied! <pre>equations_2d = sample(n=5, max_num_variables=2)\n</pre> equations_2d = sample(n=5, max_num_variables=2) <pre>/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.\n  warnings.warn(\nProcessing:   0%|          | 0/5 [00:00&lt;?, ?iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:55: RuntimeWarning: invalid value encountered in arccos\n  \"acos\": lambda a: np.arccos(a),\n/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:51: RuntimeWarning: invalid value encountered in log\n  \"log\": lambda a: np.log(a),\n/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:56: RuntimeWarning: invalid value encountered in arcsin\n  \"asin\": lambda a: np.arcsin(a),\n/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:52: RuntimeWarning: invalid value encountered in sqrt\n  \"sqrt\": lambda a: np.sqrt(a),\nProcessing: 100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 5/5 [00:00&lt;00:00, 112.51iteration/s]\n</pre> In\u00a0[27]: Copied! <pre>equations_2d\n</pre> equations_2d Out[27]: <pre>[acos(Abs(acos(x_1))),\n -Abs(x_2) + asin(log(x_1)),\n Max(c_1, x_1),\n Max(x_1, Abs(sqrt(sin(x_1)))),\n cos(x_1*(c_1 + x_2))]</pre> <p>**Note: Not all the equations have exactly 2 input variable. Some of them have only one. This is since equations with only one input variable are still defined on 2 (or more dimensions)</p> In\u00a0[28]: Copied! <pre>equations_simple = sample(n=5, depth=3)\nequations_complex = sample(n=5, depth=8)\n</pre> equations_simple = sample(n=5, depth=3) equations_complex = sample(n=5, depth=8) <pre>/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.\n  warnings.warn(\nProcessing:   0%|          | 0/5 [00:00&lt;?, ?iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:55: RuntimeWarning: invalid value encountered in arccos\n  \"acos\": lambda a: np.arccos(a),\n/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:56: RuntimeWarning: invalid value encountered in arcsin\n  \"asin\": lambda a: np.arcsin(a),\n/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:40: RuntimeWarning: invalid value encountered in scalar power\n  \"^\": lambda a, b: a**b,\nProcessing: 100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 5/5 [00:00&lt;00:00, 312.27iteration/s]\nProcessing:   0%|          | 0/5 [00:00&lt;?, ?iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:40: RuntimeWarning: divide by zero encountered in scalar power\n  \"^\": lambda a, b: a**b,\n/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:47: RuntimeWarning: invalid value encountered in sin\n  \"sin\": lambda a: np.sin(a),\nProcessing:  40%|\u2588\u2588\u2588\u2588      | 2/5 [00:00&lt;00:00, 12.82iteration/s]/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:52: RuntimeWarning: invalid value encountered in sqrt\n  \"sqrt\": lambda a: np.sqrt(a),\n/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/tree.py:51: RuntimeWarning: invalid value encountered in log\n  \"log\": lambda a: np.log(a),\nProcessing: 100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 5/5 [00:00&lt;00:00, 21.56iteration/s]\n</pre> In\u00a0[29]: Copied! <pre>print('*** simple equations ***\\n', equations_simple, '\\n')\nprint('*** complex equations ***\\n', equations_complex)\n</pre> print('*** simple equations ***\\n', equations_simple, '\\n') print('*** complex equations ***\\n', equations_complex) <pre>*** simple equations ***\n [acos(exp(x_1)), Max(c_1, x_1), x_1/c_1, asin(exp(x_1)), x_1**c_1] \n\n*** complex equations ***\n [sin(exp(sqrt(1 - sin(x_1)**2)/sin(x_1))**x_1), (x_1 + Min(x_1, sin(x_1)))/sqrt(1 - (x_1 + Min(x_1, sin(x_1)))**2), sqrt(Min(c_1**sin(sin(x_1)), x_1)), -asin(x_1)**x_1 + Min(c_1, x_1), Max(-x_1 + log(x_1), sqrt(Abs(x_1)))]\n</pre> In\u00a0[34]: Copied! <pre>p = {\n    'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n    'features': {'constants': .2, 'variables': .8},\n    'functions': {'sin': .5, 'cos': .5},\n    'operators': {'+': .8, '-': .2}\n}\nequations_with_prior = sample(n=10, prior=p, max_num_variables=10)\nequations_with_prior\n</pre> p = {     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},     'features': {'constants': .2, 'variables': .8},     'functions': {'sin': .5, 'cos': .5},     'operators': {'+': .8, '-': .2} } equations_with_prior = sample(n=10, prior=p, max_num_variables=10) equations_with_prior <pre>/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.\n  warnings.warn(\nProcessing: 100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 100/100 [00:00&lt;00:00, 190.81iteration/s]\n</pre> Out[34]: <pre>[cos(cos(x_1)),\n sin(sin(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n -x_3 + sin(x_2) + cos(x_1),\n cos(cos(x_1)),\n cos(sin(x_1)),\n sin(cos(x_1)),\n x_1 + x_2,\n sin(cos(x_1)),\n cos(sin(x_1)),\n x_1 + x_2,\n cos(sin(x_1)),\n x_1 - x_2,\n x_1 + x_2,\n sin(sin(x_1)),\n x_1 + x_2,\n sin(cos(x_1)),\n -c_1 + x_1,\n sin(cos(x_1)),\n x_1 + x_2,\n x_1 + x_2,\n x_1 + x_2,\n x_1 + x_2,\n sin(cos(x_1)),\n c_1 + x_1,\n x_1 - x_2,\n x_1 - x_2,\n x_1 + x_2,\n sin(sin(x_1)),\n c_1 + x_1,\n cos(sin(x_1)),\n cos(sin(x_1)),\n cos(sin(x_1)),\n cos(cos(x_1)),\n c_1 + x_1,\n sin(cos(x_1)),\n sin(cos(x_1)),\n x_1 - x_2,\n cos(sin(x_1)),\n cos(sin(x_1)),\n x_1 - x_2,\n cos(cos(x_1)),\n x_1 + x_2,\n x_1 + x_2,\n sin(sin(x_1)),\n c_1 + x_1,\n c_1 + x_1,\n x_1 + x_2,\n x_1 - x_2,\n sin(sin(x_1)),\n cos(cos(x_1)),\n cos(cos(x_1)),\n cos(cos(x_1)),\n sin(cos(x_1)),\n x_1 - x_2,\n sin(sin(x_1)),\n cos(cos(x_1)),\n c_1 + x_1,\n sin(sin(x_1)),\n cos(sin(x_1)),\n cos(sin(x_1)),\n x_1 + x_2,\n cos(sin(x_1)),\n sin(cos(x_1)),\n c_1 + x_1,\n -x_2,\n x_1 - x_2,\n -x_3 + sin(x_1) + sin(x_2),\n c_1 + x_1,\n x_1 + x_2,\n c_1 + x_1,\n c_1 + x_1,\n sin(sin(x_1)),\n cos(cos(x_1)),\n x_1 + x_2,\n c_1 + x_1,\n -x_1 + cos(x_1) + cos(x_2),\n x_1 - x_2,\n cos(sin(x_1)),\n sin(cos(x_1)),\n sin(cos(x_1)),\n sin(cos(x_1)),\n -x_3 + sin(x_1) + cos(x_2),\n x_1 + x_2,\n -x_3 + sin(x_2) + cos(x_1),\n -x_3 + sin(x_1) + sin(x_2),\n c_1 - x_1,\n c_1 + x_1,\n c_1 + x_1,\n cos(cos(x_1)),\n -x_2 + sin(x_2) + cos(x_1),\n c_1 + x_1,\n sin(sin(x_1)),\n c_1 + x_1,\n x_1 + x_2,\n sin(sin(x_1)),\n x_1 + x_2,\n x_1 + x_2,\n cos(sin(x_1)),\n sin(sin(x_1))]</pre> <p>We can also use conditional priors conditioned on the parent node:</p> In\u00a0[38]: Copied! <pre>p_ = {\n    'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n    'features': {'constants': .2, 'variables': .8},\n    'functions': {'sin': .5, 'cos': .5},\n    'operators': {'+': .5, '-': .5},\n    'function_conditionals': {\n        'sin': {\n            'features': {'constants': 0., 'variables': 1.},\n            'functions': {'sin': 0., 'cos': 1.},\n            'operators': {'+': .5, '-': .5}\n        },\n        'cos': {\n            'features': {'constants': 0., 'variables': 1.},\n            'functions': {'cos': 1., 'sin': 0.},\n            'operators': {'+': 0., '-': 1.}\n        }\n    },\n    'operator_conditionals': {\n        '+': {\n            'features': {'constants': .5, 'variables': .5},\n            'functions': {'sin': 1., 'cos': 0.},\n            'operators': {'+': 1., '-': 0.}\n        },\n        '-': {\n            'features': {'constants': .3, 'variables': .7},\n            'functions': {'cos': .5, 'sin': .5},\n            'operators': {'+': .9, '-': .1}\n        }\n    },\n}\nequations_with_conditional_prior = sample(n=10, prior=p_, max_num_variables=10)\nequations_with_conditional_prior\n</pre> p_ = {     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},     'features': {'constants': .2, 'variables': .8},     'functions': {'sin': .5, 'cos': .5},     'operators': {'+': .5, '-': .5},     'function_conditionals': {         'sin': {             'features': {'constants': 0., 'variables': 1.},             'functions': {'sin': 0., 'cos': 1.},             'operators': {'+': .5, '-': .5}         },         'cos': {             'features': {'constants': 0., 'variables': 1.},             'functions': {'cos': 1., 'sin': 0.},             'operators': {'+': 0., '-': 1.}         }     },     'operator_conditionals': {         '+': {             'features': {'constants': .5, 'variables': .5},             'functions': {'sin': 1., 'cos': 0.},             'operators': {'+': 1., '-': 0.}         },         '-': {             'features': {'constants': .3, 'variables': .7},             'functions': {'cos': .5, 'sin': .5},             'operators': {'+': .9, '-': .1}         }     }, } equations_with_conditional_prior = sample(n=10, prior=p_, max_num_variables=10) equations_with_conditional_prior <pre>/Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/src/equation_tree/util/io.py:27: UserWarning: No hashed prior found. Sample frequencies may diverge from the prior. Consider burning this prior first.\n  warnings.warn(\nProcessing: 100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 100/100 [00:00&lt;00:00, 128.08iteration/s]\n</pre> Out[38]: <pre>[cos(cos(x_1)),\n x_1 - x_2,\n -c_1 + x_1,\n sin(cos(x_1)),\n sin(cos(x_1)),\n c_1 + x_1,\n -c_1 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n cos(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n sin(cos(x_1)),\n c_1 - x_1,\n -x_3 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n c_1 - x_1,\n sin(cos(x_1)),\n cos(cos(x_1)),\n x_1 - x_2,\n -c_1 + sin(x_1) + sin(x_2),\n -x_3 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n c_1 - x_1,\n sin(cos(x_1)),\n x_1 - x_2,\n -x_3 - sin(x_2) + cos(x_1),\n -c_1 + x_1,\n sin(cos(x_1)),\n cos(cos(x_1)),\n sin(cos(x_1)),\n x_1 + x_2,\n cos(cos(x_1)),\n -x_3 + sin(x_1) - sin(x_2),\n c_1 + x_1,\n cos(cos(x_1)),\n cos(cos(x_1)),\n sin(cos(x_1)),\n x_1 - x_2,\n -x_3 + sin(x_1) + sin(x_2),\n -c_1 + x_1,\n c_1 - x_1,\n c_1 + x_1,\n c_1 + x_1,\n cos(cos(x_1)),\n -c_1 + sin(x_1) + sin(x_2),\n c_1 + x_1,\n sin(cos(x_1)),\n sin(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n -x_3 + sin(x_1) - cos(x_2),\n sin(cos(x_1)),\n x_1 - x_2,\n -x_3 + cos(x_1) - cos(x_2),\n x_1 - x_2,\n cos(cos(x_1)),\n sin(cos(x_1)),\n -x_2 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n -c_1 + sin(x_1) + sin(x_2),\n -x_2 + sin(x_1) - cos(x_2),\n cos(cos(x_1)),\n -x_2 + sin(x_1) + sin(x_2),\n -x_3 + sin(x_1) + sin(x_2),\n sin(cos(x_1)),\n cos(cos(x_1)),\n cos(cos(x_1)),\n -c_1 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n cos(cos(x_1)),\n cos(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n cos(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n x_1 + x_2,\n c_1 - x_1,\n -x_1 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n -c_1 + sin(x_1) + sin(x_2),\n c_1 - x_1,\n cos(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n c_1 - x_1,\n -x_3 + sin(x_1) + sin(x_2),\n cos(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n c_1 + x_1,\n x_1 - x_2,\n cos(cos(x_1)),\n c_1 + x_1,\n cos(cos(x_1)),\n sin(cos(x_1)),\n sin(cos(x_1)),\n sin(cos(x_1)),\n sin(cos(x_1)),\n sin(cos(x_1)),\n -x_3 + sin(x_1) + sin(x_2),\n c_1 + x_1]</pre> <p>WARNING If your application is dependent on these priors, you should \"burn\" samples before starting the sampling. During the sampling process, equations get simplified and invalid equations are discarded. This is likely to lead to disparities between the priors and the sampled frequencies. To counteract this, the package offers the functionality to \"burn\" samples and adjust the priors so that the outcome frequency match them more closely. To burn samples, use the following code (We don't run it in the notebook since the adjusted priors are saved to disk for future use):</p> <pre><code>burn(\n    prior,\n    max_number_variables,\n    path_to_file,\n    number_of_burned_samples,\n    learning_rate\n    )\n</code></pre> <p>*this function should be run multiple times. The learning rate defines how much adjusted from previous runs are adjusted. After burning, you can load the adjusted priors via:</p> <pre><code>    sample(..., file=path_to_file)\n</code></pre> <p>*multiple adjusted priors can be stored in the same file.</p> In\u00a0[\u00a0]: Copied! <pre>\n</pre>"},{"location":"Basic%20Usage/#basic-usage","title":"Basic Usage\u00b6","text":"<p>Here, we demonstrate core functionalities of the Equation Tree:</p> <ul> <li>Basic Functionality for sampling and processing equations</li> <li>Advanced settings for sampling equations</li> </ul>"},{"location":"Basic%20Usage/#installation","title":"Installation\u00b6","text":""},{"location":"Basic%20Usage/#basic-functionality","title":"Basic Functionality\u00b6","text":""},{"location":"Basic%20Usage/#sampling-with-default-settings","title":"Sampling With Default Settings\u00b6","text":"<p>First, we need to import the functionality. Here we also set a seed to ensure reproducible results.</p>"},{"location":"Basic%20Usage/#equation-representations-and-features","title":"Equation Representations And Features\u00b6","text":"<p>First, lets look at the type of the equation</p>"},{"location":"Basic%20Usage/#instantiate-equations","title":"Instantiate Equations\u00b6","text":"<p>Note: the sampled equation are abstract: c_1 are representation of a constant. We can instantiate constants to be numbers:</p>"},{"location":"Basic%20Usage/#evaluating-equations","title":"Evaluating Equations\u00b6","text":"<p>After instantiating equations, we can also evaluate on arbitrary input:</p>"},{"location":"Basic%20Usage/#sample-settings","title":"Sample Settings\u00b6","text":"<p>When sampling equations, we can control for a variety of features of the underlying distribution.</p>"},{"location":"Basic%20Usage/#input-dimensions","title":"Input Dimensions\u00b6","text":"<p>We can manipulate the space on witch the equation is defined. For example, if we want equations that are defined on 2-dimensions, we can write:</p>"},{"location":"Basic%20Usage/#equation-complexity","title":"Equation Complexity\u00b6","text":"<p>We can also manipulate the equation complexity (as number of nodes)</p>"},{"location":"Basic%20Usage/#using-priors","title":"Using Priors\u00b6","text":"<p>We can also make use of priors to fully customize the sampling. Here, the entries for the structures, features, functions and operators represent the probability of the respective attribute being sampled.</p>"},{"location":"quickstart/","title":"Quickstart Guide","text":"<p>You will need:</p> <ul> <li><code>python</code> 3.8 or greater: https://www.python.org/downloads/</li> </ul> <pre><code>pip install -U equation-tree\n</code></pre> <p>Check your installation by running: <pre><code>python -c \"from equation_tree import EquationTree\"\n</code></pre></p>"},{"location":"reference/SUMMARY/","title":"Code Reference","text":"<ul> <li>src<ul> <li>equation_tree<ul> <li>analysis</li> <li>defaults</li> <li>prior</li> <li>sample</li> <li>src<ul> <li>sample_tree_structure</li> <li>tree_node</li> </ul> </li> <li>tree</li> <li>util<ul> <li>conversions</li> <li>io</li> <li>priors</li> <li>type_check</li> </ul> </li> </ul> </li> </ul> </li> </ul>"},{"location":"reference/src/equation_tree/","title":"Equation tree","text":""},{"location":"reference/src/equation_tree/analysis/","title":"Analysis","text":""},{"location":"reference/src/equation_tree/analysis/#src.equation_tree.analysis.get_counts","title":"<code>get_counts(trees)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; import numpy as np\n&gt;&gt;&gt; import pprint\n&gt;&gt;&gt; np.random.seed(42)\n&gt;&gt;&gt; p = {\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .5, 'variables': .5},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': .5, '-': .5},\n...     'function_conditionals': {\n...                             'sin': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': .5, 'cos': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             },\n...                             'cos': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             }\n...                         },\n...     'operator_conditionals': {\n...                             '+': {\n...                                 'features': {'constants': .5, 'variables': .5},\n...                                 'functions': {'sin': .5, 'cos': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             },\n...                             '-': {\n...                                 'features': {'constants': .5, 'variables': .5},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             }\n...                         },\n... }\n&gt;&gt;&gt; pprint.pprint(p)\n{'features': {'constants': 0.5, 'variables': 0.5},\n 'function_conditionals': {'cos': {'features': {'constants': 0.0,\n                                                'variables': 1.0},\n                                   'functions': {'cos': 0.5, 'sin': 0.5},\n                                   'operators': {'+': 0.5, '-': 0.5}},\n                           'sin': {'features': {'constants': 0.0,\n                                                'variables': 1.0},\n                                   'functions': {'cos': 0.5, 'sin': 0.5},\n                                   'operators': {'+': 0.5, '-': 0.5}}},\n 'functions': {'cos': 0.5, 'sin': 0.5},\n 'operator_conditionals': {'+': {'features': {'constants': 0.5,\n                                              'variables': 0.5},\n                                 'functions': {'cos': 0.5, 'sin': 0.5},\n                                 'operators': {'+': 0.5, '-': 0.5}},\n                           '-': {'features': {'constants': 0.5,\n                                              'variables': 0.5},\n                                 'functions': {'cos': 0.5, 'sin': 0.5},\n                                 'operators': {'+': 0.5, '-': 0.5}}},\n 'operators': {'+': 0.5, '-': 0.5},\n 'structures': {'[0, 1, 1]': 0.3,\n                '[0, 1, 2, 3, 2, 3, 1]': 0.4,\n                '[0, 1, 2]': 0.3}}\n</code></pre> <pre><code>&gt;&gt;&gt; tree_list = [EquationTree.from_prior(p, 4) for _ in range(100)]\n&gt;&gt;&gt; len(tree_list)\n100\n&gt;&gt;&gt; example_tree = tree_list[2]\n&gt;&gt;&gt; example_tree.expr\n['+', '-', 'sin', 'x_1', 'cos', 'x_2', 'c_1']\n&gt;&gt;&gt; example_tree.sympy_expr\nc_1 + sin(x_1) - cos(x_2)\n&gt;&gt;&gt; pprint.pprint(example_tree.info)\n{'depth': 3,\n 'features': {'constants': 1, 'variables': 2},\n 'function_conditionals': {'cos': {'features': {'constants': 0, 'variables': 1},\n                                   'functions': {},\n                                   'operators': {}},\n                           'sin': {'features': {'constants': 0, 'variables': 1},\n                                   'functions': {},\n                                   'operators': {}}},\n 'functions': {'cos': 1, 'sin': 1},\n 'max_depth': 7,\n 'operator_conditionals': {'+': {'features': {'constants': 1, 'variables': 0},\n                                 'functions': {},\n                                 'operators': {'-': 1}},\n                           '-': {'features': {'constants': 0, 'variables': 0},\n                                 'functions': {'cos': 1, 'sin': 1},\n                                 'operators': {}}},\n 'operators': {'+': 1, '-': 1},\n 'structures': [0, 1, 2, 3, 2, 3, 1]}\n</code></pre> <pre><code>&gt;&gt;&gt; counts = get_counts(tree_list)\n&gt;&gt;&gt; pprint.pprint(counts)\n{'depth': {1: 32, 2: 27, 3: 41},\n 'features': {'constants': 44, 'variables': 170},\n 'function_conditionals': {'cos': {'features': {'constants': 0,\n                                                'variables': 54},\n                                   'functions': {'cos': 7, 'sin': 6},\n                                   'operators': {}},\n                           'sin': {'features': {'constants': 0,\n                                                'variables': 55},\n                                   'functions': {'cos': 7, 'sin': 7},\n                                   'operators': {}}},\n 'functions': {'cos': 67, 'sin': 69},\n 'max_depth': {3: 59, 7: 41},\n 'operator_conditionals': {'+': {'features': {'constants': 24, 'variables': 29},\n                                 'functions': {'cos': 27, 'sin': 21},\n                                 'operators': {'+': 14, '-': 9}},\n                           '-': {'features': {'constants': 20, 'variables': 32},\n                                 'functions': {'cos': 13, 'sin': 21},\n                                 'operators': {'+': 10, '-': 8}}},\n 'operators': {'+': 62, '-': 52},\n 'structures': {'[0, 1, 1]': 32, '[0, 1, 2, 3, 2, 3, 1]': 41, '[0, 1, 2]': 27}}\n</code></pre> Source code in <code>src/equation_tree/analysis.py</code> <pre><code>def get_counts(trees: List[EquationTree]):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; import numpy as np\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; np.random.seed(42)\n        &gt;&gt;&gt; p = {\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .5, 'variables': .5},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': .5, '-': .5},\n        ...     'function_conditionals': {\n        ...                             'sin': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': .5, 'cos': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             },\n        ...                             'cos': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             }\n        ...                         },\n        ...     'operator_conditionals': {\n        ...                             '+': {\n        ...                                 'features': {'constants': .5, 'variables': .5},\n        ...                                 'functions': {'sin': .5, 'cos': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             },\n        ...                             '-': {\n        ...                                 'features': {'constants': .5, 'variables': .5},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             }\n        ...                         },\n        ... }\n        &gt;&gt;&gt; pprint.pprint(p)\n        {'features': {'constants': 0.5, 'variables': 0.5},\n         'function_conditionals': {'cos': {'features': {'constants': 0.0,\n                                                        'variables': 1.0},\n                                           'functions': {'cos': 0.5, 'sin': 0.5},\n                                           'operators': {'+': 0.5, '-': 0.5}},\n                                   'sin': {'features': {'constants': 0.0,\n                                                        'variables': 1.0},\n                                           'functions': {'cos': 0.5, 'sin': 0.5},\n                                           'operators': {'+': 0.5, '-': 0.5}}},\n         'functions': {'cos': 0.5, 'sin': 0.5},\n         'operator_conditionals': {'+': {'features': {'constants': 0.5,\n                                                      'variables': 0.5},\n                                         'functions': {'cos': 0.5, 'sin': 0.5},\n                                         'operators': {'+': 0.5, '-': 0.5}},\n                                   '-': {'features': {'constants': 0.5,\n                                                      'variables': 0.5},\n                                         'functions': {'cos': 0.5, 'sin': 0.5},\n                                         'operators': {'+': 0.5, '-': 0.5}}},\n         'operators': {'+': 0.5, '-': 0.5},\n         'structures': {'[0, 1, 1]': 0.3,\n                        '[0, 1, 2, 3, 2, 3, 1]': 0.4,\n                        '[0, 1, 2]': 0.3}}\n\n\n        &gt;&gt;&gt; tree_list = [EquationTree.from_prior(p, 4) for _ in range(100)]\n        &gt;&gt;&gt; len(tree_list)\n        100\n        &gt;&gt;&gt; example_tree = tree_list[2]\n        &gt;&gt;&gt; example_tree.expr\n        ['+', '-', 'sin', 'x_1', 'cos', 'x_2', 'c_1']\n        &gt;&gt;&gt; example_tree.sympy_expr\n        c_1 + sin(x_1) - cos(x_2)\n        &gt;&gt;&gt; pprint.pprint(example_tree.info)\n        {'depth': 3,\n         'features': {'constants': 1, 'variables': 2},\n         'function_conditionals': {'cos': {'features': {'constants': 0, 'variables': 1},\n                                           'functions': {},\n                                           'operators': {}},\n                                   'sin': {'features': {'constants': 0, 'variables': 1},\n                                           'functions': {},\n                                           'operators': {}}},\n         'functions': {'cos': 1, 'sin': 1},\n         'max_depth': 7,\n         'operator_conditionals': {'+': {'features': {'constants': 1, 'variables': 0},\n                                         'functions': {},\n                                         'operators': {'-': 1}},\n                                   '-': {'features': {'constants': 0, 'variables': 0},\n                                         'functions': {'cos': 1, 'sin': 1},\n                                         'operators': {}}},\n         'operators': {'+': 1, '-': 1},\n         'structures': [0, 1, 2, 3, 2, 3, 1]}\n\n        &gt;&gt;&gt; counts = get_counts(tree_list)\n        &gt;&gt;&gt; pprint.pprint(counts)\n        {'depth': {1: 32, 2: 27, 3: 41},\n         'features': {'constants': 44, 'variables': 170},\n         'function_conditionals': {'cos': {'features': {'constants': 0,\n                                                        'variables': 54},\n                                           'functions': {'cos': 7, 'sin': 6},\n                                           'operators': {}},\n                                   'sin': {'features': {'constants': 0,\n                                                        'variables': 55},\n                                           'functions': {'cos': 7, 'sin': 7},\n                                           'operators': {}}},\n         'functions': {'cos': 67, 'sin': 69},\n         'max_depth': {3: 59, 7: 41},\n         'operator_conditionals': {'+': {'features': {'constants': 24, 'variables': 29},\n                                         'functions': {'cos': 27, 'sin': 21},\n                                         'operators': {'+': 14, '-': 9}},\n                                   '-': {'features': {'constants': 20, 'variables': 32},\n                                         'functions': {'cos': 13, 'sin': 21},\n                                         'operators': {'+': 10, '-': 8}}},\n         'operators': {'+': 62, '-': 52},\n         'structures': {'[0, 1, 1]': 32, '[0, 1, 2, 3, 2, 3, 1]': 41, '[0, 1, 2]': 27}}\n    \"\"\"\n    info: Dict = {}\n    max_depth: Dict = {}\n    depth: Dict = {}\n    structures: Dict = {}\n    features: Dict = {}\n    functions: Dict = {}\n    operators: Dict = {}\n    function_conditionals: Dict = {}\n    operator_conditionals: Dict = {}\n    for t in trees:\n        _info = t.info\n        if \"max_depth\" in _info.keys():\n            _update(max_depth, _info[\"max_depth\"])\n        if \"depth\" in _info.keys():\n            _update(depth, _info[\"depth\"])\n        if \"structures\" in _info.keys():\n            _update(structures, str(_info[\"structures\"]))\n        if \"features\" in _info.keys():\n            for key, val in _info[\"features\"].items():\n                _update(features, key, val)\n        if \"functions\" in _info.keys():\n            for key, val in _info[\"functions\"].items():\n                _update(functions, key, val)\n        if \"operators\" in _info.keys():\n            for key, val in _info[\"operators\"].items():\n                _update(operators, key, val)\n        if \"function_conditionals\" in _info.keys():\n            fnc_con_dict = _info[\"function_conditionals\"]\n            for k, fnc_dict in fnc_con_dict.items():\n                if k not in function_conditionals.keys():\n                    function_conditionals[k] = {\n                        \"features\": {},\n                        \"functions\": {},\n                        \"operators\": {},\n                    }\n                fnc_dct_features = fnc_dict[\"features\"]\n                fnc_fct_functions = fnc_dict[\"functions\"]\n                fnc_fct_operators = fnc_dict[\"operators\"]\n                for key, val in fnc_dct_features.items():\n                    _update(function_conditionals[k][\"features\"], key, val)\n                for key, val in fnc_fct_functions.items():\n                    _update(function_conditionals[k][\"functions\"], key, val)\n                for key, val in fnc_fct_operators.items():\n                    _update(function_conditionals[k][\"operators\"], key, val)\n        if \"operator_conditionals\" in _info.keys():\n            op_con_dict = _info[\"operator_conditionals\"]\n            for k, op_dict in op_con_dict.items():\n                if k not in operator_conditionals.keys():\n                    operator_conditionals[k] = {\n                        \"features\": {},\n                        \"functions\": {},\n                        \"operators\": {},\n                    }\n                op_dct_features = op_dict[\"features\"]\n                op_fct_functions = op_dict[\"functions\"]\n                op_fct_operators = op_dict[\"operators\"]\n                for key, val in op_dct_features.items():\n                    _update(operator_conditionals[k][\"features\"], key, val)\n                for key, val in op_fct_functions.items():\n                    _update(operator_conditionals[k][\"functions\"], key, val)\n                for key, val in op_fct_operators.items():\n                    _update(operator_conditionals[k][\"operators\"], key, val)\n\n    info[\"max_depth\"] = max_depth\n    info[\"depth\"] = depth\n    info[\"structures\"] = structures\n    info[\"features\"] = features\n    info[\"functions\"] = functions\n    info[\"operators\"] = operators\n    info[\"function_conditionals\"] = function_conditionals\n    info[\"operator_conditionals\"] = operator_conditionals\n    return info\n</code></pre>"},{"location":"reference/src/equation_tree/analysis/#src.equation_tree.analysis.get_frequencies","title":"<code>get_frequencies(trees)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; import numpy as np\n&gt;&gt;&gt; import pprint\n&gt;&gt;&gt; np.random.seed(42)\n&gt;&gt;&gt; p = {\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .5, 'variables': .5},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': .5, '-': .5},\n...     'function_conditionals': {\n...                             'sin': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': .5, 'cos': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             },\n...                             'cos': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             }\n...                         },\n...     'operator_conditionals': {\n...                             '+': {\n...                                 'features': {'constants': .5, 'variables': .5},\n...                                 'functions': {'sin': .5, 'cos': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             },\n...                             '-': {\n...                                 'features': {'constants': .5, 'variables': .5},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .5, '-': .5}\n...                             }\n...                         },\n... }\n&gt;&gt;&gt; pprint.pprint(p)\n{'features': {'constants': 0.5, 'variables': 0.5},\n 'function_conditionals': {'cos': {'features': {'constants': 0.0,\n                                                'variables': 1.0},\n                                   'functions': {'cos': 0.5, 'sin': 0.5},\n                                   'operators': {'+': 0.5, '-': 0.5}},\n                           'sin': {'features': {'constants': 0.0,\n                                                'variables': 1.0},\n                                   'functions': {'cos': 0.5, 'sin': 0.5},\n                                   'operators': {'+': 0.5, '-': 0.5}}},\n 'functions': {'cos': 0.5, 'sin': 0.5},\n 'operator_conditionals': {'+': {'features': {'constants': 0.5,\n                                              'variables': 0.5},\n                                 'functions': {'cos': 0.5, 'sin': 0.5},\n                                 'operators': {'+': 0.5, '-': 0.5}},\n                           '-': {'features': {'constants': 0.5,\n                                              'variables': 0.5},\n                                 'functions': {'cos': 0.5, 'sin': 0.5},\n                                 'operators': {'+': 0.5, '-': 0.5}}},\n 'operators': {'+': 0.5, '-': 0.5},\n 'structures': {'[0, 1, 1]': 0.3,\n                '[0, 1, 2, 3, 2, 3, 1]': 0.4,\n                '[0, 1, 2]': 0.3}}\n</code></pre> <pre><code>&gt;&gt;&gt; tree_list = [EquationTree.from_prior(p, 4) for _ in range(100)]\n&gt;&gt;&gt; len(tree_list)\n100\n&gt;&gt;&gt; example_tree = tree_list[2]\n&gt;&gt;&gt; example_tree.expr\n['+', '-', 'sin', 'x_1', 'cos', 'x_2', 'c_1']\n&gt;&gt;&gt; example_tree.sympy_expr\nc_1 + sin(x_1) - cos(x_2)\n&gt;&gt;&gt; pprint.pprint(example_tree.info)\n{'depth': 3,\n 'features': {'constants': 1, 'variables': 2},\n 'function_conditionals': {'cos': {'features': {'constants': 0, 'variables': 1},\n                                   'functions': {},\n                                   'operators': {}},\n                           'sin': {'features': {'constants': 0, 'variables': 1},\n                                   'functions': {},\n                                   'operators': {}}},\n 'functions': {'cos': 1, 'sin': 1},\n 'max_depth': 7,\n 'operator_conditionals': {'+': {'features': {'constants': 1, 'variables': 0},\n                                 'functions': {},\n                                 'operators': {'-': 1}},\n                           '-': {'features': {'constants': 0, 'variables': 0},\n                                 'functions': {'cos': 1, 'sin': 1},\n                                 'operators': {}}},\n 'operators': {'+': 1, '-': 1},\n 'structures': [0, 1, 2, 3, 2, 3, 1]}\n</code></pre> <pre><code>&gt;&gt;&gt; frequencies = get_frequencies(tree_list)\n&gt;&gt;&gt; pprint.pprint(frequencies)\n{'depth': {1: 0.32, 2: 0.27, 3: 0.41},\n 'features': {'constants': 0.205607476635514, 'variables': 0.794392523364486},\n 'function_conditionals': {'cos': {'features': {'constants': 0.0,\n                                                'variables': 1.0},\n                                   'functions': {'cos': 0.5384615384615384,\n                                                 'sin': 0.46153846153846156},\n                                   'operators': {}},\n                           'sin': {'features': {'constants': 0.0,\n                                                'variables': 1.0},\n                                   'functions': {'cos': 0.5, 'sin': 0.5},\n                                   'operators': {}}},\n 'functions': {'cos': 0.49264705882352944, 'sin': 0.5073529411764706},\n 'max_depth': {3: 0.59, 7: 0.41},\n 'operator_conditionals': {'+': {'features': {'constants': 0.4528301886792453,\n                                              'variables': 0.5471698113207547},\n                                 'functions': {'cos': 0.5625, 'sin': 0.4375},\n                                 'operators': {'+': 0.6086956521739131,\n                                               '-': 0.391304347826087}},\n                           '-': {'features': {'constants': 0.38461538461538464,\n                                              'variables': 0.6153846153846154},\n                                 'functions': {'cos': 0.38235294117647056,\n                                               'sin': 0.6176470588235294},\n                                 'operators': {'+': 0.5555555555555556,\n                                               '-': 0.4444444444444444}}},\n 'operators': {'+': 0.543859649122807, '-': 0.45614035087719296},\n 'structures': {'[0, 1, 1]': 0.32,\n                '[0, 1, 2, 3, 2, 3, 1]': 0.41,\n                '[0, 1, 2]': 0.27}}\n</code></pre> Source code in <code>src/equation_tree/analysis.py</code> <pre><code>def get_frequencies(trees: List[EquationTree]):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; import numpy as np\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; np.random.seed(42)\n        &gt;&gt;&gt; p = {\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .5, 'variables': .5},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': .5, '-': .5},\n        ...     'function_conditionals': {\n        ...                             'sin': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': .5, 'cos': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             },\n        ...                             'cos': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             }\n        ...                         },\n        ...     'operator_conditionals': {\n        ...                             '+': {\n        ...                                 'features': {'constants': .5, 'variables': .5},\n        ...                                 'functions': {'sin': .5, 'cos': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             },\n        ...                             '-': {\n        ...                                 'features': {'constants': .5, 'variables': .5},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .5, '-': .5}\n        ...                             }\n        ...                         },\n        ... }\n        &gt;&gt;&gt; pprint.pprint(p)\n        {'features': {'constants': 0.5, 'variables': 0.5},\n         'function_conditionals': {'cos': {'features': {'constants': 0.0,\n                                                        'variables': 1.0},\n                                           'functions': {'cos': 0.5, 'sin': 0.5},\n                                           'operators': {'+': 0.5, '-': 0.5}},\n                                   'sin': {'features': {'constants': 0.0,\n                                                        'variables': 1.0},\n                                           'functions': {'cos': 0.5, 'sin': 0.5},\n                                           'operators': {'+': 0.5, '-': 0.5}}},\n         'functions': {'cos': 0.5, 'sin': 0.5},\n         'operator_conditionals': {'+': {'features': {'constants': 0.5,\n                                                      'variables': 0.5},\n                                         'functions': {'cos': 0.5, 'sin': 0.5},\n                                         'operators': {'+': 0.5, '-': 0.5}},\n                                   '-': {'features': {'constants': 0.5,\n                                                      'variables': 0.5},\n                                         'functions': {'cos': 0.5, 'sin': 0.5},\n                                         'operators': {'+': 0.5, '-': 0.5}}},\n         'operators': {'+': 0.5, '-': 0.5},\n         'structures': {'[0, 1, 1]': 0.3,\n                        '[0, 1, 2, 3, 2, 3, 1]': 0.4,\n                        '[0, 1, 2]': 0.3}}\n\n\n        &gt;&gt;&gt; tree_list = [EquationTree.from_prior(p, 4) for _ in range(100)]\n        &gt;&gt;&gt; len(tree_list)\n        100\n        &gt;&gt;&gt; example_tree = tree_list[2]\n        &gt;&gt;&gt; example_tree.expr\n        ['+', '-', 'sin', 'x_1', 'cos', 'x_2', 'c_1']\n        &gt;&gt;&gt; example_tree.sympy_expr\n        c_1 + sin(x_1) - cos(x_2)\n        &gt;&gt;&gt; pprint.pprint(example_tree.info)\n        {'depth': 3,\n         'features': {'constants': 1, 'variables': 2},\n         'function_conditionals': {'cos': {'features': {'constants': 0, 'variables': 1},\n                                           'functions': {},\n                                           'operators': {}},\n                                   'sin': {'features': {'constants': 0, 'variables': 1},\n                                           'functions': {},\n                                           'operators': {}}},\n         'functions': {'cos': 1, 'sin': 1},\n         'max_depth': 7,\n         'operator_conditionals': {'+': {'features': {'constants': 1, 'variables': 0},\n                                         'functions': {},\n                                         'operators': {'-': 1}},\n                                   '-': {'features': {'constants': 0, 'variables': 0},\n                                         'functions': {'cos': 1, 'sin': 1},\n                                         'operators': {}}},\n         'operators': {'+': 1, '-': 1},\n         'structures': [0, 1, 2, 3, 2, 3, 1]}\n\n        &gt;&gt;&gt; frequencies = get_frequencies(tree_list)\n        &gt;&gt;&gt; pprint.pprint(frequencies)\n        {'depth': {1: 0.32, 2: 0.27, 3: 0.41},\n         'features': {'constants': 0.205607476635514, 'variables': 0.794392523364486},\n         'function_conditionals': {'cos': {'features': {'constants': 0.0,\n                                                        'variables': 1.0},\n                                           'functions': {'cos': 0.5384615384615384,\n                                                         'sin': 0.46153846153846156},\n                                           'operators': {}},\n                                   'sin': {'features': {'constants': 0.0,\n                                                        'variables': 1.0},\n                                           'functions': {'cos': 0.5, 'sin': 0.5},\n                                           'operators': {}}},\n         'functions': {'cos': 0.49264705882352944, 'sin': 0.5073529411764706},\n         'max_depth': {3: 0.59, 7: 0.41},\n         'operator_conditionals': {'+': {'features': {'constants': 0.4528301886792453,\n                                                      'variables': 0.5471698113207547},\n                                         'functions': {'cos': 0.5625, 'sin': 0.4375},\n                                         'operators': {'+': 0.6086956521739131,\n                                                       '-': 0.391304347826087}},\n                                   '-': {'features': {'constants': 0.38461538461538464,\n                                                      'variables': 0.6153846153846154},\n                                         'functions': {'cos': 0.38235294117647056,\n                                                       'sin': 0.6176470588235294},\n                                         'operators': {'+': 0.5555555555555556,\n                                                       '-': 0.4444444444444444}}},\n         'operators': {'+': 0.543859649122807, '-': 0.45614035087719296},\n         'structures': {'[0, 1, 1]': 0.32,\n                        '[0, 1, 2, 3, 2, 3, 1]': 0.41,\n                        '[0, 1, 2]': 0.27}}\n    \"\"\"\n    info: Dict = {}\n    max_depth: Dict = {}\n    depth: Dict = {}\n    structures: Dict = {}\n    features: Dict = {}\n    functions: Dict = {}\n    operators: Dict = {}\n    function_conditionals: Dict = {}\n    operator_conditionals: Dict = {}\n    for t in trees:\n        _info = t.info\n        if \"max_depth\" in _info.keys():\n            _update(max_depth, _info[\"max_depth\"])\n        if \"depth\" in _info.keys():\n            _update(depth, _info[\"depth\"])\n        if \"structures\" in _info.keys():\n            _update(structures, str(_info[\"structures\"]))\n        if \"features\" in _info.keys():\n            for key, val in _info[\"features\"].items():\n                _update(features, key, val)\n        if \"functions\" in _info.keys():\n            for key, val in _info[\"functions\"].items():\n                _update(functions, key, val)\n        if \"operators\" in _info.keys():\n            for key, val in _info[\"operators\"].items():\n                _update(operators, key, val)\n        if \"function_conditionals\" in _info.keys():\n            fnc_con_dict = _info[\"function_conditionals\"]\n            for k, fnc_dict in fnc_con_dict.items():\n                if k not in function_conditionals.keys():\n                    function_conditionals[k] = {\n                        \"features\": {},\n                        \"functions\": {},\n                        \"operators\": {},\n                    }\n                fnc_dct_features = fnc_dict[\"features\"]\n                fnc_fct_functions = fnc_dict[\"functions\"]\n                fnc_fct_operators = fnc_dict[\"operators\"]\n                for key, val in fnc_dct_features.items():\n                    _update(function_conditionals[k][\"features\"], key, val)\n                for key, val in fnc_fct_functions.items():\n                    _update(function_conditionals[k][\"functions\"], key, val)\n                for key, val in fnc_fct_operators.items():\n                    _update(function_conditionals[k][\"operators\"], key, val)\n        if \"operator_conditionals\" in _info.keys():\n            op_con_dict = _info[\"operator_conditionals\"]\n            for k, op_dict in op_con_dict.items():\n                if k not in operator_conditionals.keys():\n                    operator_conditionals[k] = {\n                        \"features\": {},\n                        \"functions\": {},\n                        \"operators\": {},\n                    }\n                op_dct_features = op_dict[\"features\"]\n                op_fct_functions = op_dict[\"functions\"]\n                op_fct_operators = op_dict[\"operators\"]\n                for key, val in op_dct_features.items():\n                    _update(operator_conditionals[k][\"features\"], key, val)\n                for key, val in op_fct_functions.items():\n                    _update(operator_conditionals[k][\"functions\"], key, val)\n                for key, val in op_fct_operators.items():\n                    _update(operator_conditionals[k][\"operators\"], key, val)\n    for k_c in function_conditionals:\n        for k in [\"features\", \"functions\", \"operators\"]:\n            if k in function_conditionals[k_c]:\n                function_conditionals[k_c][k] = normalized_dict(\n                    function_conditionals[k_c][k]\n                )\n    for k_c in operator_conditionals:\n        for k in [\"features\", \"functions\", \"operators\"]:\n            if k in operator_conditionals[k_c]:\n                operator_conditionals[k_c][k] = normalized_dict(\n                    operator_conditionals[k_c][k]\n                )\n\n    info[\"max_depth\"] = normalized_dict(max_depth)\n    info[\"depth\"] = normalized_dict(depth)\n    info[\"structures\"] = normalized_dict(structures)\n    info[\"features\"] = normalized_dict(features)\n    info[\"functions\"] = normalized_dict(functions)\n    info[\"operators\"] = normalized_dict(operators)\n    info[\"function_conditionals\"] = function_conditionals\n    info[\"operator_conditionals\"] = operator_conditionals\n    return info\n</code></pre>"},{"location":"reference/src/equation_tree/defaults/","title":"Defaults","text":""},{"location":"reference/src/equation_tree/prior/","title":"Prior","text":""},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.add","title":"<code>add(prior_a, prior_b)</code>","text":"<p>import pprint a = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}} b = {'a': {'a_1': 2, 'a_2': 4}, 'c': {'b_1': 3, 'b_2': 3}} pprint.pprint(add(a, b)) {'a': {'a_1': 5, 'a_2': 6},  'b': {'b_1': 0.1, 'b_2': 0.3},  'c': {'b_1': 3, 'b_2': 3}}</p> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def add(prior_a, prior_b):\n    \"\"\"\n    &gt;&gt;&gt; import pprint\n    &gt;&gt;&gt; a = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}}\n    &gt;&gt;&gt; b = {'a': {'a_1': 2, 'a_2': 4}, 'c': {'b_1': 3, 'b_2': 3}}\n    &gt;&gt;&gt; pprint.pprint(add(a, b))\n    {'a': {'a_1': 5, 'a_2': 6},\n     'b': {'b_1': 0.1, 'b_2': 0.3},\n     'c': {'b_1': 3, 'b_2': 3}}\n\n    \"\"\"\n    tmp_a = copy.deepcopy(prior_a)\n    tmp_b = copy.deepcopy(prior_b)\n\n    def _rec_add(a, b):\n        for k, val in a.items():\n            if k in b.keys():\n                if isinstance(val, dict) and isinstance(b[k], dict):\n                    _rec_add(a[k], b[k])\n                elif not isinstance(val, dict) and not isinstance(b[k], dict):\n                    a[k] += b[k]\n\n    _rec_add(tmp_a, tmp_b)\n    return append(tmp_a, tmp_b)\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.filter_keys","title":"<code>filter_keys(dict_a, dict_b)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; import pprint\n&gt;&gt;&gt; a = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}, 'c': {}}\n&gt;&gt;&gt; b = {'a': {'a_1': 2, 'a_2': 4}, 'b': {'b_1': 3, 'c_1': 3}}\n&gt;&gt;&gt; pprint.pprint(filter_keys(a, b))\n{'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': 0.1}}\n</code></pre> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def filter_keys(dict_a, dict_b):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; a = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}, 'c': {}}\n        &gt;&gt;&gt; b = {'a': {'a_1': 2, 'a_2': 4}, 'b': {'b_1': 3, 'c_1': 3}}\n        &gt;&gt;&gt; pprint.pprint(filter_keys(a, b))\n        {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': 0.1}}\n    \"\"\"\n    tmp_a = copy.deepcopy(dict_a)\n    tmp_b = copy.deepcopy(dict_b)\n\n    def _rec_f_key(a, b):\n        for k in list(a.keys()):\n            if k in b.keys():\n                if isinstance(a[k], dict) and isinstance(b[k], dict):\n                    _rec_f_key(a[k], b[k])\n                else:\n                    a[k] = a[k]\n            else:\n                del a[k]\n\n    _rec_f_key(tmp_a, tmp_b)\n    return tmp_a\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.get_defined_functions","title":"<code>get_defined_functions(prior)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; test_prior = {\n...     'functions': {'sin': 2},\n...     'function_conditionals': {'sin': {'features': {'constants': 0, 'variables': 2},\n...                                   'functions': {},\n...                                       'operators': {}}},\n...     'operator_conditionals': {'+': {'features': {'constants': 0, 'variables': 1},\n...                                     'functions': {'cos': 2},\n...                                     'operators': {'-': 1}},\n...                               '-': {'features': {'constants': 0, 'variables': 0},\n...                                     'functions': {'sin': 2, 'abs': 1},\n...                                     'operators': {}}},\n...     'operators': {'+': 1, '-': 1},\n...     'structure': [0, 1, 2, 3, 2, 3, 1]}\n&gt;&gt;&gt; set(get_defined_functions(test_prior)) == set(['sin', 'abs', 'cos'])\nTrue\n</code></pre> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def get_defined_functions(prior):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; test_prior = {\n        ...     'functions': {'sin': 2},\n        ...     'function_conditionals': {'sin': {'features': {'constants': 0, 'variables': 2},\n        ...                                   'functions': {},\n        ...                                       'operators': {}}},\n        ...     'operator_conditionals': {'+': {'features': {'constants': 0, 'variables': 1},\n        ...                                     'functions': {'cos': 2},\n        ...                                     'operators': {'-': 1}},\n        ...                               '-': {'features': {'constants': 0, 'variables': 0},\n        ...                                     'functions': {'sin': 2, 'abs': 1},\n        ...                                     'operators': {}}},\n        ...     'operators': {'+': 1, '-': 1},\n        ...     'structure': [0, 1, 2, 3, 2, 3, 1]}\n        &gt;&gt;&gt; set(get_defined_functions(test_prior)) == set(['sin', 'abs', 'cos'])\n        True\n    \"\"\"\n    return _get_defined(prior, \"functions\", \"function_conditionals\")\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.get_defined_operators","title":"<code>get_defined_operators(prior)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; test_prior = {\n...     'function_conditionals': {'sin': {'features': {'constants': 0, 'variables': 2},\n...                                   'functions': {},\n...                                       'operators': {}}},\n...     'functions': {'sin': 2},\n...     'operator_conditionals': {'+': {'features': {'constants': 0, 'variables': 1},\n...                                     'functions': {'cos': 2},\n...                                     'operators': {'**': 1}},\n...                               '/': {'features': {'constants': 0, 'variables': 0},\n...                                     'functions': {'sin': 2},\n...                                     'operators': {}}},\n...     'operators': {'+': 1, '-': 1},\n...     'structure': [0, 1, 2, 3, 2, 3, 1]}\n&gt;&gt;&gt; set(get_defined_operators(test_prior)) == set(['+', '/', '**', '-'])\nTrue\n</code></pre> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def get_defined_operators(prior):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; test_prior = {\n        ...     'function_conditionals': {'sin': {'features': {'constants': 0, 'variables': 2},\n        ...                                   'functions': {},\n        ...                                       'operators': {}}},\n        ...     'functions': {'sin': 2},\n        ...     'operator_conditionals': {'+': {'features': {'constants': 0, 'variables': 1},\n        ...                                     'functions': {'cos': 2},\n        ...                                     'operators': {'**': 1}},\n        ...                               '/': {'features': {'constants': 0, 'variables': 0},\n        ...                                     'functions': {'sin': 2},\n        ...                                     'operators': {}}},\n        ...     'operators': {'+': 1, '-': 1},\n        ...     'structure': [0, 1, 2, 3, 2, 3, 1]}\n        &gt;&gt;&gt; set(get_defined_operators(test_prior)) == set(['+', '/', '**', '-'])\n        True\n    \"\"\"\n    return _get_defined(prior, \"operators\", \"operator_conditionals\")\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.multiply","title":"<code>multiply(a, b)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; import pprint\n&gt;&gt;&gt; prior_a = {'a':\n...                 {'a_1':  .2, 'a_2': .8},\n...             'b': {\n...                 'b_1' : {'b_1_1': .25, 'b_1_2': .5, 'b_1_3': .25}\n...             }\n...         }\n&gt;&gt;&gt; prior_b = {'a':\n...                 {'a_1':  4, 'a_2': 1},\n...             'b': {\n...                 'b_1' : {'b_1_1': 4 , 'b_1_2': 1, 'b_1_3': 4}\n...             },\n...             'c': {'c_1': .9, 'c_2': .1}\n...         }\n&gt;&gt;&gt; product = multiply(prior_a, prior_b)\n&gt;&gt;&gt; pprint.pprint(product)\n{'a': {'a_1': 0.8, 'a_2': 0.8},\n 'b': {'b_1': {'b_1_1': 1.0, 'b_1_2': 0.5, 'b_1_3': 1.0}},\n 'c': {'c_1': 0.9, 'c_2': 0.1}}\n&gt;&gt;&gt; normalize(product)\n&gt;&gt;&gt; pprint.pprint(product)\n{'a': {'a_1': 0.5, 'a_2': 0.5},\n 'b': {'b_1': {'b_1_1': 0.4, 'b_1_2': 0.2, 'b_1_3': 0.4}},\n 'c': {'c_1': 0.9, 'c_2': 0.1}}\n</code></pre> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def multiply(a, b):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; prior_a = {'a':\n        ...                 {'a_1':  .2, 'a_2': .8},\n        ...             'b': {\n        ...                 'b_1' : {'b_1_1': .25, 'b_1_2': .5, 'b_1_3': .25}\n        ...             }\n        ...         }\n        &gt;&gt;&gt; prior_b = {'a':\n        ...                 {'a_1':  4, 'a_2': 1},\n        ...             'b': {\n        ...                 'b_1' : {'b_1_1': 4 , 'b_1_2': 1, 'b_1_3': 4}\n        ...             },\n        ...             'c': {'c_1': .9, 'c_2': .1}\n        ...         }\n        &gt;&gt;&gt; product = multiply(prior_a, prior_b)\n        &gt;&gt;&gt; pprint.pprint(product)\n        {'a': {'a_1': 0.8, 'a_2': 0.8},\n         'b': {'b_1': {'b_1_1': 1.0, 'b_1_2': 0.5, 'b_1_3': 1.0}},\n         'c': {'c_1': 0.9, 'c_2': 0.1}}\n        &gt;&gt;&gt; normalize(product)\n        &gt;&gt;&gt; pprint.pprint(product)\n        {'a': {'a_1': 0.5, 'a_2': 0.5},\n         'b': {'b_1': {'b_1_1': 0.4, 'b_1_2': 0.2, 'b_1_3': 0.4}},\n         'c': {'c_1': 0.9, 'c_2': 0.1}}\n    \"\"\"\n    tmp_a = copy.deepcopy(a)\n    tmp_b = copy.deepcopy(b)\n\n    def _multiply(_a, _b):\n        for k, val in _a.items():\n            if k in _b.keys():\n                if isinstance(val, dict) and isinstance(_b[k], dict):\n                    _multiply(val, _b[k])\n                elif not isinstance(val, dict) and not isinstance(_b[k], dict):\n                    res = val * _b[k]\n                    _a[k] = res\n\n    _multiply(tmp_a, tmp_b)\n    tmp_a = append(tmp_a, tmp_b)\n\n    return tmp_a\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.prior_from_space","title":"<code>prior_from_space(space)</code>","text":"<p>Uniform prior from a list of strings Examples:     &gt;&gt;&gt; import pprint     &gt;&gt;&gt; operator_space = ['+', '-', '', '/', '^']     &gt;&gt;&gt; operator_prior = prior_from_space(operator_space)     &gt;&gt;&gt; pprint.pprint(operator_prior)     {'': 0.2, '+': 0.2, '-': 0.2, '/': 0.2, '^': 0.2}</p> <pre><code>&gt;&gt;&gt; function_space = ['sin', 'cos', 'tan', 'exp', 'log', 'sqrt', 'abs']\n&gt;&gt;&gt; function_prior = prior_from_space(function_space)\n&gt;&gt;&gt; pprint.pprint(function_prior)\n{'abs': 0.14285714285714285,\n 'cos': 0.14285714285714285,\n 'exp': 0.14285714285714285,\n 'log': 0.14285714285714285,\n 'sin': 0.14285714285714285,\n 'sqrt': 0.14285714285714285,\n 'tan': 0.14285714285714285}\n</code></pre> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def prior_from_space(space):\n    \"\"\"\n    Uniform prior from a list of strings\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; operator_space = ['+', '-', '*', '/', '^']\n        &gt;&gt;&gt; operator_prior = prior_from_space(operator_space)\n        &gt;&gt;&gt; pprint.pprint(operator_prior)\n        {'*': 0.2, '+': 0.2, '-': 0.2, '/': 0.2, '^': 0.2}\n\n        &gt;&gt;&gt; function_space = ['sin', 'cos', 'tan', 'exp', 'log', 'sqrt', 'abs']\n        &gt;&gt;&gt; function_prior = prior_from_space(function_space)\n        &gt;&gt;&gt; pprint.pprint(function_prior)\n        {'abs': 0.14285714285714285,\n         'cos': 0.14285714285714285,\n         'exp': 0.14285714285714285,\n         'log': 0.14285714285714285,\n         'sin': 0.14285714285714285,\n         'sqrt': 0.14285714285714285,\n         'tan': 0.14285714285714285}\n    \"\"\"\n    return priors_from_space(space)\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.re_normalize","title":"<code>re_normalize(target, origin)</code>","text":"Source code in <code>src/equation_tree/prior.py</code> <pre><code>def re_normalize(target, origin):\n    \"\"\" \"\"\"\n    tmp_t = copy.deepcopy(target)\n    tmp_o = copy.deepcopy(origin)\n\n    def _rec_re_normalize(t, p):\n        for k, val in t.items():\n            if isinstance(val, dict) and isinstance(p[k], dict):\n                _rec_re_normalize(t[k], p[k])\n            elif not isinstance(val, dict):\n                if not isinstance(p[k], dict) and val &lt;= 0 &lt; p[k]:\n                    t[k] = MIN\n                elif val &lt;= 0:\n                    t[k] = 0\n\n    _rec_re_normalize(tmp_t, tmp_o)\n    normalize(tmp_t)\n    return tmp_t\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.scalar_multiply","title":"<code>scalar_multiply(scalar, prior)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; import pprint\n&gt;&gt;&gt; m = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}}\n&gt;&gt;&gt; s = 2\n&gt;&gt;&gt; pprint.pprint(scalar_multiply(s, m))\n{'a': {'a_1': 6, 'a_2': 4}, 'b': {'b_1': 0.2, 'b_2': 0.6}}\n</code></pre> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def scalar_multiply(scalar, prior):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; m = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}}\n        &gt;&gt;&gt; s = 2\n        &gt;&gt;&gt; pprint.pprint(scalar_multiply(s, m))\n        {'a': {'a_1': 6, 'a_2': 4}, 'b': {'b_1': 0.2, 'b_2': 0.6}}\n    \"\"\"\n    tmp_p = copy.deepcopy(prior)\n\n    def _rec_s_mult(s, p):\n        for k, val in p.items():\n            if isinstance(val, dict):\n                _rec_s_mult(s, p[k])\n            else:\n                p[k] *= s\n\n    _rec_s_mult(scalar, tmp_p)\n    return tmp_p\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.structure_prior_from_depth","title":"<code>structure_prior_from_depth(depth)</code>","text":"<p>Uniform structure prior for a given depth Examples:     &gt;&gt;&gt; import pprint     &gt;&gt;&gt; pprint.pprint(structure_prior_from_depth(3))     {'[0, 1, 1]': 0.5, '[0, 1, 2]': 0.5}     &gt;&gt;&gt; pprint.pprint(structure_prior_from_depth(4))     {'[0, 1, 1, 2]': 0.25,      '[0, 1, 2, 1]': 0.25,      '[0, 1, 2, 2]': 0.25,      '[0, 1, 2, 3]': 0.25}</p> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def structure_prior_from_depth(depth):\n    \"\"\"\n    Uniform structure prior for a given depth\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; pprint.pprint(structure_prior_from_depth(3))\n        {'[0, 1, 1]': 0.5, '[0, 1, 2]': 0.5}\n        &gt;&gt;&gt; pprint.pprint(structure_prior_from_depth(4))\n        {'[0, 1, 1, 2]': 0.25,\n         '[0, 1, 2, 1]': 0.25,\n         '[0, 1, 2, 2]': 0.25,\n         '[0, 1, 2, 3]': 0.25}\n\n    \"\"\"\n    structures = _gen_tree_structures(depth)\n    structures = [s for s in structures if len(s) == depth]\n    return prior_from_space([str(s) for s in structures])\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.structure_prior_from_max_depth","title":"<code>structure_prior_from_max_depth(max_depth)</code>","text":"<p>Uniform structure prior up to a given depth (from min depth 3) Examples:     &gt;&gt;&gt; import pprint     &gt;&gt;&gt; pprint.pprint(structure_prior_from_max_depth(3))     {'[0, 1, 1]': 0.5, '[0, 1, 2]': 0.5}     &gt;&gt;&gt; pprint.pprint(structure_prior_from_max_depth(4))     {'[0, 1, 1, 2]': 0.16666666666666666,      '[0, 1, 1]': 0.16666666666666666,      '[0, 1, 2, 1]': 0.16666666666666666,      '[0, 1, 2, 2]': 0.16666666666666666,      '[0, 1, 2, 3]': 0.16666666666666666,      '[0, 1, 2]': 0.16666666666666666}     &gt;&gt;&gt; pprint.pprint(structure_prior_from_max_depth(5))     {'[0, 1, 1, 2, 2]': 0.06666666666666667,      '[0, 1, 1, 2, 3]': 0.06666666666666667,      '[0, 1, 1, 2]': 0.06666666666666667,      '[0, 1, 1]': 0.06666666666666667,      '[0, 1, 2, 1, 2]': 0.06666666666666667,      '[0, 1, 2, 1]': 0.06666666666666667,      '[0, 1, 2, 2, 1]': 0.06666666666666667,      '[0, 1, 2, 2, 3]': 0.06666666666666667,      '[0, 1, 2, 2]': 0.06666666666666667,      '[0, 1, 2, 3, 1]': 0.06666666666666667,      '[0, 1, 2, 3, 2]': 0.06666666666666667,      '[0, 1, 2, 3, 3]': 0.06666666666666667,      '[0, 1, 2, 3, 4]': 0.06666666666666667,      '[0, 1, 2, 3]': 0.06666666666666667,      '[0, 1, 2]': 0.06666666666666667}</p> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def structure_prior_from_max_depth(max_depth):\n    \"\"\"\n    Uniform structure prior up to a given depth (from min depth 3)\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; pprint.pprint(structure_prior_from_max_depth(3))\n        {'[0, 1, 1]': 0.5, '[0, 1, 2]': 0.5}\n        &gt;&gt;&gt; pprint.pprint(structure_prior_from_max_depth(4))\n        {'[0, 1, 1, 2]': 0.16666666666666666,\n         '[0, 1, 1]': 0.16666666666666666,\n         '[0, 1, 2, 1]': 0.16666666666666666,\n         '[0, 1, 2, 2]': 0.16666666666666666,\n         '[0, 1, 2, 3]': 0.16666666666666666,\n         '[0, 1, 2]': 0.16666666666666666}\n        &gt;&gt;&gt; pprint.pprint(structure_prior_from_max_depth(5))\n        {'[0, 1, 1, 2, 2]': 0.06666666666666667,\n         '[0, 1, 1, 2, 3]': 0.06666666666666667,\n         '[0, 1, 1, 2]': 0.06666666666666667,\n         '[0, 1, 1]': 0.06666666666666667,\n         '[0, 1, 2, 1, 2]': 0.06666666666666667,\n         '[0, 1, 2, 1]': 0.06666666666666667,\n         '[0, 1, 2, 2, 1]': 0.06666666666666667,\n         '[0, 1, 2, 2, 3]': 0.06666666666666667,\n         '[0, 1, 2, 2]': 0.06666666666666667,\n         '[0, 1, 2, 3, 1]': 0.06666666666666667,\n         '[0, 1, 2, 3, 2]': 0.06666666666666667,\n         '[0, 1, 2, 3, 3]': 0.06666666666666667,\n         '[0, 1, 2, 3, 4]': 0.06666666666666667,\n         '[0, 1, 2, 3]': 0.06666666666666667,\n         '[0, 1, 2]': 0.06666666666666667}\n    \"\"\"\n    structures = _gen_tree_structures(max_depth)\n    return prior_from_space([str(s) for s in structures])\n</code></pre>"},{"location":"reference/src/equation_tree/prior/#src.equation_tree.prior.subtract","title":"<code>subtract(minuend, subtrahend)</code>","text":"<p>Minuend - Subtrahend Examples:     &gt;&gt;&gt; import pprint     &gt;&gt;&gt; m = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}}     &gt;&gt;&gt; s = {'a': {'a_1': 2, 'a_2': 4}}     &gt;&gt;&gt; pprint.pprint(subtract(m, s))     {'a': {'a_1': 1, 'a_2': -2}, 'b': {'b_1': 0.0, 'b_2': 0.0}}</p> Source code in <code>src/equation_tree/prior.py</code> <pre><code>def subtract(minuend, subtrahend):\n    \"\"\"\n    Minuend - Subtrahend\n    Examples:\n        &gt;&gt;&gt; import pprint\n        &gt;&gt;&gt; m = {'a': {'a_1': 3, 'a_2': 2}, 'b': {'b_1': .1, 'b_2': .3}}\n        &gt;&gt;&gt; s = {'a': {'a_1': 2, 'a_2': 4}}\n        &gt;&gt;&gt; pprint.pprint(subtract(m, s))\n        {'a': {'a_1': 1, 'a_2': -2}, 'b': {'b_1': 0.0, 'b_2': 0.0}}\n\n    \"\"\"\n    tmp_m = copy.deepcopy(minuend)\n    tmp_s = copy.deepcopy(subtrahend)\n\n    def _rec_sub(m, s):\n        for k, val in m.items():\n            if k in s.keys():\n                if isinstance(val, dict) and isinstance(s[k], dict):\n                    _rec_sub(val, s[k])\n                elif (\n                    not isinstance(val, dict)\n                    and is_numeric(val)\n                    and not isinstance(s[k], dict)\n                    and is_numeric(s[k])\n                ):\n                    m[k] -= s[k]\n                else:\n                    if not isinstance(val, dict):\n                        m[k] = 0.0\n                    else:\n                        _set_zero(m[k])\n            else:\n                if not isinstance(val, dict):\n                    m[k] = 0.0\n                else:\n                    _set_zero(m[k])\n\n    _rec_sub(tmp_m, tmp_s)\n    return tmp_m\n</code></pre>"},{"location":"reference/src/equation_tree/sample/","title":"Sample","text":""},{"location":"reference/src/equation_tree/sample/#src.equation_tree.sample.sample_tree_raw_from_priors","title":"<code>sample_tree_raw_from_priors(max_num_constants=0, max_num_variables=1, feature_priors=None, function_priors=DEFAULT_FUNCTION_SPACE, operator_priors=DEFAULT_OPERATOR_SPACE, structure_priors={})</code>","text":"<p>Sample a tree from priors, simplify and check if valid tree</p> Source code in <code>src/equation_tree/sample.py</code> <pre><code>def sample_tree_raw_from_priors(\n    max_num_constants: int = 0,\n    max_num_variables: int = 1,\n    feature_priors: Optional[Dict] = None,\n    function_priors: PriorType = DEFAULT_FUNCTION_SPACE,\n    operator_priors: PriorType = DEFAULT_OPERATOR_SPACE,\n    structure_priors: PriorType = {},\n):\n    \"\"\"\n    Sample a tree from priors, simplify and check if valid tree\n    \"\"\"\n    # Assertions\n    if max_num_constants + max_num_variables &lt; 1:\n        raise Exception(\"Can not sample tree without leafs\")\n\n    # Get feature priors\n    if feature_priors is not None:\n        for key in feature_priors:\n            if not (is_variable_formatted(key) or is_constant_formatted(key)):\n                raise Exception(\n                    \"Use standard formats for feature priors: x_{int} for variables, \"\n                    \"c_{int} for constants.\"\n                )\n        _feature_priors = feature_priors.copy()\n    else:\n        _feature_space = [f\"x_{i}\" for i in range(1, max_num_variables + 1)] + [\n            f\"c_{i}\" for i in range(1, max_num_constants + 1)\n        ]\n        _feature_priors = priors_from_space(_feature_space)\n\n    # Convert priors if space is given\n    if isinstance(function_priors, List):\n        _function_priors = priors_from_space(function_priors)\n    else:\n        _function_priors = function_priors.copy()\n\n    if isinstance(operator_priors, List):\n        _operator_priors = priors_from_space(operator_priors)\n    else:\n        _operator_priors = operator_priors.copy()\n\n    if isinstance(structure_priors, List):\n        _structure_priors = priors_from_space(structure_priors)\n    else:\n        _structure_priors = structure_priors.copy()\n\n    # Create tree\n    equation_tree = EquationTree.from_priors(\n        feature_priors=_feature_priors,\n        function_priors=_function_priors,\n        operator_priors=_operator_priors,\n        structure_priors=_structure_priors,\n    )\n\n    # Check if tree is valid\n    if not equation_tree.check_validity():\n        return None\n\n    equation_tree.simplify(\n        function_test=lambda x: x in _function_priors.keys(),\n        operator_test=lambda x: x in _operator_priors.keys(),\n    )\n\n    # Check is nan\n    if equation_tree.is_nan:\n        return None\n\n    # Check if duplicate constants\n    if (\n        equation_tree.n_non_numeric_constants\n        &gt; equation_tree.n_non_numeric_constants_unique\n    ):\n        return None\n\n    # Check if more constants than max:\n    if equation_tree.n_constants &gt; max_num_constants:\n        return None\n\n    # Check if more variables than max:\n    if equation_tree.n_variables &gt; max_num_variables:\n        return None\n\n    if not equation_tree.check_validity():\n        return None\n\n    if not equation_tree.check_possible(\n        _feature_priors, _function_priors, _operator_priors, _structure_priors\n    ):\n        return None\n\n    equation_tree.get_evaluation()\n    if not equation_tree.has_valid_value:\n        return None\n\n    return equation_tree\n</code></pre>"},{"location":"reference/src/equation_tree/tree/","title":"Tree","text":""},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree","title":"<code>EquationTree</code>","text":"<p>Equation tree that represents an equation as binary tree.</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>class EquationTree:\n    \"\"\"\n    Equation tree that represents an equation as binary tree.\n    \"\"\"\n\n    def __init__(self, node: TreeNode):\n        \"\"\"\n        Initializes a tree from a TreeNode\n\n        Examples:\n            # We can inititlize from a single node\n            &gt;&gt;&gt; node_root = TreeNode(kind=NodeKind.VARIABLE, attribute=\"x\")\n            &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n            &gt;&gt;&gt; equation_tree.expr\n            ['x']\n            &gt;&gt;&gt; equation_tree.structure\n            [0]\n            &gt;&gt;&gt; equation_tree.variables\n            ['x']\n\n            # Or from a node with children\n            &gt;&gt;&gt; node_left = TreeNode(kind=NodeKind.VARIABLE, attribute=\"x\")\n            &gt;&gt;&gt; node_right = TreeNode(kind=NodeKind.CONSTANT, attribute=\"c\")\n            &gt;&gt;&gt; node_root = TreeNode(kind=NodeKind.OPERATOR, attribute=\"+\", \\\n                            left=node_left, right=node_right)\n            &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n            &gt;&gt;&gt; equation_tree.expr\n            ['+', 'x', 'c']\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 1]\n            &gt;&gt;&gt; equation_tree.variables\n            ['x']\n            &gt;&gt;&gt; equation_tree.constants\n            ['c']\n            &gt;&gt;&gt; equation_tree.operators\n            ['+']\n\n            # We can first sample a node and children and initialize from that\n            &gt;&gt;&gt; np.random.seed(42)\n            &gt;&gt;&gt; max_depth = 12\n            &gt;&gt;&gt; structure_priors = {'[0, 1, 2, 1, 2, 3]': .5, '[0, 1, 2, 2, 1, 2, 3]': .5}\n            &gt;&gt;&gt; feature_priors = {\"x_1\": 0.5, \"c_1\": 0.5}\n            &gt;&gt;&gt; function_priors = {\"sin\": 0.5, \"cos\": 0.5}\n            &gt;&gt;&gt; operator_priors = {\"+\": 0.5, \"-\": 0.5}\n            &gt;&gt;&gt; node_root = sample_tree(feature_priors, function_priors,\n            ...     operator_priors, structure_priors)\n            &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n            &gt;&gt;&gt; equation_tree.expr\n            ['-', 'cos', 'c_1', 'sin', 'sin', 'x_1']\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2, 1, 2, 3]\n            &gt;&gt;&gt; equation_tree.variables\n            ['x_1']\n            &gt;&gt;&gt; equation_tree.n_variables\n            1\n            &gt;&gt;&gt; equation_tree.n_variables_unique\n            1\n            &gt;&gt;&gt; equation_tree.constants\n            ['c_1']\n            &gt;&gt;&gt; equation_tree.n_constants\n            1\n            &gt;&gt;&gt; equation_tree.n_constants_unique\n            1\n            &gt;&gt;&gt; equation_tree.n_leafs\n            2\n            &gt;&gt;&gt; equation_tree.operators\n            ['-']\n            &gt;&gt;&gt; equation_tree.functions\n            ['cos', 'sin', 'sin']\n\n            # First we create test functions that test weather an attribute is a variable,\n            # a constant, a function, or an operater\n            &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n            &gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n            &gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n            &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n\n            # here we use the prefix notation\n            &gt;&gt;&gt; prefix_notation = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n\n            # then we create the node root\n            &gt;&gt;&gt; node_root = node_from_prefix(\n            ...     prefix_notation=prefix_notation,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     function_test=is_function,\n            ...     operator_test=is_operator\n            ...     )\n\n            # and initialize the tree\n            &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2, 2, 1, 2, 3, 2, 3]\n            &gt;&gt;&gt; equation_tree.variables\n            ['x', 'y', 'z']\n            &gt;&gt;&gt; equation_tree.constants\n            ['1']\n            &gt;&gt;&gt; equation_tree.operators\n            ['+', '-', '*']\n            &gt;&gt;&gt; equation_tree.functions\n            ['sin', 'cos']\n\n            # The tree expression is the same as the prefix notation\n            &gt;&gt;&gt; equation_tree.expr == prefix_notation\n            True\n        \"\"\"\n\n        self.root: Union[TreeNode, None] = node\n\n        self.structure: List[int] = []\n\n        self.expr: List[str] = list()\n\n        self.variables: List[str] = list()\n        self.functions: List[str] = list()\n        self.operators: List[str] = list()\n        self.constants: List[str] = list()\n\n        self.evaluation = None\n\n        self._build()\n\n    def __repr__(self):\n        return str(self.sympy_expr)\n\n    @classmethod\n    def from_prefix(\n        cls,\n        prefix_notation: List[str],\n        function_test: Callable = lambda _: False,\n        operator_test: Callable = lambda _: False,\n        variable_test: Callable = lambda _: False,\n        constant_test: Callable = lambda _: False,\n    ):\n        \"\"\"\n        Instantiate a tree from prefix notation\n\n        Args:\n            prefix_notation: The equation in prefix notation\n            function_test: A function that tests if the attribute is a function\n            operator_test: A function that tests if the attribute is an operator\n            variable_test: A function that tests if the attribute is a variable\n            constant_test: A function that tests if the attribute is a constant\n\n        Example:\n            &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n            &gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n            &gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n            &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n            &gt;&gt;&gt; prefix = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n\n            # then we create the node root\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     prefix_notation=prefix,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     function_test=is_function,\n            ...     operator_test=is_operator\n            ...     )\n\n            # and initialize the tree\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2, 2, 1, 2, 3, 2, 3]\n            &gt;&gt;&gt; equation_tree.variables\n            ['x', 'y', 'z']\n            &gt;&gt;&gt; equation_tree.constants\n            ['1']\n            &gt;&gt;&gt; equation_tree.operators\n            ['+', '-', '*']\n            &gt;&gt;&gt; equation_tree.functions\n            ['sin', 'cos']\n\n            # The tree expression is the same as the prefix notation\n            &gt;&gt;&gt; equation_tree.expr == prefix\n            True\n\n\n        \"\"\"\n        root = node_from_prefix(\n            prefix_notation, function_test, operator_test, variable_test, constant_test\n        )\n        return cls(root)\n\n    @classmethod\n    def from_full_prior(cls, prior):\n        root = sample_tree_full(prior)\n        return cls(root)\n\n    @classmethod\n    def from_prior_fast(cls, prior: Dict, tree_depth, max_variables_unique: int):\n        \"\"\"\n        Initiate a tree from a prior with fast sampling\n        Attention: structure prior is not supported\n\n        Args:\n            prior: The priors in dictionary form (structure priors are not needed)\n            tree_depth: depth of the tree\n            max_variables_unique: The maximum number of unique variables (a tree can have less then\n                this number)\n        \"\"\"\n        root = sample_tree_full_fast(prior, tree_depth, max_variables_unique)\n        return cls(root)\n\n    @classmethod\n    def from_prior(cls, prior: Dict, max_variables_unique: int):\n        \"\"\"\n        Initiate a tree from a prior\n\n        Args:\n            prior: The priors in dictionary form\n            max_variables_unique: The maximum number of unique variables (a tree can have less then\n                this number)\n\n        Examples:\n            &gt;&gt;&gt; np.random.seed(42)\n\n            # We can set priors for features, functions, operators\n            # and also conditionals based the parent\n            &gt;&gt;&gt; p = {\n            ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n            ...     'features': {'constants': .2, 'variables': .8},\n            ...     'functions': {'sin': .5, 'cos': .5},\n            ...     'operators': {'+': 1., '-': .0},\n            ...     'function_conditionals': {\n            ...                             'sin': {\n            ...                                 'features': {'constants': 0., 'variables': 1.},\n            ...                                 'functions': {'sin': 0., 'cos': 1.},\n            ...                                 'operators': {'+': 0., '-': 1.}\n            ...                             },\n            ...                             'cos': {\n            ...                                 'features': {'constants': 0., 'variables': 1.},\n            ...                                 'functions': {'cos': 1., 'sin': 0.},\n            ...                                 'operators': {'+': 0., '-': 1.}\n            ...                             }\n            ...                         },\n            ...     'operator_conditionals': {\n            ...                             '+': {\n            ...                                 'features': {'constants': .5, 'variables': .5},\n            ...                                 'functions': {'sin': 1., 'cos': 0.},\n            ...                                 'operators': {'+': 1., '-': 0.}\n            ...                             },\n            ...                             '-': {\n            ...                                 'features': {'constants': .3, 'variables': .7},\n            ...                                 'functions': {'cos': .5, 'sin': .5},\n            ...                                 'operators': {'+': .9, '-': .1}\n            ...                             }\n            ...                         },\n            ... }\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2]\n            &gt;&gt;&gt; equation_tree.expr\n            ['cos', 'cos', 'x_1']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2]\n            &gt;&gt;&gt; equation_tree.expr\n            ['sin', 'cos', 'x_1']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 1]\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2, 3, 2, 3, 1]\n            &gt;&gt;&gt; equation_tree.expr\n            ['+', '+', 'sin', 'x_1', 'sin', 'x_2', 'x_2']\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            x_2 + sin(x_1) + sin(x_2)\n\n            # Without conditionals, the unconditioned priors are the fallback option\n            &gt;&gt;&gt; p = {\n            ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n            ...     'features': {'constants': .2, 'variables': .8},\n            ...     'functions': {'sin': .5, 'cos': .5},\n            ...     'operators': {'+': .5, '-': .5},\n            ... }\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2, 3, 2, 3, 1]\n            &gt;&gt;&gt; equation_tree.expr\n            ['+', '-', 'cos', 'c_1', 'cos', 'c_2', 'c_3']\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            c_3 + cos(c_1) - cos(c_2)\n\n            # Note: this would be discarded in a future step as unnecesarry complex\n        \"\"\"\n        root = sample_tree_full(prior, max_variables_unique)\n        return cls(root)\n\n\n\n    @classmethod\n    def from_priors(\n        cls,\n        feature_priors={},\n        function_priors={},\n        operator_priors={},\n        structure_priors={},\n    ):\n        \"\"\"\n        Instantiate a tree from priors\n\n        Attention\n            - use standard notation here:   variables should be in form x_{number}\n                                            constants should be in form c_{number}\n\n        Args:\n            max_depth: Maximum depth of the tree\n            feature_priors: The priors for the features (variables + constants)\n            function_priors: The priors for the functions\n            operator_priors: The priors for the operators\n            structure_priors: The priors for the tree structures\n\n        Example:\n            &gt;&gt;&gt; np.random.seed(42)\n            &gt;&gt;&gt; max_depth = 12\n            &gt;&gt;&gt; feature_priors = {\"x_1\": 0.5, \"c_1\": 0.5}\n            &gt;&gt;&gt; function_priors = {\"sin\": 0.5, \"cos\": 0.5}\n            &gt;&gt;&gt; operator_priors = {\"+\": 0.5, \"-\": 0.5}\n            &gt;&gt;&gt; structure_priors = {'[0, 1, 2, 3, 4, 5, 5, 2, 3, 4, 4]': 1}\n            &gt;&gt;&gt; equation_tree = EquationTree.from_priors(\n            ...     feature_priors, function_priors, operator_priors, structure_priors)\n            &gt;&gt;&gt; equation_tree.expr\n            ['cos', '-', 'cos', 'sin', '+', 'x_1', 'c_1', 'cos', '-', 'x_1', 'c_1']\n            &gt;&gt;&gt; equation_tree.structure\n            [0, 1, 2, 3, 4, 5, 5, 2, 3, 4, 4]\n            &gt;&gt;&gt; equation_tree.variables\n            ['x_1', 'x_1']\n            &gt;&gt;&gt; equation_tree.n_variables\n            2\n            &gt;&gt;&gt; equation_tree.n_variables_unique\n            1\n            &gt;&gt;&gt; equation_tree.constants\n            ['c_1', 'c_1']\n            &gt;&gt;&gt; equation_tree.n_constants\n            2\n            &gt;&gt;&gt; equation_tree.n_constants_unique\n            1\n            &gt;&gt;&gt; equation_tree.n_leafs\n            4\n            &gt;&gt;&gt; equation_tree.operators\n            ['-', '+', '-']\n            &gt;&gt;&gt; equation_tree.functions\n            ['cos', 'cos', 'sin', 'cos']\n        \"\"\"\n        root = sample_tree(\n            feature_priors,\n            function_priors,\n            operator_priors,\n            structure_priors,\n        )\n        return cls(root)\n\n    @classmethod\n    def from_sympy(\n        cls,\n        expression,\n        function_test: Callable = lambda _: False,\n        operator_test: Callable = lambda _: False,\n        variable_test: Callable = lambda _: False,\n        constant_test: Callable = lambda _: False,\n    ):\n        \"\"\"\n        Instantiate a tree from a sympy function\n\n        Attention:\n            - constant and variable names get standardized\n            - unary minus get converted to binary minus\n\n        Examples:\n            &gt;&gt;&gt; expr = sympify('x_a + B * y')\n            &gt;&gt;&gt; expr\n            B*y + x_a\n            &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*']\n            &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n            &gt;&gt;&gt; is_constant = lambda x : x == 'B'\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant\n            ... )\n            &gt;&gt;&gt; equation_tree.expr\n            ['+', '*', 'c_1', 'x_2', 'x_1']\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            c_1*x_2 + x_1\n\n            # Numbers don't get standardized but are constants\n            &gt;&gt;&gt; expr = sympify('x_a + 2 * y')\n            &gt;&gt;&gt; expr\n            x_a + 2*y\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant\n            ... )\n            &gt;&gt;&gt; equation_tree.expr\n            ['+', 'x_1', '*', '2', 'x_2']\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            x_1 + 2*x_2\n            &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**']\n            &gt;&gt;&gt; is_variable = lambda x: '_' in x\n            &gt;&gt;&gt; is_constant = lambda x: x == 'B'\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     sympify('B*x_1**2'),\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant\n            ... )\n\n            &gt;&gt;&gt; expr = sympify('min(x_1, x_2)')\n            &gt;&gt;&gt; expr\n            Min(x_1, x_2)\n            &gt;&gt;&gt; is_operator = lambda x : x in ['min']\n            &gt;&gt;&gt; is_variable = lambda x : x in ['x_1', 'x_2']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ... )\n            &gt;&gt;&gt; equation_tree.expr\n            ['min', 'x_1', 'x_2']\n\n            &gt;&gt;&gt; expr = sympify('x_1**2')\n            &gt;&gt;&gt; expr\n            x_1**2\n            &gt;&gt;&gt; is_operator = lambda x : x in ['*', '/', '**', '+']\n            &gt;&gt;&gt; is_variable = lambda x : x in ['x_1']\n            &gt;&gt;&gt; is_function = lambda x : x in ['squared']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ...     function_test=is_function\n            ... )\n            &gt;&gt;&gt; equation_tree.expr\n            ['squared', 'x_1']\n\n        \"\"\"\n        standard = standardize_sympy(expression, variable_test, constant_test)\n        standard = unary_minus_to_binary(standard, operator_test)\n        standard = op_const_to_func(standard)\n        prefix = infix_to_prefix(str(standard), function_test, operator_test)\n        root = node_from_prefix(\n            prefix,\n            function_test,\n            operator_test,\n            lambda x: \"x_\" in x,\n            lambda x: \"c_\" in x,\n        )\n        return cls(root)\n\n    @property\n    def constants_unique(self):\n        return list(set(self.constants))\n\n    @property\n    def n_constants(self):\n        return len(self.constants)\n\n    @property\n    def n_constants_unique(self):\n        return len(set(self.constants))\n\n    @property\n    def non_numeric_constants(self):\n        return [\n            c for c in self.constants if not is_numeric(c) and not is_known_constant(c)\n        ]\n\n    @property\n    def non_numeric_constants_unique(self):\n        return list(set(self.non_numeric_constants))\n\n    @property\n    def n_non_numeric_constants_unique(self):\n        return len(self.non_numeric_constants_unique)\n\n    @property\n    def n_non_numeric_constants(self):\n        return len(self.non_numeric_constants)\n\n    @property\n    def variables_unique(self):\n        return list(set(self.variables))\n\n    @property\n    def n_variables(self):\n        return len(self.variables)\n\n    @property\n    def n_variables_unique(self):\n        return len(set(self.variables))\n\n    @property\n    def functions_unique(self):\n        return list(set(self.functions))\n\n    @property\n    def operators_unique(self):\n        return list(set(self.operators))\n\n    @property\n    def n_leafs(self):\n        return self.n_constants + self.n_variables\n\n    # TODO: implement this\n    @property\n    def standard_structure(self):\n        return self.structure\n\n    @property\n    def prefix(self):\n        return self.expr\n\n    @property\n    def infix(self):\n        return prefix_to_infix(\n            self.prefix, lambda x: x in self.functions, lambda x: x in self.operators\n        )\n\n    @property\n    def sympy_expr(self):\n        _infix = func_to_op_const(self.infix)\n        sympy_expr = sympify(_infix)\n        if sympy_expr.free_symbols:\n            symbol_names = [str(symbol) for symbol in sympy_expr.free_symbols]\n            real_symbols = symbols(\" \".join(symbol_names), real=True)\n            if not isinstance(real_symbols, list) and not isinstance(\n                real_symbols, tuple\n            ):\n                real_symbols = [real_symbols]\n            subs_dict = {old: new for old, new in zip(symbol_names, real_symbols)}\n            sympy_expr = sympy_expr.subs(subs_dict)\n        return sympy_expr\n\n    @property\n    def is_nan(self):\n        return self.root is None\n\n    @property\n    def value_samples_as_df(self):\n        if self.evaluation is None:\n            warnings.warn(\n                \"Tree not yet evaluated. Use method get_evaluation to evaluate the tree\"\n            )\n            return None\n        data = {\"observation\": self.evaluation[:, 0]}\n        for idx, key in enumerate(self.expr):\n            if key in self.variables:\n                data[key] = self.evaluation[:, idx]\n            if key in self.non_numeric_constants:\n                data[key] = self.evaluation[:, idx]\n        return pd.DataFrame(data)\n\n    @property\n    def has_valid_value(self):\n        if self.evaluation is None:\n            warnings.warn(\n                \"Tree not yet evaluated. Use method get_evaluation to evaluate the tree\"\n            )\n            return False\n        ev = self.evaluation[0, :]\n        return np.any(np.isfinite(ev) &amp; ~np.isnan(ev))\n\n    @property\n    def depth(self):\n        return max(self.structure)\n\n    @property\n    def n_nodes(self):\n        return len(self.structure)\n\n    @property\n    def info(self):\n        \"\"\"\n        Get al information as dictionary\n        \"\"\"\n        info = {}\n        info[\"max_depth\"] = len(self.structure)\n        info[\"depth\"] = max(self.structure)\n        info[\"structures\"] = self.structure\n        info[\"features\"] = {\n            \"constants\": self.n_constants,\n            \"variables\": self.n_variables,\n        }\n        functions = {}\n        function_conditionals = {key: {} for key in self.functions_unique}\n        for f in self.functions_unique:\n            functions[f] = len([_f for _f in self.functions if _f == f])\n            p_functions, p_operators, p_features = self._get_conditionals(f)\n            function_conditionals[f][\"functions\"] = p_functions\n            function_conditionals[f][\"operators\"] = p_operators\n            function_conditionals[f][\"features\"] = p_features\n        operators = {}\n        operator_conditionals = {key: {} for key in self.operators_unique}\n        for o in self.operators_unique:\n            operators[o] = len([_o for _o in self.operators if _o == o])\n            p_functions, p_operators, p_features = self._get_conditionals(o)\n            operator_conditionals[o][\"functions\"] = p_functions\n            operator_conditionals[o][\"operators\"] = p_operators\n            operator_conditionals[o][\"features\"] = p_features\n        info[\"functions\"] = functions\n        info[\"function_conditionals\"] = function_conditionals\n        info[\"operators\"] = operators\n        info[\"operator_conditionals\"] = operator_conditionals\n        return info\n\n    def evaluate(self, variables: Union[dict, pd.DataFrame]):\n        \"\"\"\n        Examples:\n            &gt;&gt;&gt; expr = sympify('x_a + 3 * y')\n            &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*']\n            &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ... )\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            x_1 + 3*x_2\n\n            # We can use dicts:\n            &gt;&gt;&gt; equation_tree.evaluate({'x_1': np.array([2, 3]), 'x_2': np.array([1, 1])})\n            array([5, 6])\n\n            # Or pandas dataframe:\n            &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': np.array([2, 3]), 'x_2': np.array([1, 1])})\n            &gt;&gt;&gt; dataFrame\n               x_1  x_2\n            0    2    1\n            1    3    1\n            &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n            array([5, 6])\n\n            # Or pandas dataframe:\n            &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [2, 3], 'x_2': [1, 1]})\n            &gt;&gt;&gt; dataFrame\n               x_1  x_2\n            0    2    1\n            1    3    1\n            &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n            array([5, 6])\n\n            &gt;&gt;&gt; expr = sympify('min(x_1,x_2)')\n            &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', 'min']\n            &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1', 'x_2']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable,\n            ... )\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            Min(x_1, x_2)\n\n            &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [1, 2, 3, 4], 'x_2': [2, 1, 4, 3]})\n            &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n            array([1, 1, 3, 3])\n\n            &gt;&gt;&gt; expr = sympify('max(3, x_1)')\n            &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', 'min', 'max']\n            &gt;&gt;&gt; is_function = lambda x : x in ['sqrt', 'log', 'abs']\n            &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1', 'x_2']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     function_test=is_function,\n            ...     operator_test=is_operator,\n            ...     variable_test=is_variable)\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            Max(3, x_1)\n            &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [1, 2, 3, 4]})\n            &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n            array([3, 3, 3, 4])\n\n            &gt;&gt;&gt; expr = sympify('x_1 + sqrt(x_1)')\n            &gt;&gt;&gt; is_operator = lambda x : x in ['+']\n            &gt;&gt;&gt; is_function = lambda x: x in ['sqrt']\n            &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n            ...     expr,\n            ...     operator_test=is_operator,\n            ...     function_test=is_function,\n            ...     variable_test=is_variable,\n            ... )\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            sqrt(x_1) + x_1\n\n            &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [4, 9, 16]})\n            &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n            array([ 6., 12., 20.])\n        \"\"\"\n\n        df = pd.DataFrame(variables)\n        symbol_list = list(self.sympy_expr.free_symbols)\n\n        if set(list(df.columns)).issubset(set(symbol_list)):\n            raise Exception(\n                f\"Variables in expression {self.sympy_expr} \"\n                f\"do not match the given ones: {df.columns}\"\n            )\n\n        symbol_names = [str(s) for s in symbol_list]\n\n        f = sympy.lambdify(symbol_list, self.sympy_expr, \"numpy\")\n        try:\n            res = np.array(f(*[df[name] for name in symbol_names]))\n        except ValueError:  # Workaround till sympy gets updated\n            lst = [df[name] for name in symbol_names]\n            res = []\n            for i in range(len(lst[0])):\n                args = []\n                for j in range(len(lst)):\n                    args.append(lst[j].iloc[i])\n                res.append(f(*args))\n        return np.array(res)\n\n    def save_samples(\n        self,\n        path,\n        num_samples,\n        ranges: Optional[Dict] = None,\n        default_range: float = 10,\n        dv_name: str = \"y\",\n        random_state: Optional[int] = None,\n        compression: str = \"gzip\",\n    ):\n        \"\"\"\n        Creates a file with samples of ivs and dvs\n        Args:\n            path: The path were to store the file\n            num_samples: The number of samples\n            ranges: A dictionary with the ranges for the variables in form of a dict\n            default_range: Default range to fall back to if no range for a\n                specific variable is given\n            dv_name: The name to give to the observation\n            random_state: The random seed to be used\n            compression: Compression method\n        \"\"\"\n        if not path.endswith(\"gz\") and compression == \"gzip\":\n            warnings.warn(\n                f\"Compression is gzip but file {path} does not have the ending .gz\"\n            )\n        _ranges = {\n            key: (-default_range, default_range) for key in self.variables_unique\n        }\n        if ranges is not None:\n            for key in ranges.keys():\n                if key in _ranges.keys():\n                    _ranges[key] = ranges[key]\n\n        rng = np.random.default_rng(random_state)\n\n        def _get_conditions_once():\n            raw_conditions = {}\n            for key in _ranges.keys():\n                raw_conditions[key] = rng.uniform(*_ranges[key], size=num_samples)\n            return pd.DataFrame(raw_conditions)\n\n        conditions_ = pd.DataFrame(columns=self.variables_unique + [dv_name])\n        i = 0\n        while i &lt; 1_000_000 and len(conditions_.index) &lt; num_samples:\n            _sample = _get_conditions_once()\n            evaluation = self.evaluate(_sample)\n            _sample[dv_name] = evaluation\n            bad_indices = np.where(np.isnan(evaluation) | np.isinf(evaluation))[0]\n            _sample = _sample.drop(bad_indices)\n            conditions_ = pd.concat([conditions_, _sample], ignore_index=True)\n            i += 1\n            if i &gt;= 1_000_000:\n                break\n        conditions_ = conditions_.head(num_samples)\n        conditions_.to_csv(path, compression=compression, index=False, sep=\"\\t\")\n\n    def save_samples_srbench(\n        self,\n        path,\n        num_samples,\n        ranges: Optional[Dict] = None,\n        default_range: float = 10,\n        random_state: Optional[int] = None,\n    ):\n        self.save_samples(\n            path, num_samples, ranges, default_range, \"target\", random_state\n        )\n\n    def save_meta_srbench(self, path, name_dataset, name_target=\"y\"):\n        info = {}\n        info[\"dataset\"] = name_dataset\n        info[\"description\"] = name_target + \" = \" + str(self.sympy_expr)\n        info[\"source\"] = \"https://github.com/AutoResearch/equation-tree\"\n        info[\"publication\"] = \"Not yet implemented\"\n        info[\"task\"] = \"regression\"\n        info[\"keywords\"] = [\"abstract\", \"math\", \"symbolic regression\"]\n        info[\"target\"] = {\n            \"type\": \"continuous\",\n            \"description\": \"abstract dependent variable\",\n        }\n        info[\"features\"] = [\n            {\n                \"name\": v,\n                \"type\": \"continuous\",\n                \"description\": \"abstract independent variable\",\n            }\n            for v in self.variables_unique\n        ]\n\n        with open(path, \"w\") as f:\n            yaml.dump(info, f, sort_keys=False)\n\n    def export_to_srbench(\n        self,\n        folder: str,\n        data_file_name: Optional[str] = None,\n        num_samples: int = 1000,\n        name_target: str = \"y\",\n        ranges: Optional[Dict] = None,\n        default_range: float = 10,\n        random_state: Optional[int] = None,\n    ):\n        \"\"\"\n        Creates a folder and adds data and metadata to the folder that can be used with sr bench:\n        https://cavalab.org/srbench/\n        Args:\n            folder: Name of the folder\n            data_file_name: Name of the datafile (if none same as folder name)\n            num_samples: Number of samples\n            name_target: Name of the tartget\n            ranges: A dictionary with the ranges for the variables in form of a dict\n            default_range: Default range to fall back to if no range for a\n                specific variable is given\n            random_state: The random seed to be used\n        \"\"\"\n        if data_file_name is None:\n            data_file_name = folder\n        os.mkdir(folder)\n        path_data = f\"{folder}/{data_file_name}.tsv.gz\"\n        path_meta = f\"{folder}/metadata.yaml\"\n        self.save_samples_srbench(\n            path_data, num_samples, ranges, default_range, random_state\n        )\n        self.save_meta_srbench(path_meta, \"data\", name_target)\n\n    def check_validity(\n        self,\n        zero_representations=[\"0\"],\n        log_representations=[\"log\", \"Log\"],\n        division_representations=[\"/\", \":\"],\n        verbose=False,\n    ):\n        \"\"\"\n        Check if the tree is valid:\n            - Check if log(0) or x / 0 exists\n            - Check if function(constant) or operator(constant_1, constant_2) exists\n                    -&gt; unnecessary complexity\n            - Check if each function has exactly one child\n            - Check if each operator has exactly two children\n\n        Args:\n            zero_representations: A list of attributes that represent zero\n            log_representations: A list of attributes that represent log\n            division_representations: A list of attributes that represent division\n            verbose: If set true, print out the reason for the invalid tree\n\n        Example:\n            &gt;&gt;&gt; is_variable = lambda x : x == 'x'\n            &gt;&gt;&gt; is_constant = lambda x : x == 'c' or x == '0'\n            &gt;&gt;&gt; is_operator = lambda x : x == '/'\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     ['/', 'x', '0'],\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     operator_test=is_operator,\n            ... )\n            &gt;&gt;&gt; equation_tree.check_validity()\n            False\n            &gt;&gt;&gt; equation_tree.check_validity(verbose=True)\n            division by 0 is not allowed.\n            False\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     ['/', 'x', 'c'],\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     operator_test=is_operator,\n            ... )\n            &gt;&gt;&gt; equation_tree.check_validity()\n            True\n\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     ['/', '0', 'c'],\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     operator_test=is_operator,\n            ... )\n            &gt;&gt;&gt; equation_tree.check_validity(verbose=True)\n            0 and c are constants applied to the operator /\n            False\n        \"\"\"\n        return self.root.check_validity(\n            zero_representations, log_representations, division_representations, verbose\n        )\n\n    def draw_tree(self, out):\n        try:\n            from graphviz import Source\n        except ImportError:\n            print(\n                \"drawing uses requires `graphviz` to be installed: `pip install graphviz`\"\n            )\n        src = Source(dotprint(self.sympy_expr))\n        src.render(out, view=False)\n\n    def check_possible(\n        self,\n        feature_priors: Dict,\n        function_priors: Dict,\n        operator_priors: Dict,\n        structure_priors: Dict,\n    ):\n        \"\"\"\n        Check weather a tree is a possible tree given the priors\n        Attention:\n            If no prior is given, interpreted as all possibilities are allowed\n        \"\"\"\n        if feature_priors != {}:\n            for c in self.constants:\n                if c not in feature_priors.keys() or feature_priors[c] &lt;= 0:\n                    return False\n            for v in self.variables:\n                if v not in feature_priors.keys() or feature_priors[v] &lt;= 0:\n                    return False\n        if function_priors != {}:\n            for fun in self.functions:\n                if fun not in function_priors.keys() or function_priors[fun] &lt;= 0:\n                    return False\n        if operator_priors != {}:\n            for op in self.operators:\n                if op not in operator_priors.keys() or operator_priors[op] &lt;= 0:\n                    return False\n        if structure_priors != {}:\n            if (\n                str(self.structure) not in structure_priors.keys()\n                or structure_priors[str(self.structure)] &lt;= 0\n            ):\n                return False\n        return True\n\n    def check_possible_from_prior(self, prior: Dict):\n        structure_priors = prior[\"structures\"] if \"structures\" in prior.keys() else {}\n        feature_priors = prior[\"features\"] if \"features\" in prior.keys() else {}\n        function_priors = prior[\"functions\"] if \"functions\" in prior.keys() else {}\n        operator_priors = prior[\"operators\"] if \"operators\" in prior.keys() else {}\n        function_conditionals = (\n            prior[\"function_conditionals\"]\n            if \"function_conditionals\" in prior.keys()\n            else {}\n        )\n        operator_conditionals = (\n            prior[\"operator_conditionals\"]\n            if \"operator_conditionals\" in prior.keys()\n            else {}\n        )\n        if structure_priors:\n            if (\n                str(self.structure) not in structure_priors.keys()\n                or structure_priors[str(self.structure)] &lt;= 0\n            ):\n                return False\n        if feature_priors:\n            if (\n                self.n_variables &gt; 0\n                and (\n                    \"variables\" not in feature_priors.keys()\n                    or feature_priors[\"variables\"] &lt;= 0\n                )\n            ) or (\n                self.n_constants &gt; 0\n                and (\n                    \"constants\" not in feature_priors.keys()\n                    or feature_priors[\"constants\"] &lt;= 0\n                )\n            ):\n                return False\n        if function_priors:\n            for fun in self.functions_unique:\n                if fun not in function_priors.keys() or function_priors[fun] &lt;= 0:\n                    return False\n\n        if operator_priors:\n            for op in self.operators_unique:\n                if op not in operator_priors.keys() or operator_priors[op] &lt;= 0:\n                    return False\n\n        test_lst = []\n\n        def test_node(child):\n            nonlocal test_lst\n            if child is None or child.parent is None:\n                test_lst.append(True)\n                return\n            node = child.parent\n            _prior = {}\n            if (\n                node.kind == NodeKind.FUNCTION\n                and node.attribute in function_conditionals.keys()\n            ):\n                _prior = function_conditionals[node.attribute]\n            elif (\n                node.kind == NodeKind.OPERATOR\n                and node.attribute in operator_conditionals.keys()\n            ):\n                _prior = operator_conditionals[node.attribute]\n            if child.kind == NodeKind.FUNCTION:\n                _p = _prior[node.attribute][\"functions\"]\n                if (\n                    _p != {}\n                    and node.attribute not in _p.keys()\n                    or _p[node.attribute] &lt;= 0\n                ):\n                    test_lst.append(False)\n            elif child.kind == NodeKind.OPERATOR:\n                _p = _prior[node.attribute][\"operators\"]\n                if (\n                    _p != {}\n                    and node.attribute not in _p.keys()\n                    or _p[node.attribute] &lt;= 0\n                ):\n                    test_lst.append(False)\n            else:\n                _p = _prior[\"features\"] if \"features\" in _prior else {}\n                if child.kind == NodeKind.VARIABLE:\n                    if (\n                        _p != {}\n                        and \"variables\" not in _p.keys()\n                        or _p[\"variables\"] &lt;= 0\n                    ):\n                        test_lst.append(False)\n                if child.kind == NodeKind.CONSTANT:\n                    if (\n                        _p != {}\n                        and \"constants\" not in _p.keys()\n                        or _p[\"constants\"] &lt;= 0\n                    ):\n                        test_lst.append(False)\n            for c in child.children:\n                test_node(c)\n\n        conditionals = not any(item is False for item in test_lst)\n        if not conditionals:\n            return False\n        return True\n\n    def standardize(self):\n        \"\"\"\n        Standardize variable and constant names\n\n        Example:\n            &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n            &gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n            &gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n            &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n            &gt;&gt;&gt; prefix = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n\n            # then we create the node root\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     prefix_notation=prefix,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     function_test=is_function,\n            ...     operator_test=is_operator\n            ...     )\n\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            x + sin(y)*cos(z) - 1\n\n            &gt;&gt;&gt; equation_tree.standardize()\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            x_1 + sin(x_2)*cos(x_3) - 1\n\n        \"\"\"\n        variable_count = 0\n        constant_count = 0\n        variables = {}\n        constants = {}\n\n        def rec_stand(node):\n            if node is None:\n                return\n            nonlocal variable_count, constant_count\n            nonlocal variables, constants\n            if node.kind == NodeKind.VARIABLE:\n                if node.attribute not in variables.keys():\n                    variable_count += 1\n                    variables[node.attribute] = f\"x_{variable_count}\"\n                node.attribute = variables[node.attribute]\n            if node.kind == NodeKind.CONSTANT and not is_numeric(node.attribute):\n                if node.attribute not in constants.keys():\n                    constant_count += 1\n                    constants[node.attribute] = f\"c_{constant_count}\"\n                node.attribute = constants[node.attribute]\n            else:\n                rec_stand(node.left)\n                rec_stand(node.right)\n            return node\n\n        self.root = rec_stand(self.root)\n        self._build()\n\n    def simplify(\n        self,\n        function_test: Union[Callable, None] = None,\n        operator_test: Union[Callable, None] = None,\n        is_binary_minus_only: bool = True,\n        is_power_caret: bool = True,\n        verbose: bool = False,\n    ):\n        \"\"\"\n        Simplify equation if the simplified equation has a shorter prefix\n        Args:\n            function_test: A function that tests weather an attribute is a function\n                Attention: simplifying may lead to new functions that were not in the equation\n                    before. If so, add this to the test here.\n            operator_test: A function that tests weather an attribute is an operator\n                Attention: simplifying may lead to new operators that were not in the equation\n                    before. If so, add this to the test here.\n            is_binary_minus_only: Convert all unary minus to binary after simplification\n            is_power_caret: Represent power as a caret after simplification\n            verbose: Show messages if simplification results in errors\n\n        Examples:\n            &gt;&gt;&gt; is_variable = lambda x: 'x_' in x\n            &gt;&gt;&gt; is_constant = lambda x: 'c_' in x or is_numeric(x) or is_known_constant(x)\n            &gt;&gt;&gt; is_operator = lambda x: x in ['+', '*', '/', '^', '-']\n            &gt;&gt;&gt; is_function = lambda x: x.lower() in ['sqrt', 'abs']\n            &gt;&gt;&gt; prefix_notation = ['+', 'x_1', 'x_1' ]\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     prefix_notation=prefix_notation,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     operator_test=is_operator,\n            ...     function_test=is_function)\n            &gt;&gt;&gt; equation_tree.expr\n            ['+', 'x_1', 'x_1']\n\n            # it takes care of multiplication:\n            &gt;&gt;&gt; equation_tree.simplify(function_test=is_function,operator_test=is_operator)\n            &gt;&gt;&gt; equation_tree.expr\n            ['*', '2', 'x_1']\n\n            &gt;&gt;&gt; prefix_notation = ['sqrt', '*', 'x_1', 'x_1']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     prefix_notation=prefix_notation,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     operator_test=is_operator,\n            ...     function_test=is_function)\n            &gt;&gt;&gt; equation_tree.expr\n            ['sqrt', '*', 'x_1', 'x_1']\n\n            # it is good practice to define tests at the begining of a script and use them\n            # throughout the project\n            &gt;&gt;&gt; equation_tree.simplify(\n            ...     operator_test=is_operator,\n            ...     function_test=is_function\n            ... )\n            &gt;&gt;&gt; equation_tree.expr\n            ['abs', 'x_1']\n\n            &gt;&gt;&gt; prefix_notation = ['*', '-', 'c_1', 'x_1', '-', 'x_1', 'c_1']\n            &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n            ...     prefix_notation=prefix_notation,\n            ...     variable_test=is_variable,\n            ...     constant_test=is_constant,\n            ...     operator_test=is_operator,\n            ...     function_test=is_function)\n            &gt;&gt;&gt; equation_tree.expr\n            ['*', '-', 'c_1', 'x_1', '-', 'x_1', 'c_1']\n\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            (-c_1 + x_1)*(c_1 - x_1)\n\n            # it is good practice to define tests at the begining of a script and use them\n            # throughout the project\n            &gt;&gt;&gt; equation_tree.simplify(\n            ...     operator_test=is_operator,\n            ...     function_test=is_function\n            ... )\n            &gt;&gt;&gt; equation_tree.sympy_expr\n            (-c_1 + x_1)**2\n\n            # &gt;&gt;&gt; equation_tree.expr\n            # ['^', '-', 'x_1', 'c_1', '2']\n        \"\"\"\n\n        if function_test is None:\n\n            def function_test(x):\n                return x in self.functions\n\n        else:\n            tmp_f = function_test\n\n            def function_test(x):\n                return tmp_f(x) or x in self.functions\n\n        if operator_test is None:\n\n            def operator_test(x):\n                return x in self.operators\n\n        else:\n            tmp_o = operator_test\n\n            def operator_test(x):\n                return tmp_o(x) or x in self.operators\n\n        class TimeoutError(Exception):\n            pass\n\n        def timeout_handler(signum, frame):\n            raise TimeoutError(\"Function call timed out\")\n\n        signal.signal(signal.SIGALRM, timeout_handler)\n        signal.alarm(SIMPLIFY_TIMEOUT)\n        try:\n            simplified_equation = simplify(self.sympy_expr)\n            signal.alarm(0)\n        except TimeoutError:\n            simplified_equation = self.sympy_expr\n        if not check_functions(simplified_equation, function_test):\n            warnings.warn(\n                f\"{simplified_equation} has functions that are not in function_test type\"\n            )\n            self.root = None\n            self._build()\n            return\n        if (\n            \"I\" in str(simplified_equation)\n            or \"accumbounds\" in str(simplified_equation).lower()\n        ):\n            if verbose:\n                print(f\"Simplify {str(self.sympy_expr)} results in complex values\")\n            self.root = None\n            self._build()\n            return\n        if is_power_caret:\n            simplified_equation = str(simplified_equation).replace(\"**\", \"^\")\n        simplified_equation = simplified_equation.replace(\"re\", \"\")\n        if is_binary_minus_only:\n            simplified_equation = unary_minus_to_binary(\n                simplified_equation, operator_test\n            )\n        simplified_equation = simplified_equation.replace(\" \", \"\")\n\n        prefix = infix_to_prefix(simplified_equation, function_test, operator_test)\n        if verbose:\n            print(\"prefix\", simplified_equation)\n            print(\"prefix tree\", prefix)\n        if \"re\" in prefix:\n            prefix.remove(\"re\")\n        if len(prefix) &gt; len(self.expr):\n            prefix = self.expr\n        if \"zoo\" in prefix or \"oo\" in prefix:\n            if verbose:\n                print(f\"Simplify {str(self.sympy_expr)} results in None\")\n            self.root = None\n            self._build()\n            return\n        self.root = node_from_prefix(\n            prefix,\n            function_test,\n            operator_test,\n            lambda x: x in self.variables,\n            lambda x: x in self.constants or is_numeric(x) or is_known_constant(x),\n        )\n        self._build()\n\n    def get_evaluation(\n        self, min_val: int = -1, max_val: int = 1, num_samples: int = 100\n    ):\n        \"\"\"\n        Evaluate the nodes with random samples for variables and constants.\n        \"\"\"\n\n        crossings = self._create_crossing(min_val, max_val, num_samples)\n        evaluation = np.zeros((len(crossings), len(self.expr)))\n\n        for i, crossing in enumerate(crossings):\n            eqn_input = dict()\n            k = 0\n            for c in self.constants_unique:\n                if is_numeric(c):\n                    eqn_input[c] = float(c)\n                elif c == \"e\":\n                    eqn_input[c] = 2.71828182846\n                elif c == \"pi\":\n                    eqn_input[c] = 3.14159265359\n                else:\n                    eqn_input[c] = crossing[self.n_variables_unique + k]\n                    k += 1\n            for idx, x in enumerate(self.variables_unique):\n                eqn_input[x] = crossing[idx]\n            evaluation[i, :] = self._evaluate(eqn_input)\n\n        self.evaluation = evaluation\n        return evaluation\n\n    def _evaluate(self, features: Dict):\n        values: List[float] = list()\n\n        if self.root is not None:\n            self._evaluate_node(features, self.root)\n            values = self._get_full_evaluation(self.root)\n\n        return values\n\n    def _evaluate_node(self, features: Dict, node: TreeNode):\n        if node.kind == NodeKind.FUNCTION:\n            if node.left is None:\n                raise Exception(\"Invalid tree: %s\" % self.expr)\n            value = FUNCTIONS[node.attribute](self._evaluate_node(features, node.left))\n\n        elif node.kind == NodeKind.OPERATOR:\n            if node.left is None or node.right is None:\n                raise Exception(\"Invalid tree: %s\" % self.expr)\n            value = OPERATORS[node.attribute](\n                self._evaluate_node(features, node.left),\n                self._evaluate_node(features, node.right),\n            )\n\n        elif node.kind == NodeKind.CONSTANT or node.kind == NodeKind.VARIABLE:\n            value = features[node.attribute]\n        else:\n            raise Exception(\"Invalid attribute %s\" % node.attribute)\n        node.evaluation = value\n        return value\n\n    def _get_full_evaluation(self, node: TreeNode):\n        values = list()\n        values.append(node.evaluation)\n\n        if node.kind == NodeKind.FUNCTION:\n            if node.left is None:\n                raise Exception(\"Invalid tree: %s\" % self.expr)\n            eval_add = self._get_full_evaluation(node.left)\n            for eval_element in eval_add:\n                values.append(eval_element)\n\n        if node.kind == NodeKind.OPERATOR:\n            if node.left is None or node.right is None:\n                raise Exception(\"Invalid tree: %s\" % self.expr)\n            eval_add = self._get_full_evaluation(node.left)\n            for eval_element in eval_add:\n                values.append(eval_element)\n            eval_add = self._get_full_evaluation(node.right)\n            for eval_element in eval_add:\n                values.append(eval_element)\n\n        return values\n\n    def _create_crossing(\n        self, min_val: float = -1, max_val: float = 1, num_samples: int = 100\n    ):\n        crossings = []\n\n        total_unique = self.n_variables_unique + self.n_non_numeric_constants_unique\n\n        for _ in range(num_samples):\n            sample = []\n            for _ in range(total_unique):\n                value = np.random.uniform(min_val, max_val)\n                sample.append(value)\n            crossings.append(sample)\n\n        return np.array(crossings)\n\n    def _build(self):\n        self.structure: List[int] = []\n\n        # make function to get this here\n        self.expr: List[str] = list()\n\n        self.variables: List[str] = list()\n        self.functions: List[str] = list()\n        self.operators: List[str] = list()\n        self.constants: List[str] = list()\n\n        self.evaluation = None\n\n        self._collect_structure(self.structure, 0, self.root)\n\n        self._collect_attributes(\n            lambda node: node.kind == NodeKind.VARIABLE, self.variables, self.root\n        )\n        self._collect_attributes(\n            lambda node: node.kind == NodeKind.FUNCTION, self.functions, self.root\n        )\n        self._collect_attributes(\n            lambda node: node.kind == NodeKind.CONSTANT, self.constants, self.root\n        )\n        self._collect_attributes(\n            lambda node: node.kind == NodeKind.OPERATOR, self.operators, self.root\n        )\n        self._collect_expr(self.expr, self.root)\n\n    def _collect_structure(self, structure=[], level=0, node=None):\n        if node is None:\n            return\n        structure.append(level)\n        self._collect_structure(structure, level + 1, node.left)\n        self._collect_structure(structure, level + 1, node.right)\n        return\n\n    def _collect_expr(self, expression=[], node=None):\n        if node is None:\n            return\n        expression.append(node.attribute)\n        self._collect_expr(expression, node.left)\n        self._collect_expr(expression, node.right)\n\n    def _collect_attributes(\n        self, attribute_identifier: Callable = lambda _: True, attributes=[], node=None\n    ):\n        if node is None:\n            return list()\n        if attribute_identifier(node):\n            attributes.append(node.attribute)\n        if node.left is not None:\n            self._collect_attributes(attribute_identifier, attributes, node.left)\n        if node.right is not None:\n            self._collect_attributes(attribute_identifier, attributes, node.right)\n        return attributes\n\n    def _get_conditionals(self, attribute):\n        functions = {}\n        operators = {}\n        features = {\"constants\": 0, \"variables\": 0}\n\n        def get_child(node):\n            nonlocal functions, operators, features\n            if node is None:\n                return\n            if node.attribute == attribute:\n                if node.kind == NodeKind.FUNCTION or NodeKind.OPERATOR:\n                    if node.left.kind == NodeKind.FUNCTION:\n                        if node.left.attribute in functions.keys():\n                            functions[node.left.attribute] += 1\n                        else:\n                            functions[node.left.attribute] = 1\n                    if node.left.kind == NodeKind.OPERATOR:\n                        if node.left.attribute in operators.keys():\n                            operators[node.left.attribute] += 1\n                        else:\n                            operators[node.left.attribute] = 1\n                    if node.left.kind == NodeKind.CONSTANT:\n                        features[\"constants\"] += 1\n                    if node.left.kind == NodeKind.VARIABLE:\n                        features[\"variables\"] += 1\n                if node.kind == NodeKind.OPERATOR:\n                    if node.right.kind == NodeKind.FUNCTION:\n                        if node.right.attribute in functions.keys():\n                            functions[node.right.attribute] += 1\n                        else:\n                            functions[node.right.attribute] = 1\n                    if node.right.kind == NodeKind.OPERATOR:\n                        if node.right.attribute in operators.keys():\n                            operators[node.right.attribute] += 1\n                        else:\n                            operators[node.right.attribute] = 1\n                    if node.right.kind == NodeKind.CONSTANT:\n                        features[\"constants\"] += 1\n                    if node.right.kind == NodeKind.VARIABLE:\n                        features[\"variables\"] += 1\n            get_child(node.left)\n            get_child(node.right)\n\n        get_child(self.root)\n\n        return functions, operators, features\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.info","title":"<code>info</code>  <code>property</code>","text":"<p>Get al information as dictionary</p>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__","title":"<code>__init__(node)</code>","text":"<p>Initializes a tree from a TreeNode</p> <p>Examples:</p>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--we-can-inititlize-from-a-single-node","title":"We can inititlize from a single node","text":"<pre><code>&gt;&gt;&gt; node_root = TreeNode(kind=NodeKind.VARIABLE, attribute=\"x\")\n&gt;&gt;&gt; equation_tree = EquationTree(node_root)\n&gt;&gt;&gt; equation_tree.expr\n['x']\n&gt;&gt;&gt; equation_tree.structure\n[0]\n&gt;&gt;&gt; equation_tree.variables\n['x']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--or-from-a-node-with-children","title":"Or from a node with children","text":"<pre><code>&gt;&gt;&gt; node_left = TreeNode(kind=NodeKind.VARIABLE, attribute=\"x\")\n&gt;&gt;&gt; node_right = TreeNode(kind=NodeKind.CONSTANT, attribute=\"c\")\n&gt;&gt;&gt; node_root = TreeNode(kind=NodeKind.OPERATOR, attribute=\"+\",                             left=node_left, right=node_right)\n&gt;&gt;&gt; equation_tree = EquationTree(node_root)\n&gt;&gt;&gt; equation_tree.expr\n['+', 'x', 'c']\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 1]\n&gt;&gt;&gt; equation_tree.variables\n['x']\n&gt;&gt;&gt; equation_tree.constants\n['c']\n&gt;&gt;&gt; equation_tree.operators\n['+']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--we-can-first-sample-a-node-and-children-and-initialize-from-that","title":"We can first sample a node and children and initialize from that","text":"<pre><code>&gt;&gt;&gt; np.random.seed(42)\n&gt;&gt;&gt; max_depth = 12\n&gt;&gt;&gt; structure_priors = {'[0, 1, 2, 1, 2, 3]': .5, '[0, 1, 2, 2, 1, 2, 3]': .5}\n&gt;&gt;&gt; feature_priors = {\"x_1\": 0.5, \"c_1\": 0.5}\n&gt;&gt;&gt; function_priors = {\"sin\": 0.5, \"cos\": 0.5}\n&gt;&gt;&gt; operator_priors = {\"+\": 0.5, \"-\": 0.5}\n&gt;&gt;&gt; node_root = sample_tree(feature_priors, function_priors,\n...     operator_priors, structure_priors)\n&gt;&gt;&gt; equation_tree = EquationTree(node_root)\n&gt;&gt;&gt; equation_tree.expr\n['-', 'cos', 'c_1', 'sin', 'sin', 'x_1']\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 2, 1, 2, 3]\n&gt;&gt;&gt; equation_tree.variables\n['x_1']\n&gt;&gt;&gt; equation_tree.n_variables\n1\n&gt;&gt;&gt; equation_tree.n_variables_unique\n1\n&gt;&gt;&gt; equation_tree.constants\n['c_1']\n&gt;&gt;&gt; equation_tree.n_constants\n1\n&gt;&gt;&gt; equation_tree.n_constants_unique\n1\n&gt;&gt;&gt; equation_tree.n_leafs\n2\n&gt;&gt;&gt; equation_tree.operators\n['-']\n&gt;&gt;&gt; equation_tree.functions\n['cos', 'sin', 'sin']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--first-we-create-test-functions-that-test-weather-an-attribute-is-a-variable","title":"First we create test functions that test weather an attribute is a variable,","text":""},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--a-constant-a-function-or-an-operater","title":"a constant, a function, or an operater","text":"<pre><code>&gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n&gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n&gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n&gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--here-we-use-the-prefix-notation","title":"here we use the prefix notation","text":"<pre><code>&gt;&gt;&gt; prefix_notation = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--then-we-create-the-node-root","title":"then we create the node root","text":"<pre><code>&gt;&gt;&gt; node_root = node_from_prefix(\n...     prefix_notation=prefix_notation,\n...     variable_test=is_variable,\n...     constant_test=is_constant,\n...     function_test=is_function,\n...     operator_test=is_operator\n...     )\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--and-initialize-the-tree","title":"and initialize the tree","text":"<pre><code>&gt;&gt;&gt; equation_tree = EquationTree(node_root)\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 2, 2, 1, 2, 3, 2, 3]\n&gt;&gt;&gt; equation_tree.variables\n['x', 'y', 'z']\n&gt;&gt;&gt; equation_tree.constants\n['1']\n&gt;&gt;&gt; equation_tree.operators\n['+', '-', '*']\n&gt;&gt;&gt; equation_tree.functions\n['sin', 'cos']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.__init__--the-tree-expression-is-the-same-as-the-prefix-notation","title":"The tree expression is the same as the prefix notation","text":"<pre><code>&gt;&gt;&gt; equation_tree.expr == prefix_notation\nTrue\n</code></pre> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def __init__(self, node: TreeNode):\n    \"\"\"\n    Initializes a tree from a TreeNode\n\n    Examples:\n        # We can inititlize from a single node\n        &gt;&gt;&gt; node_root = TreeNode(kind=NodeKind.VARIABLE, attribute=\"x\")\n        &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n        &gt;&gt;&gt; equation_tree.expr\n        ['x']\n        &gt;&gt;&gt; equation_tree.structure\n        [0]\n        &gt;&gt;&gt; equation_tree.variables\n        ['x']\n\n        # Or from a node with children\n        &gt;&gt;&gt; node_left = TreeNode(kind=NodeKind.VARIABLE, attribute=\"x\")\n        &gt;&gt;&gt; node_right = TreeNode(kind=NodeKind.CONSTANT, attribute=\"c\")\n        &gt;&gt;&gt; node_root = TreeNode(kind=NodeKind.OPERATOR, attribute=\"+\", \\\n                        left=node_left, right=node_right)\n        &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n        &gt;&gt;&gt; equation_tree.expr\n        ['+', 'x', 'c']\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 1]\n        &gt;&gt;&gt; equation_tree.variables\n        ['x']\n        &gt;&gt;&gt; equation_tree.constants\n        ['c']\n        &gt;&gt;&gt; equation_tree.operators\n        ['+']\n\n        # We can first sample a node and children and initialize from that\n        &gt;&gt;&gt; np.random.seed(42)\n        &gt;&gt;&gt; max_depth = 12\n        &gt;&gt;&gt; structure_priors = {'[0, 1, 2, 1, 2, 3]': .5, '[0, 1, 2, 2, 1, 2, 3]': .5}\n        &gt;&gt;&gt; feature_priors = {\"x_1\": 0.5, \"c_1\": 0.5}\n        &gt;&gt;&gt; function_priors = {\"sin\": 0.5, \"cos\": 0.5}\n        &gt;&gt;&gt; operator_priors = {\"+\": 0.5, \"-\": 0.5}\n        &gt;&gt;&gt; node_root = sample_tree(feature_priors, function_priors,\n        ...     operator_priors, structure_priors)\n        &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n        &gt;&gt;&gt; equation_tree.expr\n        ['-', 'cos', 'c_1', 'sin', 'sin', 'x_1']\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2, 1, 2, 3]\n        &gt;&gt;&gt; equation_tree.variables\n        ['x_1']\n        &gt;&gt;&gt; equation_tree.n_variables\n        1\n        &gt;&gt;&gt; equation_tree.n_variables_unique\n        1\n        &gt;&gt;&gt; equation_tree.constants\n        ['c_1']\n        &gt;&gt;&gt; equation_tree.n_constants\n        1\n        &gt;&gt;&gt; equation_tree.n_constants_unique\n        1\n        &gt;&gt;&gt; equation_tree.n_leafs\n        2\n        &gt;&gt;&gt; equation_tree.operators\n        ['-']\n        &gt;&gt;&gt; equation_tree.functions\n        ['cos', 'sin', 'sin']\n\n        # First we create test functions that test weather an attribute is a variable,\n        # a constant, a function, or an operater\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n        &gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n        &gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n        &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n\n        # here we use the prefix notation\n        &gt;&gt;&gt; prefix_notation = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n\n        # then we create the node root\n        &gt;&gt;&gt; node_root = node_from_prefix(\n        ...     prefix_notation=prefix_notation,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     function_test=is_function,\n        ...     operator_test=is_operator\n        ...     )\n\n        # and initialize the tree\n        &gt;&gt;&gt; equation_tree = EquationTree(node_root)\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2, 2, 1, 2, 3, 2, 3]\n        &gt;&gt;&gt; equation_tree.variables\n        ['x', 'y', 'z']\n        &gt;&gt;&gt; equation_tree.constants\n        ['1']\n        &gt;&gt;&gt; equation_tree.operators\n        ['+', '-', '*']\n        &gt;&gt;&gt; equation_tree.functions\n        ['sin', 'cos']\n\n        # The tree expression is the same as the prefix notation\n        &gt;&gt;&gt; equation_tree.expr == prefix_notation\n        True\n    \"\"\"\n\n    self.root: Union[TreeNode, None] = node\n\n    self.structure: List[int] = []\n\n    self.expr: List[str] = list()\n\n    self.variables: List[str] = list()\n    self.functions: List[str] = list()\n    self.operators: List[str] = list()\n    self.constants: List[str] = list()\n\n    self.evaluation = None\n\n    self._build()\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.check_possible","title":"<code>check_possible(feature_priors, function_priors, operator_priors, structure_priors)</code>","text":"<p>Check weather a tree is a possible tree given the priors Attention:     If no prior is given, interpreted as all possibilities are allowed</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def check_possible(\n    self,\n    feature_priors: Dict,\n    function_priors: Dict,\n    operator_priors: Dict,\n    structure_priors: Dict,\n):\n    \"\"\"\n    Check weather a tree is a possible tree given the priors\n    Attention:\n        If no prior is given, interpreted as all possibilities are allowed\n    \"\"\"\n    if feature_priors != {}:\n        for c in self.constants:\n            if c not in feature_priors.keys() or feature_priors[c] &lt;= 0:\n                return False\n        for v in self.variables:\n            if v not in feature_priors.keys() or feature_priors[v] &lt;= 0:\n                return False\n    if function_priors != {}:\n        for fun in self.functions:\n            if fun not in function_priors.keys() or function_priors[fun] &lt;= 0:\n                return False\n    if operator_priors != {}:\n        for op in self.operators:\n            if op not in operator_priors.keys() or operator_priors[op] &lt;= 0:\n                return False\n    if structure_priors != {}:\n        if (\n            str(self.structure) not in structure_priors.keys()\n            or structure_priors[str(self.structure)] &lt;= 0\n        ):\n            return False\n    return True\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.check_validity","title":"<code>check_validity(zero_representations=['0'], log_representations=['log', 'Log'], division_representations=['/', ':'], verbose=False)</code>","text":"Check if the tree is valid <ul> <li>Check if log(0) or x / 0 exists</li> <li>Check if function(constant) or operator(constant_1, constant_2) exists         -&gt; unnecessary complexity</li> <li>Check if each function has exactly one child</li> <li>Check if each operator has exactly two children</li> </ul> <p>Parameters:</p> Name Type Description Default <code>zero_representations</code> <p>A list of attributes that represent zero</p> <code>['0']</code> <code>log_representations</code> <p>A list of attributes that represent log</p> <code>['log', 'Log']</code> <code>division_representations</code> <p>A list of attributes that represent division</p> <code>['/', ':']</code> <code>verbose</code> <p>If set true, print out the reason for the invalid tree</p> <code>False</code> Example <p>is_variable = lambda x : x == 'x' is_constant = lambda x : x == 'c' or x == '0' is_operator = lambda x : x == '/' equation_tree = EquationTree.from_prefix( ...     ['/', 'x', '0'], ...     variable_test=is_variable, ...     constant_test=is_constant, ...     operator_test=is_operator, ... ) equation_tree.check_validity() False equation_tree.check_validity(verbose=True) division by 0 is not allowed. False equation_tree = EquationTree.from_prefix( ...     ['/', 'x', 'c'], ...     variable_test=is_variable, ...     constant_test=is_constant, ...     operator_test=is_operator, ... ) equation_tree.check_validity() True</p> <p>equation_tree = EquationTree.from_prefix( ...     ['/', '0', 'c'], ...     variable_test=is_variable, ...     constant_test=is_constant, ...     operator_test=is_operator, ... ) equation_tree.check_validity(verbose=True) 0 and c are constants applied to the operator / False</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def check_validity(\n    self,\n    zero_representations=[\"0\"],\n    log_representations=[\"log\", \"Log\"],\n    division_representations=[\"/\", \":\"],\n    verbose=False,\n):\n    \"\"\"\n    Check if the tree is valid:\n        - Check if log(0) or x / 0 exists\n        - Check if function(constant) or operator(constant_1, constant_2) exists\n                -&gt; unnecessary complexity\n        - Check if each function has exactly one child\n        - Check if each operator has exactly two children\n\n    Args:\n        zero_representations: A list of attributes that represent zero\n        log_representations: A list of attributes that represent log\n        division_representations: A list of attributes that represent division\n        verbose: If set true, print out the reason for the invalid tree\n\n    Example:\n        &gt;&gt;&gt; is_variable = lambda x : x == 'x'\n        &gt;&gt;&gt; is_constant = lambda x : x == 'c' or x == '0'\n        &gt;&gt;&gt; is_operator = lambda x : x == '/'\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     ['/', 'x', '0'],\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     operator_test=is_operator,\n        ... )\n        &gt;&gt;&gt; equation_tree.check_validity()\n        False\n        &gt;&gt;&gt; equation_tree.check_validity(verbose=True)\n        division by 0 is not allowed.\n        False\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     ['/', 'x', 'c'],\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     operator_test=is_operator,\n        ... )\n        &gt;&gt;&gt; equation_tree.check_validity()\n        True\n\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     ['/', '0', 'c'],\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     operator_test=is_operator,\n        ... )\n        &gt;&gt;&gt; equation_tree.check_validity(verbose=True)\n        0 and c are constants applied to the operator /\n        False\n    \"\"\"\n    return self.root.check_validity(\n        zero_representations, log_representations, division_representations, verbose\n    )\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.evaluate","title":"<code>evaluate(variables)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; expr = sympify('x_a + 3 * y')\n&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*']\n&gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; equation_tree.sympy_expr\nx_1 + 3*x_2\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.evaluate--we-can-use-dicts","title":"We can use dicts:","text":"<pre><code>&gt;&gt;&gt; equation_tree.evaluate({'x_1': np.array([2, 3]), 'x_2': np.array([1, 1])})\narray([5, 6])\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.evaluate--or-pandas-dataframe","title":"Or pandas dataframe:","text":"<pre><code>&gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': np.array([2, 3]), 'x_2': np.array([1, 1])})\n&gt;&gt;&gt; dataFrame\n   x_1  x_2\n0    2    1\n1    3    1\n&gt;&gt;&gt; equation_tree.evaluate(dataFrame)\narray([5, 6])\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.evaluate--or-pandas-dataframe","title":"Or pandas dataframe:","text":"<pre><code>&gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [2, 3], 'x_2': [1, 1]})\n&gt;&gt;&gt; dataFrame\n   x_1  x_2\n0    2    1\n1    3    1\n&gt;&gt;&gt; equation_tree.evaluate(dataFrame)\narray([5, 6])\n</code></pre> <pre><code>&gt;&gt;&gt; expr = sympify('min(x_1,x_2)')\n&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', 'min']\n&gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1', 'x_2']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; equation_tree.sympy_expr\nMin(x_1, x_2)\n</code></pre> <pre><code>&gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [1, 2, 3, 4], 'x_2': [2, 1, 4, 3]})\n&gt;&gt;&gt; equation_tree.evaluate(dataFrame)\narray([1, 1, 3, 3])\n</code></pre> <pre><code>&gt;&gt;&gt; expr = sympify('max(3, x_1)')\n&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', 'min', 'max']\n&gt;&gt;&gt; is_function = lambda x : x in ['sqrt', 'log', 'abs']\n&gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1', 'x_2']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     function_test=is_function,\n...     operator_test=is_operator,\n...     variable_test=is_variable)\n&gt;&gt;&gt; equation_tree.sympy_expr\nMax(3, x_1)\n&gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [1, 2, 3, 4]})\n&gt;&gt;&gt; equation_tree.evaluate(dataFrame)\narray([3, 3, 3, 4])\n</code></pre> <pre><code>&gt;&gt;&gt; expr = sympify('x_1 + sqrt(x_1)')\n&gt;&gt;&gt; is_operator = lambda x : x in ['+']\n&gt;&gt;&gt; is_function = lambda x: x in ['sqrt']\n&gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     function_test=is_function,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; equation_tree.sympy_expr\nsqrt(x_1) + x_1\n</code></pre> <pre><code>&gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [4, 9, 16]})\n&gt;&gt;&gt; equation_tree.evaluate(dataFrame)\narray([ 6., 12., 20.])\n</code></pre> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def evaluate(self, variables: Union[dict, pd.DataFrame]):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; expr = sympify('x_a + 3 * y')\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*']\n        &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        x_1 + 3*x_2\n\n        # We can use dicts:\n        &gt;&gt;&gt; equation_tree.evaluate({'x_1': np.array([2, 3]), 'x_2': np.array([1, 1])})\n        array([5, 6])\n\n        # Or pandas dataframe:\n        &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': np.array([2, 3]), 'x_2': np.array([1, 1])})\n        &gt;&gt;&gt; dataFrame\n           x_1  x_2\n        0    2    1\n        1    3    1\n        &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n        array([5, 6])\n\n        # Or pandas dataframe:\n        &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [2, 3], 'x_2': [1, 1]})\n        &gt;&gt;&gt; dataFrame\n           x_1  x_2\n        0    2    1\n        1    3    1\n        &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n        array([5, 6])\n\n        &gt;&gt;&gt; expr = sympify('min(x_1,x_2)')\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', 'min']\n        &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1', 'x_2']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        Min(x_1, x_2)\n\n        &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [1, 2, 3, 4], 'x_2': [2, 1, 4, 3]})\n        &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n        array([1, 1, 3, 3])\n\n        &gt;&gt;&gt; expr = sympify('max(3, x_1)')\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', 'min', 'max']\n        &gt;&gt;&gt; is_function = lambda x : x in ['sqrt', 'log', 'abs']\n        &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1', 'x_2']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     function_test=is_function,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable)\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        Max(3, x_1)\n        &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [1, 2, 3, 4]})\n        &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n        array([3, 3, 3, 4])\n\n        &gt;&gt;&gt; expr = sympify('x_1 + sqrt(x_1)')\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+']\n        &gt;&gt;&gt; is_function = lambda x: x in ['sqrt']\n        &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['x_1']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     function_test=is_function,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        sqrt(x_1) + x_1\n\n        &gt;&gt;&gt; dataFrame = pd.DataFrame({'x_1': [4, 9, 16]})\n        &gt;&gt;&gt; equation_tree.evaluate(dataFrame)\n        array([ 6., 12., 20.])\n    \"\"\"\n\n    df = pd.DataFrame(variables)\n    symbol_list = list(self.sympy_expr.free_symbols)\n\n    if set(list(df.columns)).issubset(set(symbol_list)):\n        raise Exception(\n            f\"Variables in expression {self.sympy_expr} \"\n            f\"do not match the given ones: {df.columns}\"\n        )\n\n    symbol_names = [str(s) for s in symbol_list]\n\n    f = sympy.lambdify(symbol_list, self.sympy_expr, \"numpy\")\n    try:\n        res = np.array(f(*[df[name] for name in symbol_names]))\n    except ValueError:  # Workaround till sympy gets updated\n        lst = [df[name] for name in symbol_names]\n        res = []\n        for i in range(len(lst[0])):\n            args = []\n            for j in range(len(lst)):\n                args.append(lst[j].iloc[i])\n            res.append(f(*args))\n    return np.array(res)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.export_to_srbench","title":"<code>export_to_srbench(folder, data_file_name=None, num_samples=1000, name_target='y', ranges=None, default_range=10, random_state=None)</code>","text":"<p>Creates a folder and adds data and metadata to the folder that can be used with sr bench: https://cavalab.org/srbench/ Args:     folder: Name of the folder     data_file_name: Name of the datafile (if none same as folder name)     num_samples: Number of samples     name_target: Name of the tartget     ranges: A dictionary with the ranges for the variables in form of a dict     default_range: Default range to fall back to if no range for a         specific variable is given     random_state: The random seed to be used</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def export_to_srbench(\n    self,\n    folder: str,\n    data_file_name: Optional[str] = None,\n    num_samples: int = 1000,\n    name_target: str = \"y\",\n    ranges: Optional[Dict] = None,\n    default_range: float = 10,\n    random_state: Optional[int] = None,\n):\n    \"\"\"\n    Creates a folder and adds data and metadata to the folder that can be used with sr bench:\n    https://cavalab.org/srbench/\n    Args:\n        folder: Name of the folder\n        data_file_name: Name of the datafile (if none same as folder name)\n        num_samples: Number of samples\n        name_target: Name of the tartget\n        ranges: A dictionary with the ranges for the variables in form of a dict\n        default_range: Default range to fall back to if no range for a\n            specific variable is given\n        random_state: The random seed to be used\n    \"\"\"\n    if data_file_name is None:\n        data_file_name = folder\n    os.mkdir(folder)\n    path_data = f\"{folder}/{data_file_name}.tsv.gz\"\n    path_meta = f\"{folder}/metadata.yaml\"\n    self.save_samples_srbench(\n        path_data, num_samples, ranges, default_range, random_state\n    )\n    self.save_meta_srbench(path_meta, \"data\", name_target)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prefix","title":"<code>from_prefix(prefix_notation, function_test=lambda : False, operator_test=lambda : False, variable_test=lambda : False, constant_test=lambda : False)</code>  <code>classmethod</code>","text":"<p>Instantiate a tree from prefix notation</p> <p>Parameters:</p> Name Type Description Default <code>prefix_notation</code> <code>List[str]</code> <p>The equation in prefix notation</p> required <code>function_test</code> <code>Callable</code> <p>A function that tests if the attribute is a function</p> <code>lambda : False</code> <code>operator_test</code> <code>Callable</code> <p>A function that tests if the attribute is an operator</p> <code>lambda : False</code> <code>variable_test</code> <code>Callable</code> <p>A function that tests if the attribute is a variable</p> <code>lambda : False</code> <code>constant_test</code> <code>Callable</code> <p>A function that tests if the attribute is a constant</p> <code>lambda : False</code> Example <p>is_variable = lambda x : x in ['x', 'y', 'z'] is_constant = lambda x : x in ['0', '1', '2'] is_function = lambda x : x in ['sin', 'cos'] is_operator = lambda x: x in ['+', '-', '', '/'] prefix = ['+', '-', 'x', '1', '', 'sin', 'y', 'cos', 'z']</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>@classmethod\ndef from_prefix(\n    cls,\n    prefix_notation: List[str],\n    function_test: Callable = lambda _: False,\n    operator_test: Callable = lambda _: False,\n    variable_test: Callable = lambda _: False,\n    constant_test: Callable = lambda _: False,\n):\n    \"\"\"\n    Instantiate a tree from prefix notation\n\n    Args:\n        prefix_notation: The equation in prefix notation\n        function_test: A function that tests if the attribute is a function\n        operator_test: A function that tests if the attribute is an operator\n        variable_test: A function that tests if the attribute is a variable\n        constant_test: A function that tests if the attribute is a constant\n\n    Example:\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n        &gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n        &gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n        &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n        &gt;&gt;&gt; prefix = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n\n        # then we create the node root\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     prefix_notation=prefix,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     function_test=is_function,\n        ...     operator_test=is_operator\n        ...     )\n\n        # and initialize the tree\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2, 2, 1, 2, 3, 2, 3]\n        &gt;&gt;&gt; equation_tree.variables\n        ['x', 'y', 'z']\n        &gt;&gt;&gt; equation_tree.constants\n        ['1']\n        &gt;&gt;&gt; equation_tree.operators\n        ['+', '-', '*']\n        &gt;&gt;&gt; equation_tree.functions\n        ['sin', 'cos']\n\n        # The tree expression is the same as the prefix notation\n        &gt;&gt;&gt; equation_tree.expr == prefix\n        True\n\n\n    \"\"\"\n    root = node_from_prefix(\n        prefix_notation, function_test, operator_test, variable_test, constant_test\n    )\n    return cls(root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prefix--then-we-create-the-node-root","title":"then we create the node root","text":"<p>equation_tree = EquationTree.from_prefix( ...     prefix_notation=prefix, ...     variable_test=is_variable, ...     constant_test=is_constant, ...     function_test=is_function, ...     operator_test=is_operator ...     )</p>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prefix--and-initialize-the-tree","title":"and initialize the tree","text":"<p>equation_tree.structure [0, 1, 2, 2, 1, 2, 3, 2, 3] equation_tree.variables ['x', 'y', 'z'] equation_tree.constants ['1'] equation_tree.operators ['+', '-', '*'] equation_tree.functions ['sin', 'cos']</p>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prefix--the-tree-expression-is-the-same-as-the-prefix-notation","title":"The tree expression is the same as the prefix notation","text":"<p>equation_tree.expr == prefix True</p>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prior","title":"<code>from_prior(prior, max_variables_unique)</code>  <code>classmethod</code>","text":"<p>Initiate a tree from a prior</p> <p>Parameters:</p> Name Type Description Default <code>prior</code> <code>Dict</code> <p>The priors in dictionary form</p> required <code>max_variables_unique</code> <code>int</code> <p>The maximum number of unique variables (a tree can have less then this number)</p> required <p>Examples:</p> <pre><code>&gt;&gt;&gt; np.random.seed(42)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prior--we-can-set-priors-for-features-functions-operators","title":"We can set priors for features, functions, operators","text":""},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prior--and-also-conditionals-based-the-parent","title":"and also conditionals based the parent","text":"<pre><code>&gt;&gt;&gt; p = {\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .2, 'variables': .8},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': 1., '-': .0},\n...     'function_conditionals': {\n...                             'sin': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': 0., 'cos': 1.},\n...                                 'operators': {'+': 0., '-': 1.}\n...                             },\n...                             'cos': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'cos': 1., 'sin': 0.},\n...                                 'operators': {'+': 0., '-': 1.}\n...                             }\n...                         },\n...     'operator_conditionals': {\n...                             '+': {\n...                                 'features': {'constants': .5, 'variables': .5},\n...                                 'functions': {'sin': 1., 'cos': 0.},\n...                                 'operators': {'+': 1., '-': 0.}\n...                             },\n...                             '-': {\n...                                 'features': {'constants': .3, 'variables': .7},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .9, '-': .1}\n...                             }\n...                         },\n... }\n&gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 2]\n&gt;&gt;&gt; equation_tree.expr\n['cos', 'cos', 'x_1']\n&gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 2]\n&gt;&gt;&gt; equation_tree.expr\n['sin', 'cos', 'x_1']\n&gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 1]\n&gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 2, 3, 2, 3, 1]\n&gt;&gt;&gt; equation_tree.expr\n['+', '+', 'sin', 'x_1', 'sin', 'x_2', 'x_2']\n&gt;&gt;&gt; equation_tree.sympy_expr\nx_2 + sin(x_1) + sin(x_2)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prior--without-conditionals-the-unconditioned-priors-are-the-fallback-option","title":"Without conditionals, the unconditioned priors are the fallback option","text":"<pre><code>&gt;&gt;&gt; p = {\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .2, 'variables': .8},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': .5, '-': .5},\n... }\n&gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n&gt;&gt;&gt; equation_tree.structure\n[0, 1, 2, 3, 2, 3, 1]\n&gt;&gt;&gt; equation_tree.expr\n['+', '-', 'cos', 'c_1', 'cos', 'c_2', 'c_3']\n&gt;&gt;&gt; equation_tree.sympy_expr\nc_3 + cos(c_1) - cos(c_2)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prior--note-this-would-be-discarded-in-a-future-step-as-unnecesarry-complex","title":"Note: this would be discarded in a future step as unnecesarry complex","text":"Source code in <code>src/equation_tree/tree.py</code> <pre><code>@classmethod\ndef from_prior(cls, prior: Dict, max_variables_unique: int):\n    \"\"\"\n    Initiate a tree from a prior\n\n    Args:\n        prior: The priors in dictionary form\n        max_variables_unique: The maximum number of unique variables (a tree can have less then\n            this number)\n\n    Examples:\n        &gt;&gt;&gt; np.random.seed(42)\n\n        # We can set priors for features, functions, operators\n        # and also conditionals based the parent\n        &gt;&gt;&gt; p = {\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .2, 'variables': .8},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': 1., '-': .0},\n        ...     'function_conditionals': {\n        ...                             'sin': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': 0., 'cos': 1.},\n        ...                                 'operators': {'+': 0., '-': 1.}\n        ...                             },\n        ...                             'cos': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'cos': 1., 'sin': 0.},\n        ...                                 'operators': {'+': 0., '-': 1.}\n        ...                             }\n        ...                         },\n        ...     'operator_conditionals': {\n        ...                             '+': {\n        ...                                 'features': {'constants': .5, 'variables': .5},\n        ...                                 'functions': {'sin': 1., 'cos': 0.},\n        ...                                 'operators': {'+': 1., '-': 0.}\n        ...                             },\n        ...                             '-': {\n        ...                                 'features': {'constants': .3, 'variables': .7},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .9, '-': .1}\n        ...                             }\n        ...                         },\n        ... }\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2]\n        &gt;&gt;&gt; equation_tree.expr\n        ['cos', 'cos', 'x_1']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2]\n        &gt;&gt;&gt; equation_tree.expr\n        ['sin', 'cos', 'x_1']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 1]\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2, 3, 2, 3, 1]\n        &gt;&gt;&gt; equation_tree.expr\n        ['+', '+', 'sin', 'x_1', 'sin', 'x_2', 'x_2']\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        x_2 + sin(x_1) + sin(x_2)\n\n        # Without conditionals, the unconditioned priors are the fallback option\n        &gt;&gt;&gt; p = {\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .2, 'variables': .8},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': .5, '-': .5},\n        ... }\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prior(p, 3)\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2, 3, 2, 3, 1]\n        &gt;&gt;&gt; equation_tree.expr\n        ['+', '-', 'cos', 'c_1', 'cos', 'c_2', 'c_3']\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        c_3 + cos(c_1) - cos(c_2)\n\n        # Note: this would be discarded in a future step as unnecesarry complex\n    \"\"\"\n    root = sample_tree_full(prior, max_variables_unique)\n    return cls(root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_prior_fast","title":"<code>from_prior_fast(prior, tree_depth, max_variables_unique)</code>  <code>classmethod</code>","text":"<p>Initiate a tree from a prior with fast sampling Attention: structure prior is not supported</p> <p>Parameters:</p> Name Type Description Default <code>prior</code> <code>Dict</code> <p>The priors in dictionary form (structure priors are not needed)</p> required <code>tree_depth</code> <p>depth of the tree</p> required <code>max_variables_unique</code> <code>int</code> <p>The maximum number of unique variables (a tree can have less then this number)</p> required Source code in <code>src/equation_tree/tree.py</code> <pre><code>@classmethod\ndef from_prior_fast(cls, prior: Dict, tree_depth, max_variables_unique: int):\n    \"\"\"\n    Initiate a tree from a prior with fast sampling\n    Attention: structure prior is not supported\n\n    Args:\n        prior: The priors in dictionary form (structure priors are not needed)\n        tree_depth: depth of the tree\n        max_variables_unique: The maximum number of unique variables (a tree can have less then\n            this number)\n    \"\"\"\n    root = sample_tree_full_fast(prior, tree_depth, max_variables_unique)\n    return cls(root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_priors","title":"<code>from_priors(feature_priors={}, function_priors={}, operator_priors={}, structure_priors={})</code>  <code>classmethod</code>","text":"<p>Instantiate a tree from priors</p> <p>Attention     - use standard notation here:   variables should be in form x_{number}                                     constants should be in form c_{number}</p> <p>Parameters:</p> Name Type Description Default <code>max_depth</code> <p>Maximum depth of the tree</p> required <code>feature_priors</code> <p>The priors for the features (variables + constants)</p> <code>{}</code> <code>function_priors</code> <p>The priors for the functions</p> <code>{}</code> <code>operator_priors</code> <p>The priors for the operators</p> <code>{}</code> <code>structure_priors</code> <p>The priors for the tree structures</p> <code>{}</code> Example <p>np.random.seed(42) max_depth = 12 feature_priors = {\"x_1\": 0.5, \"c_1\": 0.5} function_priors = {\"sin\": 0.5, \"cos\": 0.5} operator_priors = {\"+\": 0.5, \"-\": 0.5} structure_priors = {'[0, 1, 2, 3, 4, 5, 5, 2, 3, 4, 4]': 1} equation_tree = EquationTree.from_priors( ...     feature_priors, function_priors, operator_priors, structure_priors) equation_tree.expr ['cos', '-', 'cos', 'sin', '+', 'x_1', 'c_1', 'cos', '-', 'x_1', 'c_1'] equation_tree.structure [0, 1, 2, 3, 4, 5, 5, 2, 3, 4, 4] equation_tree.variables ['x_1', 'x_1'] equation_tree.n_variables 2 equation_tree.n_variables_unique 1 equation_tree.constants ['c_1', 'c_1'] equation_tree.n_constants 2 equation_tree.n_constants_unique 1 equation_tree.n_leafs 4 equation_tree.operators ['-', '+', '-'] equation_tree.functions ['cos', 'cos', 'sin', 'cos']</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>@classmethod\ndef from_priors(\n    cls,\n    feature_priors={},\n    function_priors={},\n    operator_priors={},\n    structure_priors={},\n):\n    \"\"\"\n    Instantiate a tree from priors\n\n    Attention\n        - use standard notation here:   variables should be in form x_{number}\n                                        constants should be in form c_{number}\n\n    Args:\n        max_depth: Maximum depth of the tree\n        feature_priors: The priors for the features (variables + constants)\n        function_priors: The priors for the functions\n        operator_priors: The priors for the operators\n        structure_priors: The priors for the tree structures\n\n    Example:\n        &gt;&gt;&gt; np.random.seed(42)\n        &gt;&gt;&gt; max_depth = 12\n        &gt;&gt;&gt; feature_priors = {\"x_1\": 0.5, \"c_1\": 0.5}\n        &gt;&gt;&gt; function_priors = {\"sin\": 0.5, \"cos\": 0.5}\n        &gt;&gt;&gt; operator_priors = {\"+\": 0.5, \"-\": 0.5}\n        &gt;&gt;&gt; structure_priors = {'[0, 1, 2, 3, 4, 5, 5, 2, 3, 4, 4]': 1}\n        &gt;&gt;&gt; equation_tree = EquationTree.from_priors(\n        ...     feature_priors, function_priors, operator_priors, structure_priors)\n        &gt;&gt;&gt; equation_tree.expr\n        ['cos', '-', 'cos', 'sin', '+', 'x_1', 'c_1', 'cos', '-', 'x_1', 'c_1']\n        &gt;&gt;&gt; equation_tree.structure\n        [0, 1, 2, 3, 4, 5, 5, 2, 3, 4, 4]\n        &gt;&gt;&gt; equation_tree.variables\n        ['x_1', 'x_1']\n        &gt;&gt;&gt; equation_tree.n_variables\n        2\n        &gt;&gt;&gt; equation_tree.n_variables_unique\n        1\n        &gt;&gt;&gt; equation_tree.constants\n        ['c_1', 'c_1']\n        &gt;&gt;&gt; equation_tree.n_constants\n        2\n        &gt;&gt;&gt; equation_tree.n_constants_unique\n        1\n        &gt;&gt;&gt; equation_tree.n_leafs\n        4\n        &gt;&gt;&gt; equation_tree.operators\n        ['-', '+', '-']\n        &gt;&gt;&gt; equation_tree.functions\n        ['cos', 'cos', 'sin', 'cos']\n    \"\"\"\n    root = sample_tree(\n        feature_priors,\n        function_priors,\n        operator_priors,\n        structure_priors,\n    )\n    return cls(root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_sympy","title":"<code>from_sympy(expression, function_test=lambda : False, operator_test=lambda : False, variable_test=lambda : False, constant_test=lambda : False)</code>  <code>classmethod</code>","text":"<p>Instantiate a tree from a sympy function</p> Attention <ul> <li>constant and variable names get standardized</li> <li>unary minus get converted to binary minus</li> </ul> <p>Examples:</p> <pre><code>&gt;&gt;&gt; expr = sympify('x_a + B * y')\n&gt;&gt;&gt; expr\nB*y + x_a\n&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*']\n&gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n&gt;&gt;&gt; is_constant = lambda x : x == 'B'\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n...     constant_test=is_constant\n... )\n&gt;&gt;&gt; equation_tree.expr\n['+', '*', 'c_1', 'x_2', 'x_1']\n&gt;&gt;&gt; equation_tree.sympy_expr\nc_1*x_2 + x_1\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.from_sympy--numbers-dont-get-standardized-but-are-constants","title":"Numbers don't get standardized but are constants","text":"<pre><code>&gt;&gt;&gt; expr = sympify('x_a + 2 * y')\n&gt;&gt;&gt; expr\nx_a + 2*y\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n...     constant_test=is_constant\n... )\n&gt;&gt;&gt; equation_tree.expr\n['+', 'x_1', '*', '2', 'x_2']\n&gt;&gt;&gt; equation_tree.sympy_expr\nx_1 + 2*x_2\n&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**']\n&gt;&gt;&gt; is_variable = lambda x: '_' in x\n&gt;&gt;&gt; is_constant = lambda x: x == 'B'\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     sympify('B*x_1**2'),\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n...     constant_test=is_constant\n... )\n</code></pre> <pre><code>&gt;&gt;&gt; expr = sympify('min(x_1, x_2)')\n&gt;&gt;&gt; expr\nMin(x_1, x_2)\n&gt;&gt;&gt; is_operator = lambda x : x in ['min']\n&gt;&gt;&gt; is_variable = lambda x : x in ['x_1', 'x_2']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; equation_tree.expr\n['min', 'x_1', 'x_2']\n</code></pre> <pre><code>&gt;&gt;&gt; expr = sympify('x_1**2')\n&gt;&gt;&gt; expr\nx_1**2\n&gt;&gt;&gt; is_operator = lambda x : x in ['*', '/', '**', '+']\n&gt;&gt;&gt; is_variable = lambda x : x in ['x_1']\n&gt;&gt;&gt; is_function = lambda x : x in ['squared']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n...     function_test=is_function\n... )\n&gt;&gt;&gt; equation_tree.expr\n['squared', 'x_1']\n</code></pre> Source code in <code>src/equation_tree/tree.py</code> <pre><code>@classmethod\ndef from_sympy(\n    cls,\n    expression,\n    function_test: Callable = lambda _: False,\n    operator_test: Callable = lambda _: False,\n    variable_test: Callable = lambda _: False,\n    constant_test: Callable = lambda _: False,\n):\n    \"\"\"\n    Instantiate a tree from a sympy function\n\n    Attention:\n        - constant and variable names get standardized\n        - unary minus get converted to binary minus\n\n    Examples:\n        &gt;&gt;&gt; expr = sympify('x_a + B * y')\n        &gt;&gt;&gt; expr\n        B*y + x_a\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*']\n        &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n        &gt;&gt;&gt; is_constant = lambda x : x == 'B'\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant\n        ... )\n        &gt;&gt;&gt; equation_tree.expr\n        ['+', '*', 'c_1', 'x_2', 'x_1']\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        c_1*x_2 + x_1\n\n        # Numbers don't get standardized but are constants\n        &gt;&gt;&gt; expr = sympify('x_a + 2 * y')\n        &gt;&gt;&gt; expr\n        x_a + 2*y\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant\n        ... )\n        &gt;&gt;&gt; equation_tree.expr\n        ['+', 'x_1', '*', '2', 'x_2']\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        x_1 + 2*x_2\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**']\n        &gt;&gt;&gt; is_variable = lambda x: '_' in x\n        &gt;&gt;&gt; is_constant = lambda x: x == 'B'\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     sympify('B*x_1**2'),\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant\n        ... )\n\n        &gt;&gt;&gt; expr = sympify('min(x_1, x_2)')\n        &gt;&gt;&gt; expr\n        Min(x_1, x_2)\n        &gt;&gt;&gt; is_operator = lambda x : x in ['min']\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x_1', 'x_2']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; equation_tree.expr\n        ['min', 'x_1', 'x_2']\n\n        &gt;&gt;&gt; expr = sympify('x_1**2')\n        &gt;&gt;&gt; expr\n        x_1**2\n        &gt;&gt;&gt; is_operator = lambda x : x in ['*', '/', '**', '+']\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x_1']\n        &gt;&gt;&gt; is_function = lambda x : x in ['squared']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ...     function_test=is_function\n        ... )\n        &gt;&gt;&gt; equation_tree.expr\n        ['squared', 'x_1']\n\n    \"\"\"\n    standard = standardize_sympy(expression, variable_test, constant_test)\n    standard = unary_minus_to_binary(standard, operator_test)\n    standard = op_const_to_func(standard)\n    prefix = infix_to_prefix(str(standard), function_test, operator_test)\n    root = node_from_prefix(\n        prefix,\n        function_test,\n        operator_test,\n        lambda x: \"x_\" in x,\n        lambda x: \"c_\" in x,\n    )\n    return cls(root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.get_evaluation","title":"<code>get_evaluation(min_val=-1, max_val=1, num_samples=100)</code>","text":"<p>Evaluate the nodes with random samples for variables and constants.</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def get_evaluation(\n    self, min_val: int = -1, max_val: int = 1, num_samples: int = 100\n):\n    \"\"\"\n    Evaluate the nodes with random samples for variables and constants.\n    \"\"\"\n\n    crossings = self._create_crossing(min_val, max_val, num_samples)\n    evaluation = np.zeros((len(crossings), len(self.expr)))\n\n    for i, crossing in enumerate(crossings):\n        eqn_input = dict()\n        k = 0\n        for c in self.constants_unique:\n            if is_numeric(c):\n                eqn_input[c] = float(c)\n            elif c == \"e\":\n                eqn_input[c] = 2.71828182846\n            elif c == \"pi\":\n                eqn_input[c] = 3.14159265359\n            else:\n                eqn_input[c] = crossing[self.n_variables_unique + k]\n                k += 1\n        for idx, x in enumerate(self.variables_unique):\n            eqn_input[x] = crossing[idx]\n        evaluation[i, :] = self._evaluate(eqn_input)\n\n    self.evaluation = evaluation\n    return evaluation\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.save_samples","title":"<code>save_samples(path, num_samples, ranges=None, default_range=10, dv_name='y', random_state=None, compression='gzip')</code>","text":"<p>Creates a file with samples of ivs and dvs Args:     path: The path were to store the file     num_samples: The number of samples     ranges: A dictionary with the ranges for the variables in form of a dict     default_range: Default range to fall back to if no range for a         specific variable is given     dv_name: The name to give to the observation     random_state: The random seed to be used     compression: Compression method</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def save_samples(\n    self,\n    path,\n    num_samples,\n    ranges: Optional[Dict] = None,\n    default_range: float = 10,\n    dv_name: str = \"y\",\n    random_state: Optional[int] = None,\n    compression: str = \"gzip\",\n):\n    \"\"\"\n    Creates a file with samples of ivs and dvs\n    Args:\n        path: The path were to store the file\n        num_samples: The number of samples\n        ranges: A dictionary with the ranges for the variables in form of a dict\n        default_range: Default range to fall back to if no range for a\n            specific variable is given\n        dv_name: The name to give to the observation\n        random_state: The random seed to be used\n        compression: Compression method\n    \"\"\"\n    if not path.endswith(\"gz\") and compression == \"gzip\":\n        warnings.warn(\n            f\"Compression is gzip but file {path} does not have the ending .gz\"\n        )\n    _ranges = {\n        key: (-default_range, default_range) for key in self.variables_unique\n    }\n    if ranges is not None:\n        for key in ranges.keys():\n            if key in _ranges.keys():\n                _ranges[key] = ranges[key]\n\n    rng = np.random.default_rng(random_state)\n\n    def _get_conditions_once():\n        raw_conditions = {}\n        for key in _ranges.keys():\n            raw_conditions[key] = rng.uniform(*_ranges[key], size=num_samples)\n        return pd.DataFrame(raw_conditions)\n\n    conditions_ = pd.DataFrame(columns=self.variables_unique + [dv_name])\n    i = 0\n    while i &lt; 1_000_000 and len(conditions_.index) &lt; num_samples:\n        _sample = _get_conditions_once()\n        evaluation = self.evaluate(_sample)\n        _sample[dv_name] = evaluation\n        bad_indices = np.where(np.isnan(evaluation) | np.isinf(evaluation))[0]\n        _sample = _sample.drop(bad_indices)\n        conditions_ = pd.concat([conditions_, _sample], ignore_index=True)\n        i += 1\n        if i &gt;= 1_000_000:\n            break\n    conditions_ = conditions_.head(num_samples)\n    conditions_.to_csv(path, compression=compression, index=False, sep=\"\\t\")\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify","title":"<code>simplify(function_test=None, operator_test=None, is_binary_minus_only=True, is_power_caret=True, verbose=False)</code>","text":"<p>Simplify equation if the simplified equation has a shorter prefix Args:     function_test: A function that tests weather an attribute is a function         Attention: simplifying may lead to new functions that were not in the equation             before. If so, add this to the test here.     operator_test: A function that tests weather an attribute is an operator         Attention: simplifying may lead to new operators that were not in the equation             before. If so, add this to the test here.     is_binary_minus_only: Convert all unary minus to binary after simplification     is_power_caret: Represent power as a caret after simplification     verbose: Show messages if simplification results in errors</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; is_variable = lambda x: 'x_' in x\n&gt;&gt;&gt; is_constant = lambda x: 'c_' in x or is_numeric(x) or is_known_constant(x)\n&gt;&gt;&gt; is_operator = lambda x: x in ['+', '*', '/', '^', '-']\n&gt;&gt;&gt; is_function = lambda x: x.lower() in ['sqrt', 'abs']\n&gt;&gt;&gt; prefix_notation = ['+', 'x_1', 'x_1' ]\n&gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n...     prefix_notation=prefix_notation,\n...     variable_test=is_variable,\n...     constant_test=is_constant,\n...     operator_test=is_operator,\n...     function_test=is_function)\n&gt;&gt;&gt; equation_tree.expr\n['+', 'x_1', 'x_1']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify--it-takes-care-of-multiplication","title":"it takes care of multiplication:","text":"<pre><code>&gt;&gt;&gt; equation_tree.simplify(function_test=is_function,operator_test=is_operator)\n&gt;&gt;&gt; equation_tree.expr\n['*', '2', 'x_1']\n</code></pre> <pre><code>&gt;&gt;&gt; prefix_notation = ['sqrt', '*', 'x_1', 'x_1']\n&gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n...     prefix_notation=prefix_notation,\n...     variable_test=is_variable,\n...     constant_test=is_constant,\n...     operator_test=is_operator,\n...     function_test=is_function)\n&gt;&gt;&gt; equation_tree.expr\n['sqrt', '*', 'x_1', 'x_1']\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify--it-is-good-practice-to-define-tests-at-the-begining-of-a-script-and-use-them","title":"it is good practice to define tests at the begining of a script and use them","text":""},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify--throughout-the-project","title":"throughout the project","text":"<pre><code>&gt;&gt;&gt; equation_tree.simplify(\n...     operator_test=is_operator,\n...     function_test=is_function\n... )\n&gt;&gt;&gt; equation_tree.expr\n['abs', 'x_1']\n</code></pre> <pre><code>&gt;&gt;&gt; prefix_notation = ['*', '-', 'c_1', 'x_1', '-', 'x_1', 'c_1']\n&gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n...     prefix_notation=prefix_notation,\n...     variable_test=is_variable,\n...     constant_test=is_constant,\n...     operator_test=is_operator,\n...     function_test=is_function)\n&gt;&gt;&gt; equation_tree.expr\n['*', '-', 'c_1', 'x_1', '-', 'x_1', 'c_1']\n</code></pre> <pre><code>&gt;&gt;&gt; equation_tree.sympy_expr\n(-c_1 + x_1)*(c_1 - x_1)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify--it-is-good-practice-to-define-tests-at-the-begining-of-a-script-and-use-them","title":"it is good practice to define tests at the begining of a script and use them","text":""},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify--throughout-the-project","title":"throughout the project","text":"<pre><code>&gt;&gt;&gt; equation_tree.simplify(\n...     operator_test=is_operator,\n...     function_test=is_function\n... )\n&gt;&gt;&gt; equation_tree.sympy_expr\n(-c_1 + x_1)**2\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify--equation_treeexpr","title":"&gt;&gt;&gt; equation_tree.expr","text":""},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.simplify---x_1-c_1-2","title":"['^', '-', 'x_1', 'c_1', '2']","text":"Source code in <code>src/equation_tree/tree.py</code> <pre><code>def simplify(\n    self,\n    function_test: Union[Callable, None] = None,\n    operator_test: Union[Callable, None] = None,\n    is_binary_minus_only: bool = True,\n    is_power_caret: bool = True,\n    verbose: bool = False,\n):\n    \"\"\"\n    Simplify equation if the simplified equation has a shorter prefix\n    Args:\n        function_test: A function that tests weather an attribute is a function\n            Attention: simplifying may lead to new functions that were not in the equation\n                before. If so, add this to the test here.\n        operator_test: A function that tests weather an attribute is an operator\n            Attention: simplifying may lead to new operators that were not in the equation\n                before. If so, add this to the test here.\n        is_binary_minus_only: Convert all unary minus to binary after simplification\n        is_power_caret: Represent power as a caret after simplification\n        verbose: Show messages if simplification results in errors\n\n    Examples:\n        &gt;&gt;&gt; is_variable = lambda x: 'x_' in x\n        &gt;&gt;&gt; is_constant = lambda x: 'c_' in x or is_numeric(x) or is_known_constant(x)\n        &gt;&gt;&gt; is_operator = lambda x: x in ['+', '*', '/', '^', '-']\n        &gt;&gt;&gt; is_function = lambda x: x.lower() in ['sqrt', 'abs']\n        &gt;&gt;&gt; prefix_notation = ['+', 'x_1', 'x_1' ]\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     prefix_notation=prefix_notation,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     operator_test=is_operator,\n        ...     function_test=is_function)\n        &gt;&gt;&gt; equation_tree.expr\n        ['+', 'x_1', 'x_1']\n\n        # it takes care of multiplication:\n        &gt;&gt;&gt; equation_tree.simplify(function_test=is_function,operator_test=is_operator)\n        &gt;&gt;&gt; equation_tree.expr\n        ['*', '2', 'x_1']\n\n        &gt;&gt;&gt; prefix_notation = ['sqrt', '*', 'x_1', 'x_1']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     prefix_notation=prefix_notation,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     operator_test=is_operator,\n        ...     function_test=is_function)\n        &gt;&gt;&gt; equation_tree.expr\n        ['sqrt', '*', 'x_1', 'x_1']\n\n        # it is good practice to define tests at the begining of a script and use them\n        # throughout the project\n        &gt;&gt;&gt; equation_tree.simplify(\n        ...     operator_test=is_operator,\n        ...     function_test=is_function\n        ... )\n        &gt;&gt;&gt; equation_tree.expr\n        ['abs', 'x_1']\n\n        &gt;&gt;&gt; prefix_notation = ['*', '-', 'c_1', 'x_1', '-', 'x_1', 'c_1']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     prefix_notation=prefix_notation,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     operator_test=is_operator,\n        ...     function_test=is_function)\n        &gt;&gt;&gt; equation_tree.expr\n        ['*', '-', 'c_1', 'x_1', '-', 'x_1', 'c_1']\n\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        (-c_1 + x_1)*(c_1 - x_1)\n\n        # it is good practice to define tests at the begining of a script and use them\n        # throughout the project\n        &gt;&gt;&gt; equation_tree.simplify(\n        ...     operator_test=is_operator,\n        ...     function_test=is_function\n        ... )\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        (-c_1 + x_1)**2\n\n        # &gt;&gt;&gt; equation_tree.expr\n        # ['^', '-', 'x_1', 'c_1', '2']\n    \"\"\"\n\n    if function_test is None:\n\n        def function_test(x):\n            return x in self.functions\n\n    else:\n        tmp_f = function_test\n\n        def function_test(x):\n            return tmp_f(x) or x in self.functions\n\n    if operator_test is None:\n\n        def operator_test(x):\n            return x in self.operators\n\n    else:\n        tmp_o = operator_test\n\n        def operator_test(x):\n            return tmp_o(x) or x in self.operators\n\n    class TimeoutError(Exception):\n        pass\n\n    def timeout_handler(signum, frame):\n        raise TimeoutError(\"Function call timed out\")\n\n    signal.signal(signal.SIGALRM, timeout_handler)\n    signal.alarm(SIMPLIFY_TIMEOUT)\n    try:\n        simplified_equation = simplify(self.sympy_expr)\n        signal.alarm(0)\n    except TimeoutError:\n        simplified_equation = self.sympy_expr\n    if not check_functions(simplified_equation, function_test):\n        warnings.warn(\n            f\"{simplified_equation} has functions that are not in function_test type\"\n        )\n        self.root = None\n        self._build()\n        return\n    if (\n        \"I\" in str(simplified_equation)\n        or \"accumbounds\" in str(simplified_equation).lower()\n    ):\n        if verbose:\n            print(f\"Simplify {str(self.sympy_expr)} results in complex values\")\n        self.root = None\n        self._build()\n        return\n    if is_power_caret:\n        simplified_equation = str(simplified_equation).replace(\"**\", \"^\")\n    simplified_equation = simplified_equation.replace(\"re\", \"\")\n    if is_binary_minus_only:\n        simplified_equation = unary_minus_to_binary(\n            simplified_equation, operator_test\n        )\n    simplified_equation = simplified_equation.replace(\" \", \"\")\n\n    prefix = infix_to_prefix(simplified_equation, function_test, operator_test)\n    if verbose:\n        print(\"prefix\", simplified_equation)\n        print(\"prefix tree\", prefix)\n    if \"re\" in prefix:\n        prefix.remove(\"re\")\n    if len(prefix) &gt; len(self.expr):\n        prefix = self.expr\n    if \"zoo\" in prefix or \"oo\" in prefix:\n        if verbose:\n            print(f\"Simplify {str(self.sympy_expr)} results in None\")\n        self.root = None\n        self._build()\n        return\n    self.root = node_from_prefix(\n        prefix,\n        function_test,\n        operator_test,\n        lambda x: x in self.variables,\n        lambda x: x in self.constants or is_numeric(x) or is_known_constant(x),\n    )\n    self._build()\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.standardize","title":"<code>standardize()</code>","text":"<p>Standardize variable and constant names</p> Example <p>is_variable = lambda x : x in ['x', 'y', 'z'] is_constant = lambda x : x in ['0', '1', '2'] is_function = lambda x : x in ['sin', 'cos'] is_operator = lambda x: x in ['+', '-', '', '/'] prefix = ['+', '-', 'x', '1', '', 'sin', 'y', 'cos', 'z']</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def standardize(self):\n    \"\"\"\n    Standardize variable and constant names\n\n    Example:\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n        &gt;&gt;&gt; is_constant = lambda x : x in ['0', '1', '2']\n        &gt;&gt;&gt; is_function = lambda x : x in ['sin', 'cos']\n        &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '/']\n        &gt;&gt;&gt; prefix = ['+', '-', 'x', '1', '*', 'sin', 'y', 'cos', 'z']\n\n        # then we create the node root\n        &gt;&gt;&gt; equation_tree = EquationTree.from_prefix(\n        ...     prefix_notation=prefix,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant,\n        ...     function_test=is_function,\n        ...     operator_test=is_operator\n        ...     )\n\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        x + sin(y)*cos(z) - 1\n\n        &gt;&gt;&gt; equation_tree.standardize()\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        x_1 + sin(x_2)*cos(x_3) - 1\n\n    \"\"\"\n    variable_count = 0\n    constant_count = 0\n    variables = {}\n    constants = {}\n\n    def rec_stand(node):\n        if node is None:\n            return\n        nonlocal variable_count, constant_count\n        nonlocal variables, constants\n        if node.kind == NodeKind.VARIABLE:\n            if node.attribute not in variables.keys():\n                variable_count += 1\n                variables[node.attribute] = f\"x_{variable_count}\"\n            node.attribute = variables[node.attribute]\n        if node.kind == NodeKind.CONSTANT and not is_numeric(node.attribute):\n            if node.attribute not in constants.keys():\n                constant_count += 1\n                constants[node.attribute] = f\"c_{constant_count}\"\n            node.attribute = constants[node.attribute]\n        else:\n            rec_stand(node.left)\n            rec_stand(node.right)\n        return node\n\n    self.root = rec_stand(self.root)\n    self._build()\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.EquationTree.standardize--then-we-create-the-node-root","title":"then we create the node root","text":"<p>equation_tree = EquationTree.from_prefix( ...     prefix_notation=prefix, ...     variable_test=is_variable, ...     constant_test=is_constant, ...     function_test=is_function, ...     operator_test=is_operator ...     )</p> <p>equation_tree.sympy_expr x + sin(y)*cos(z) - 1</p> <p>equation_tree.standardize() equation_tree.sympy_expr x_1 + sin(x_2)*cos(x_3) - 1</p>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.instantiate_constants","title":"<code>instantiate_constants(tree, fct)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; expr = sympify('e ** (- e **( x + y))')\n&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**', '-']\n&gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']\n&gt;&gt;&gt; is_constant = lambda x : x in ['e']\n&gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n...     expr,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; equation_tree.sympy_expr\ne**((-e)**(x_1 + x_2))\n&gt;&gt;&gt; instantiated = instantiate_constants(equation_tree, lambda: 2)\n&gt;&gt;&gt; instantiated.sympy_expr\ne**((-e)**(x_1 + x_2))\n&gt;&gt;&gt; expr_2 = sympify('c_1 ** (- e **( x + y))')\n&gt;&gt;&gt; equation_tree_2 = EquationTree.from_sympy(\n...     expr_2,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; instantiated = instantiate_constants(equation_tree_2, lambda: 2)\n&gt;&gt;&gt; instantiated.sympy_expr\n2**((-e)**(x_1 + x_2))\n</code></pre> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def instantiate_constants(tree, fct: Callable):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; expr = sympify('e ** (- e **( x + y))')\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**', '-']\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']\n        &gt;&gt;&gt; is_constant = lambda x : x in ['e']\n        &gt;&gt;&gt; equation_tree = EquationTree.from_sympy(\n        ...     expr,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; equation_tree.sympy_expr\n        e**((-e)**(x_1 + x_2))\n        &gt;&gt;&gt; instantiated = instantiate_constants(equation_tree, lambda: 2)\n        &gt;&gt;&gt; instantiated.sympy_expr\n        e**((-e)**(x_1 + x_2))\n        &gt;&gt;&gt; expr_2 = sympify('c_1 ** (- e **( x + y))')\n        &gt;&gt;&gt; equation_tree_2 = EquationTree.from_sympy(\n        ...     expr_2,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; instantiated = instantiate_constants(equation_tree_2, lambda: 2)\n        &gt;&gt;&gt; instantiated.sympy_expr\n        2**((-e)**(x_1 + x_2))\n\n\n\n    \"\"\"\n    root = copy.deepcopy(tree.root)\n\n    def _rec_apply(node):\n        if (\n            node.kind == NodeKind.CONSTANT\n            and not is_known_constant(node.attribute)\n            and not is_numeric(node.attribute)\n        ):\n            node.attribute = str(fct())\n        for c in node.children:\n            _rec_apply(c)\n\n    _rec_apply(root)\n    return EquationTree(root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.normalized_tree_distance","title":"<code>normalized_tree_distance(e_a, e_b)</code>","text":"<p>Normalized edit distance between two trees according to <code>Li, Y., &amp; Chenguang, Z. (2011). A metric normalization of tree edit distance. Frontiers of Computer Science in China, 5, 119-125.</code></p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def normalized_tree_distance(e_a: EquationTree, e_b: EquationTree):\n    \"\"\"\n    Normalized edit distance between two trees according to\n    `Li, Y., &amp; Chenguang, Z. (2011). A metric normalization of tree edit distance.\n    Frontiers of Computer Science in China, 5, 119-125.`\n\n    \"\"\"\n    if e_a.root is None or e_b.root is None:\n        return 1\n    return ned(e_a.root, e_b.root)\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.prediction_distance","title":"<code>prediction_distance(e_a, e_b, X)</code>","text":"<p>Mean squared difference between the prediction of two equations on X</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**', '-']\n&gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']\n&gt;&gt;&gt; expr_1 = sympify('x + y')\n&gt;&gt;&gt; expr_2 = sympify('x')\n&gt;&gt;&gt; et_1 = EquationTree.from_sympy(\n...     expr_1,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; et_1.sympy_expr\nx_1 + x_2\n&gt;&gt;&gt; et_2 = EquationTree.from_sympy(\n...     expr_2,\n...     operator_test=is_operator,\n...     variable_test=is_variable,\n... )\n&gt;&gt;&gt; et_2.sympy_expr\nx_1\n&gt;&gt;&gt; prediction_distance(et_1, et_2, {'x_1': [1], 'x_2': [1]})\n1.0\n&gt;&gt;&gt; prediction_distance(et_1, et_2, {'x_1': [1, 2, 3], 'x_2': [0, 0, 0]})\n0.0\n&gt;&gt;&gt; prediction_distance(et_1, et_2, {'x_1': [1, 2], 'x_2': [1, 2]})\n2.5\n</code></pre> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def prediction_distance(\n    e_a: EquationTree, e_b: EquationTree, X: Union[dict, pd.DataFrame]\n):\n    \"\"\"\n    Mean squared difference between the prediction of two equations on X\n\n    Examples:\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**', '-']\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']\n        &gt;&gt;&gt; expr_1 = sympify('x + y')\n        &gt;&gt;&gt; expr_2 = sympify('x')\n        &gt;&gt;&gt; et_1 = EquationTree.from_sympy(\n        ...     expr_1,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; et_1.sympy_expr\n        x_1 + x_2\n        &gt;&gt;&gt; et_2 = EquationTree.from_sympy(\n        ...     expr_2,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; et_2.sympy_expr\n        x_1\n        &gt;&gt;&gt; prediction_distance(et_1, et_2, {'x_1': [1], 'x_2': [1]})\n        1.0\n        &gt;&gt;&gt; prediction_distance(et_1, et_2, {'x_1': [1, 2, 3], 'x_2': [0, 0, 0]})\n        0.0\n        &gt;&gt;&gt; prediction_distance(et_1, et_2, {'x_1': [1, 2], 'x_2': [1, 2]})\n        2.5\n\n    \"\"\"\n    predict_a = e_a.evaluate(X)\n    predict_b = e_b.evaluate(X)\n    squared_diff = (predict_a - predict_b) ** 2\n    return squared_diff.mean()\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.symbolic_solution_diff","title":"<code>symbolic_solution_diff(e_a, e_b)</code>","text":"<p>Symbolic solution with difference constant based on <code>La Cava, W. et al (2021). Contemporary symbolic regression methods and their relative performance.</code> Examples:     &gt;&gt;&gt; is_operator = lambda x : x in ['+', '', '*', '-']     &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']     &gt;&gt;&gt; is_constant = lambda x: is_numeric(x)     &gt;&gt;&gt; expr_1 = sympify('x + .1')     &gt;&gt;&gt; expr_2 = sympify('x')     &gt;&gt;&gt; et_1 = EquationTree.from_sympy(     ...     expr_1,     ...     operator_test=is_operator,     ...     variable_test=is_variable,     ...     constant_test=is_constant     ... )     &gt;&gt;&gt; et_1.sympy_expr     x_1 + 0.1     &gt;&gt;&gt; et_2 = EquationTree.from_sympy(     ...     expr_2,     ...     operator_test=is_operator,     ...     variable_test=is_variable,     ... )     &gt;&gt;&gt; et_2.sympy_expr     x_1     &gt;&gt;&gt; symbolic_solution_diff(et_1, et_2)     0.1</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def symbolic_solution_diff(e_a: EquationTree, e_b: EquationTree):\n    \"\"\"\n    Symbolic solution with difference constant based on\n    `La Cava, W. et al (2021).\n    Contemporary symbolic regression methods and their relative performance.`\n    Examples:\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**', '-']\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']\n        &gt;&gt;&gt; is_constant = lambda x: is_numeric(x)\n        &gt;&gt;&gt; expr_1 = sympify('x + .1')\n        &gt;&gt;&gt; expr_2 = sympify('x')\n        &gt;&gt;&gt; et_1 = EquationTree.from_sympy(\n        ...     expr_1,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant\n        ... )\n        &gt;&gt;&gt; et_1.sympy_expr\n        x_1 + 0.1\n        &gt;&gt;&gt; et_2 = EquationTree.from_sympy(\n        ...     expr_2,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; et_2.sympy_expr\n        x_1\n        &gt;&gt;&gt; symbolic_solution_diff(et_1, et_2)\n        0.1\n    \"\"\"\n    diff = simplify(e_a.sympy_expr - e_b.sympy_expr)\n    if diff.is_constant():\n        return float(diff)\n    else:\n        return np.infty\n</code></pre>"},{"location":"reference/src/equation_tree/tree/#src.equation_tree.tree.symbolic_solution_quot","title":"<code>symbolic_solution_quot(e_a, e_b)</code>","text":"<p>Symbolic solution with quotient constant based on <code>La Cava, W. et al (2021). Contemporary symbolic regression methods and their relative performance.</code> Examples:     &gt;&gt;&gt; is_operator = lambda x : x in ['+', '', '', '-']     &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']     &gt;&gt;&gt; is_constant = lambda x: is_numeric(x)     &gt;&gt;&gt; expr_1 = sympify('x * .1')     &gt;&gt;&gt; expr_2 = sympify('x')     &gt;&gt;&gt; et_1 = EquationTree.from_sympy(     ...     expr_1,     ...     operator_test=is_operator,     ...     variable_test=is_variable,     ...     constant_test=is_constant     ... )     &gt;&gt;&gt; et_1.sympy_expr     0.1x_1     &gt;&gt;&gt; et_2 = EquationTree.from_sympy(     ...     expr_2,     ...     operator_test=is_operator,     ...     variable_test=is_variable,     ... )     &gt;&gt;&gt; et_2.sympy_expr     x_1     &gt;&gt;&gt; symbolic_solution_quot(et_1, et_2)     0.1</p> Source code in <code>src/equation_tree/tree.py</code> <pre><code>def symbolic_solution_quot(e_a: EquationTree, e_b: EquationTree):\n    \"\"\"\n    Symbolic solution with quotient constant based on\n    `La Cava, W. et al (2021).\n    Contemporary symbolic regression methods and their relative performance.`\n    Examples:\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '*', '**', '-']\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y']\n        &gt;&gt;&gt; is_constant = lambda x: is_numeric(x)\n        &gt;&gt;&gt; expr_1 = sympify('x * .1')\n        &gt;&gt;&gt; expr_2 = sympify('x')\n        &gt;&gt;&gt; et_1 = EquationTree.from_sympy(\n        ...     expr_1,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ...     constant_test=is_constant\n        ... )\n        &gt;&gt;&gt; et_1.sympy_expr\n        0.1*x_1\n        &gt;&gt;&gt; et_2 = EquationTree.from_sympy(\n        ...     expr_2,\n        ...     operator_test=is_operator,\n        ...     variable_test=is_variable,\n        ... )\n        &gt;&gt;&gt; et_2.sympy_expr\n        x_1\n        &gt;&gt;&gt; symbolic_solution_quot(et_1, et_2)\n        0.1\n    \"\"\"\n    quot_1 = simplify(e_a.sympy_expr / e_b.sympy_expr)\n    quot_2 = simplify(e_a.sympy_expr / e_b.sympy_expr)\n    if quot_1.is_constant():\n        return min(float(quot_1), float(quot_2))\n    else:\n        return np.infty\n</code></pre>"},{"location":"reference/src/equation_tree/src/","title":"Src","text":""},{"location":"reference/src/equation_tree/src/sample_tree_structure/","title":"Sample tree structure","text":""},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure","title":"<code>sample_tree_structure(prior={})</code>","text":"<p>Sample a tree structure.</p> <p>Parameters:</p> Name Type Description Default <code>prior</code> <code>Dict</code> <p>priors in form of a dictionary. The keys are the tree structures as strings</p> <code>{}</code> <p>Examples:</p>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure--set-seed-for-reproducibility","title":"Set seed for reproducibility","text":"<pre><code>&gt;&gt;&gt; np.random.seed(42)\n</code></pre> <pre><code>&gt;&gt;&gt; [sample_tree_structure({'[0, 1, 1]': 1}) for _ in range(4)]\n[[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 1]]\n</code></pre> <pre><code>&gt;&gt;&gt; [sample_tree_structure({'[0, 1, 1]': .5, '[0, 1, 2]': .5}) for _ in range(4)]\n[[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 2]]\n</code></pre> <pre><code>&gt;&gt;&gt; sample_tree_structure({'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 1, 2': .4})\n[0, 1, 2, 3, 1]\n</code></pre> Source code in <code>src/equation_tree/src/sample_tree_structure.py</code> <pre><code>def sample_tree_structure(prior: Dict = {}):\n    \"\"\"\n    Sample a tree structure.\n\n    Args:\n        prior: priors in form of a dictionary. The keys are the tree structures as strings\n\n    Examples:\n        # Set seed for reproducibility\n        &gt;&gt;&gt; np.random.seed(42)\n\n        &gt;&gt;&gt; [sample_tree_structure({'[0, 1, 1]': 1}) for _ in range(4)]\n        [[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 1]]\n\n        &gt;&gt;&gt; [sample_tree_structure({'[0, 1, 1]': .5, '[0, 1, 2]': .5}) for _ in range(4)]\n        [[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 2]]\n\n        &gt;&gt;&gt; sample_tree_structure({'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 1, 2': .4})\n        [0, 1, 2, 3, 1]\n\n    \"\"\"\n    tree_structures = [parse_string_list_int(str(key)) for key in prior.keys()]\n    probabilities = [prior[key] for key in prior.keys()]\n\n    for _ in range(MAX_ITER):\n        sample_index = np.random.choice(len(tree_structures), p=probabilities)\n        tree_structure = tree_structures[sample_index]\n        if not _is_binary_tree(tree_structure):\n            warnings.warn(\n                \"Found a non binary tree structure, \"\n                \"this might lead to discrepancies between set priors and sample frequencies.\"\n            )\n            continue\n        return tree_structure\n    raise Exception(f\"Could not generate tree structure with prior: {prior}\")\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso","title":"<code>sample_tree_structure_non_iso(max_depth, priors={})</code>","text":"<p>Sample a tree structure.</p> <p>Parameters:</p> Name Type Description Default <code>max_depth</code> <code>int</code> <p>the maximum depth of a tree</p> required <code>priors</code> <code>Dict</code> <p>priors in form of a dictionary. The keys are the tree structures as strings</p> <code>{}</code> <p>Examples:</p>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--set-seed-for-reproducibility","title":"Set seed for reproducibility","text":"<pre><code>&gt;&gt;&gt; np.random.seed(42)\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--sample-a-single-structure","title":"Sample a single structure","text":"<pre><code>&gt;&gt;&gt; sample_tree_structure_non_iso(7)\n[0, 1, 2, 3, 3, 2]\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--get-a-list-of-4-samples-with-max_depth-4","title":"Get a list of 4 samples with max_depth = 4","text":"<pre><code>&gt;&gt;&gt; [sample_tree_structure_non_iso(5) for _ in range(4)]\n[[0, 1, 2, 1, 2], [0, 1, 2, 3, 1], [0, 1, 2, 3, 3], [0, 1, 1]]\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--set-a-prior","title":"Set a prior","text":"<pre><code>&gt;&gt;&gt; [sample_tree_structure_non_iso(5, {'[0, 1, 1]': 1}) for _ in range(4)]\n[[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 1]]\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--set-a-different-prior","title":"Set a different prior","text":"<pre><code>&gt;&gt;&gt; [sample_tree_structure_non_iso(5, {'[0, 1, 1]': .5, '[0, 1, 2]': .5}) for _ in range(4)]\n[[0, 1, 1], [0, 1, 2], [0, 1, 1], [0, 1, 1]]\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--we-can-also-set-a-full-prior-here-the-max_depth-for-the-structure-is-3-which-only-allows","title":"We can also set a full prior( here the max_depth for the structure is 3 which only allows","text":""},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--for-two-structures-0-1-1-and-0-1-2","title":"for two structures: [0, 1, 1] and [0, 1, 2]","text":"<pre><code>&gt;&gt;&gt; [sample_tree_structure_non_iso(3, {'[0, 1, 1]': .3, '[0, 1, 2]': .7}) for _ in range(4)]\n[[0, 1, 2], [0, 1, 2], [0, 1, 2], [0, 1, 2]]\n</code></pre>"},{"location":"reference/src/equation_tree/src/sample_tree_structure/#src.equation_tree.src.sample_tree_structure.sample_tree_structure_non_iso--if-we-set-an-invalid-prior-an-exeption-is-raised-doctest-ellipsis","title":"If we set an invalid prior, an Exeption is raised  # doctest: +ELLIPSIS","text":"<pre><code>&gt;&gt;&gt; [sample_tree_structure_non_iso(3, {'[0, 1, 3]': .5}) for _ in range(4)]\nTraceback (most recent call last):\n...\nException: Priors {'[0, 1, 3]': 0.5} are not subset of space ['[0, 1, 2]', '[0, 1, 1]']\n</code></pre> Source code in <code>src/equation_tree/src/sample_tree_structure.py</code> <pre><code>def sample_tree_structure_non_iso(max_depth: int, priors: Dict = {}):\n    \"\"\"\n    Sample a tree structure.\n\n    Args:\n        max_depth: the maximum depth of a tree\n        priors: priors in form of a dictionary. The keys are the tree structures as strings\n\n    Examples:\n        # Set seed for reproducibility\n        &gt;&gt;&gt; np.random.seed(42)\n\n        # Sample a single structure\n        &gt;&gt;&gt; sample_tree_structure_non_iso(7)\n        [0, 1, 2, 3, 3, 2]\n\n        # Get a list of 4 samples with max_depth = 4\n        &gt;&gt;&gt; [sample_tree_structure_non_iso(5) for _ in range(4)]\n        [[0, 1, 2, 1, 2], [0, 1, 2, 3, 1], [0, 1, 2, 3, 3], [0, 1, 1]]\n\n        # Set a prior\n        &gt;&gt;&gt; [sample_tree_structure_non_iso(5, {'[0, 1, 1]': 1}) for _ in range(4)]\n        [[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 1]]\n\n        # Set a different prior\n        &gt;&gt;&gt; [sample_tree_structure_non_iso(5, {'[0, 1, 1]': .5, '[0, 1, 2]': .5}) for _ in range(4)]\n        [[0, 1, 1], [0, 1, 2], [0, 1, 1], [0, 1, 1]]\n\n        # We can also set a full prior( here the max_depth for the structure is 3 which only allows\n        # for two structures: [0, 1, 1] and [0, 1, 2]\n        &gt;&gt;&gt; [sample_tree_structure_non_iso(3, {'[0, 1, 1]': .3, '[0, 1, 2]': .7}) for _ in range(4)]\n        [[0, 1, 2], [0, 1, 2], [0, 1, 2], [0, 1, 2]]\n\n        # If we set an invalid prior, an Exeption is raised  # doctest: +ELLIPSIS\n        &gt;&gt;&gt; [sample_tree_structure_non_iso(3, {'[0, 1, 3]': .5}) for _ in range(4)]\n        Traceback (most recent call last):\n        ...\n        Exception: Priors {'[0, 1, 3]': 0.5} are not subset of space ['[0, 1, 2]', '[0, 1, 1]']\n\n    \"\"\"\n    tree_structures = _gen_all_tree_structures_non_iso(max_depth)\n\n    priors = set_priors(priors, [str(structure) for structure in tree_structures])\n    probabilities = [priors[key] for key in priors.keys()]\n\n    for _ in range(MAX_ITER):\n        sample_index = np.random.choice(len(tree_structures), p=probabilities)\n        tree_structure = tree_structures[sample_index]\n        if not _is_binary_tree(tree_structure):\n            warnings.warn(\n                \"Found a non binary tree structure, \"\n                \"this might lead to discrepancies between set priors and sample frequencies.\"\n            )\n            continue\n        return tree_structure\n    raise Exception(f\"Could not generate tree structure with max depth {max_depth}\")\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/","title":"Tree node","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.TreeNode","title":"<code>TreeNode</code>","text":"Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>class TreeNode:\n    def __init__(\n        self,\n        left=None,\n        right=None,\n        kind=NodeKind.NONE,\n        attribute=\"\",\n    ):\n        \"\"\"\n        Examples:\n            &gt;&gt;&gt; gc_1 = TreeNode(attribute='grand_child_1')\n            &gt;&gt;&gt; gc_1.size\n            1\n            &gt;&gt;&gt; child_1 = TreeNode(attribute='child_1', left=gc_1)\n            &gt;&gt;&gt; child_1.size\n            2\n            &gt;&gt;&gt; child_2 = TreeNode(attribute='child_2')\n            &gt;&gt;&gt; child_2.size\n            1\n            &gt;&gt;&gt; root = TreeNode(left=child_1,right=child_2,attribute='root')\n            &gt;&gt;&gt; root.size\n            4\n        \"\"\"\n\n        self.attribute = attribute\n        self.kind = kind\n        self.parent = None\n        self.left = left\n        self.right = right\n        self.evaluation = 0\n\n        self.children = []\n        if left is not None:\n            self.children.append(left)\n            left.parent = self\n        if right is not None:\n            self.children.append(right)\n            right.parent = self\n        self.is_leaf = self.children == []\n\n    def check_validity(\n        self,\n        zero_representations=[\"0\"],\n        log_representations=[\"log\", \"Log\"],\n        division_representations=[\"/\", \":\"],\n        verbose=False,\n    ):\n        return check_node_validity(\n            self,\n            zero_representations,\n            log_representations,\n            division_representations,\n            verbose,\n        )\n\n    @property\n    def size(self):\n        s_ = 1\n        for c in self.children:\n            s_ += c.size\n        return s_\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.TreeNode.__init__","title":"<code>__init__(left=None, right=None, kind=NodeKind.NONE, attribute='')</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; gc_1 = TreeNode(attribute='grand_child_1')\n&gt;&gt;&gt; gc_1.size\n1\n&gt;&gt;&gt; child_1 = TreeNode(attribute='child_1', left=gc_1)\n&gt;&gt;&gt; child_1.size\n2\n&gt;&gt;&gt; child_2 = TreeNode(attribute='child_2')\n&gt;&gt;&gt; child_2.size\n1\n&gt;&gt;&gt; root = TreeNode(left=child_1,right=child_2,attribute='root')\n&gt;&gt;&gt; root.size\n4\n</code></pre> Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>def __init__(\n    self,\n    left=None,\n    right=None,\n    kind=NodeKind.NONE,\n    attribute=\"\",\n):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; gc_1 = TreeNode(attribute='grand_child_1')\n        &gt;&gt;&gt; gc_1.size\n        1\n        &gt;&gt;&gt; child_1 = TreeNode(attribute='child_1', left=gc_1)\n        &gt;&gt;&gt; child_1.size\n        2\n        &gt;&gt;&gt; child_2 = TreeNode(attribute='child_2')\n        &gt;&gt;&gt; child_2.size\n        1\n        &gt;&gt;&gt; root = TreeNode(left=child_1,right=child_2,attribute='root')\n        &gt;&gt;&gt; root.size\n        4\n    \"\"\"\n\n    self.attribute = attribute\n    self.kind = kind\n    self.parent = None\n    self.left = left\n    self.right = right\n    self.evaluation = 0\n\n    self.children = []\n    if left is not None:\n        self.children.append(left)\n        left.parent = self\n    if right is not None:\n        self.children.append(right)\n        right.parent = self\n    self.is_leaf = self.children == []\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.edit_distance","title":"<code>edit_distance(tree_a, tree_b)</code>","text":"<p>Computes the tree edit distance between trees A and B</p> Implements the algorithm described here <p><code>Zhang, K., &amp; Shasha, D. (1989). Simple fast algorithms for the editing distance between trees and related problems. SIAM journal on computing, 18(6), 1245-1262.</code></p> <p>Inspired and adjusted(simplified) for the purpose of this repository from:     <code>https://github.com/timtadh/zhang-shasha</code></p> <p>Parameters:</p> Name Type Description Default <code>tree_a</code> <code>TreeNode</code> <p>Root of tree A</p> required <code>tree_b</code> <code>TreeNode</code> <p>Root of tree B</p> required Return <p>An integer distance [0, inf+)</p> <p>Examples:     &gt;&gt;&gt; gc_1_a = TreeNode(attribute='grand_child_1')     &gt;&gt;&gt; gc_1_b = TreeNode(attribute='grand_child_1')     &gt;&gt;&gt; edit_distance(gc_1_a, gc_1_b)     0     &gt;&gt;&gt; child_1_a = TreeNode(attribute='child_1', left=gc_1_a)     &gt;&gt;&gt; child_1_b = TreeNode(attribute='child_1_', left=gc_1_b)     &gt;&gt;&gt; edit_distance(child_1_a, child_1_b)     1     &gt;&gt;&gt; child_2_a = TreeNode(attribute='child_2')     &gt;&gt;&gt; child_2_b = TreeNode(attribute='child_2')     &gt;&gt;&gt; edit_distance(child_2_a, child_2_b)     0     &gt;&gt;&gt; root_a = TreeNode(attribute='root', left=child_1_a, right=child_2_a)     &gt;&gt;&gt; root_b = TreeNode(attribute='root', left=child_1_b, right=child_2_b)     &gt;&gt;&gt; edit_distance(root_a, root_b)     1     &gt;&gt;&gt; root_a_ = TreeNode(attribute='root', left=child_2_a, right=child_1_a)     &gt;&gt;&gt; edit_distance(root_a, root_a_)     2     &gt;&gt;&gt; edit_distance(root_a_, root_b)     3</p> Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>def edit_distance(tree_a: TreeNode, tree_b: TreeNode):\n    \"\"\"\n    Computes the tree edit distance between trees A and B\n\n    Implements the algorithm described here:\n        `Zhang, K., &amp; Shasha, D. (1989).\n        Simple fast algorithms for the editing distance between trees and related problems.\n        SIAM journal on computing, 18(6), 1245-1262.`\n    Inspired and adjusted(simplified) for the purpose of this repository from:\n        `https://github.com/timtadh/zhang-shasha`\n\n    Args:\n        tree_a: Root of tree A\n        tree_b: Root of tree B\n\n    Return:\n        An integer distance [0, inf+)\n    Examples:\n        &gt;&gt;&gt; gc_1_a = TreeNode(attribute='grand_child_1')\n        &gt;&gt;&gt; gc_1_b = TreeNode(attribute='grand_child_1')\n        &gt;&gt;&gt; edit_distance(gc_1_a, gc_1_b)\n        0\n        &gt;&gt;&gt; child_1_a = TreeNode(attribute='child_1', left=gc_1_a)\n        &gt;&gt;&gt; child_1_b = TreeNode(attribute='child_1_', left=gc_1_b)\n        &gt;&gt;&gt; edit_distance(child_1_a, child_1_b)\n        1\n        &gt;&gt;&gt; child_2_a = TreeNode(attribute='child_2')\n        &gt;&gt;&gt; child_2_b = TreeNode(attribute='child_2')\n        &gt;&gt;&gt; edit_distance(child_2_a, child_2_b)\n        0\n        &gt;&gt;&gt; root_a = TreeNode(attribute='root', left=child_1_a, right=child_2_a)\n        &gt;&gt;&gt; root_b = TreeNode(attribute='root', left=child_1_b, right=child_2_b)\n        &gt;&gt;&gt; edit_distance(root_a, root_b)\n        1\n        &gt;&gt;&gt; root_a_ = TreeNode(attribute='root', left=child_2_a, right=child_1_a)\n        &gt;&gt;&gt; edit_distance(root_a, root_a_)\n        2\n        &gt;&gt;&gt; edit_distance(root_a_, root_b)\n        3\n\n    \"\"\"\n    tree_a_helper = _HelperTree(tree_a)\n    tree_b_helper = _HelperTree(tree_b)\n\n    treedists = np.zeros((tree_a.size, tree_b.size), float)\n\n    def update_cost(node_a, node_b):\n        return int(node_a.attribute != node_b.attribute)\n\n    def treedist(i, j):\n        al = tree_a_helper.lmds\n        bl = tree_b_helper.lmds\n\n        an = tree_a_helper.nodes\n        bn = tree_b_helper.nodes\n\n        m = i - al[i] + 2\n        n = j - bl[j] + 2\n\n        ioff = al[i] - 1\n        joff = bl[j] - 1\n\n        # Initialize the fd array\n        fd = np.zeros((m, n), float)\n        fd[1:, 0] = np.arange(1, m)\n        fd[0, 1:] = np.arange(1, n)\n\n        partial_ops = [[([1] if x == 0 else []) for x in range(n)] for _ in range(m)]\n\n        for x in range(1, m):\n            for y in range(1, n):\n                if al[i] == al[x + ioff] and bl[j] == bl[y + joff]:\n                    costs = [\n                        fd[x - 1][y] + 1,\n                        fd[x][y - 1] + 1,\n                        fd[x - 1][y - 1] + update_cost(an[x + ioff], bn[y + joff]),\n                    ]\n                    fd[x][y] = min(costs)\n                    min_index = costs.index(fd[x][y])\n                    if min_index == 0:\n                        partial_ops[x][y] = partial_ops[x - 1][y] + [1]\n                    elif min_index == 1:\n                        partial_ops[x][y] = partial_ops[x][y - 1] + [1]\n                    else:\n                        partial_ops[x][y] = partial_ops[x - 1][y - 1] + [1]\n\n                    treedists[x + ioff][y + joff] = fd[x][y]\n                else:\n                    p = al[x + ioff] - 1 - ioff\n                    q = bl[y + joff] - 1 - joff\n                    costs = [\n                        fd[x - 1][y] + 1,\n                        fd[x][y - 1] + 1,\n                        fd[p][q] + treedists[x + ioff][y + joff],\n                    ]\n                    fd[x][y] = min(costs)\n                    min_index = costs.index(fd[x][y])\n                    if min_index == 0:\n                        partial_ops[x][y] = partial_ops[x - 1][y] + [1]\n                    elif min_index == 1:\n                        partial_ops[x][y] = partial_ops[x][y - 1] + [1]\n                    else:\n                        partial_ops[x][y] = partial_ops[p][q] + [1]\n\n    for i in tree_a_helper.keyroots:\n        for j in tree_b_helper.keyroots:\n            treedist(i, j)\n    return int(treedists[-1][-1])\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.ned","title":"<code>ned(tree_a, tree_b)</code>","text":"<p>Normalized tree edit distance according to: <code>Li, Y., &amp; Chenguang, Z. (2011). A metric normalization of tree edit distance. Frontiers of Computer Science in China, 5, 119-125.</code> Examples:     &gt;&gt;&gt; gc_1_a = TreeNode(attribute='grand_child_1')     &gt;&gt;&gt; gc_1_b = TreeNode(attribute='grand_child_1')     &gt;&gt;&gt; ned(gc_1_a, gc_1_b)     0.0     &gt;&gt;&gt; child_1_a = TreeNode(attribute='child_1', left=gc_1_a)     &gt;&gt;&gt; child_1_b = TreeNode(attribute='child_1_', left=gc_1_b)     &gt;&gt;&gt; ned(child_1_a, child_1_b)     0.4     &gt;&gt;&gt; child_2_a = TreeNode(attribute='child_2')     &gt;&gt;&gt; child_2_b = TreeNode(attribute='child_2')     &gt;&gt;&gt; ned(child_2_a, child_2_b)     0.0     &gt;&gt;&gt; root_a = TreeNode(attribute='root', left=child_1_a, right=child_2_a)     &gt;&gt;&gt; root_b = TreeNode(attribute='root', left=child_1_b, right=child_2_b)     &gt;&gt;&gt; ned(root_a, root_b)     0.2222222222222222     &gt;&gt;&gt; root_a_ = TreeNode(attribute='root', left=child_2_a, right=child_1_a)     &gt;&gt;&gt; ned(root_a, root_a_)     0.4     &gt;&gt;&gt; ned(root_a_, root_b)     0.5454545454545454</p> Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>def ned(tree_a: TreeNode, tree_b: TreeNode):\n    \"\"\"\n    Normalized tree edit distance according to:\n    `Li, Y., &amp; Chenguang, Z. (2011). A metric normalization of tree edit distance.\n    Frontiers of Computer Science in China, 5, 119-125.`\n    Examples:\n        &gt;&gt;&gt; gc_1_a = TreeNode(attribute='grand_child_1')\n        &gt;&gt;&gt; gc_1_b = TreeNode(attribute='grand_child_1')\n        &gt;&gt;&gt; ned(gc_1_a, gc_1_b)\n        0.0\n        &gt;&gt;&gt; child_1_a = TreeNode(attribute='child_1', left=gc_1_a)\n        &gt;&gt;&gt; child_1_b = TreeNode(attribute='child_1_', left=gc_1_b)\n        &gt;&gt;&gt; ned(child_1_a, child_1_b)\n        0.4\n        &gt;&gt;&gt; child_2_a = TreeNode(attribute='child_2')\n        &gt;&gt;&gt; child_2_b = TreeNode(attribute='child_2')\n        &gt;&gt;&gt; ned(child_2_a, child_2_b)\n        0.0\n        &gt;&gt;&gt; root_a = TreeNode(attribute='root', left=child_1_a, right=child_2_a)\n        &gt;&gt;&gt; root_b = TreeNode(attribute='root', left=child_1_b, right=child_2_b)\n        &gt;&gt;&gt; ned(root_a, root_b)\n        0.2222222222222222\n        &gt;&gt;&gt; root_a_ = TreeNode(attribute='root', left=child_2_a, right=child_1_a)\n        &gt;&gt;&gt; ned(root_a, root_a_)\n        0.4\n        &gt;&gt;&gt; ned(root_a_, root_b)\n        0.5454545454545454\n    \"\"\"\n    ed = edit_distance(tree_a, tree_b)\n    return 2 * ed / (tree_a.size + tree_b.size + ed)\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.node_from_prefix","title":"<code>node_from_prefix(prefix_notation, function_test=lambda : False, operator_test=lambda : False, variable_test=lambda : False, constant_test=lambda : False)</code>","text":"<p>Create a tree from a prefix notation</p> <p>Parameters:</p> Name Type Description Default <code>prefix_notation</code> <code>List[str]</code> <p>The equation in prefix notation</p> required <code>function_test</code> <code>Callable</code> <p>A function that tests if the attribute is a function</p> <code>lambda : False</code> <code>operator_test</code> <code>Callable</code> <p>A function that tests if the attribute is an operator</p> <code>lambda : False</code> <code>variable_test</code> <code>Callable</code> <p>A function that tests if the attribute is a variable</p> <code>lambda : False</code> <code>constant_test</code> <code>Callable</code> <p>A function that tests if the attribute is a constant</p> <code>lambda : False</code> <p>Examples:</p>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.node_from_prefix--the-equation-is-a-single-variable-the-test-for-variables-is-a-check-in-a-hard","title":"The equation is a single variable. The test for variables is a check in a hard","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.node_from_prefix--coded-list","title":"coded list","text":"<pre><code>&gt;&gt;&gt; tree = node_from_prefix(['x'], variable_test=lambda x: 'x' in ['x', 'y', 'z'])\n&gt;&gt;&gt; tree.kind == NodeKind.VARIABLE\nTrue\n&gt;&gt;&gt; tree.attribute\n'x'\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.node_from_prefix--we-can-also-use-more-elaborate-tests-depending-for-example-checking-weather-the","title":"We can also use more elaborate tests depending. For example checking, weather the","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.node_from_prefix--attribute-contains-an-underscore","title":"attribute contains an underscore","text":"<pre><code>&gt;&gt;&gt; tree = node_from_prefix(\n...     prefix_notation=['sin', 'x_1'],\n...     function_test=lambda x: x in ['sin', 'cos'],\n...     variable_test=lambda x: '_' in x)\n&gt;&gt;&gt; tree.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; tree.attribute\n'sin'\n&gt;&gt;&gt; tree.left.kind == NodeKind.VARIABLE\nTrue\n&gt;&gt;&gt; tree.left.attribute\n'x_1'\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.node_from_prefix--we-can-also-pass-other-functions","title":"We can also pass other functions","text":"<pre><code>&gt;&gt;&gt; def is_variable(x):\n...     return x == 'x' or x == 'y'\n&gt;&gt;&gt; def is_operator(x):\n...     return not is_variable(x) and len(x) == 1\n&gt;&gt;&gt; def is_function(x):\n...     return not is_variable(x) and not is_operator(x)\n&gt;&gt;&gt; tree = node_from_prefix(\n...     prefix_notation=['+', 'sin', 'x', 'cos', 'y'],\n...     variable_test=is_variable,\n...     operator_test=is_operator,\n...     function_test=is_function\n...     )\n&gt;&gt;&gt; tree.kind == NodeKind.OPERATOR\nTrue\n&gt;&gt;&gt; tree.attribute\n'+'\n&gt;&gt;&gt; tree.left.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; tree.left.attribute\n'sin'\n&gt;&gt;&gt; tree.left.left.kind == NodeKind.VARIABLE\nTrue\n&gt;&gt;&gt; tree.left.left.attribute\n'x'\n&gt;&gt;&gt; tree.right.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; tree.right.attribute\n'cos'\n&gt;&gt;&gt; tree.right.left.kind == NodeKind.VARIABLE\nTrue\n&gt;&gt;&gt; tree.right.left.attribute\n'y'\n</code></pre> Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>def node_from_prefix(\n    prefix_notation: List[str],\n    function_test: Callable = lambda _: False,\n    operator_test: Callable = lambda _: False,\n    variable_test: Callable = lambda _: False,\n    constant_test: Callable = lambda _: False,\n):\n    \"\"\"\n    Create a tree from a prefix notation\n\n    Args:\n        prefix_notation: The equation in prefix notation\n        function_test: A function that tests if the attribute is a function\n        operator_test: A function that tests if the attribute is an operator\n        variable_test: A function that tests if the attribute is a variable\n        constant_test: A function that tests if the attribute is a constant\n\n    Examples:\n        # The equation is a single variable. The test for variables is a check in a hard\n        # coded list\n        &gt;&gt;&gt; tree = node_from_prefix(['x'], variable_test=lambda x: 'x' in ['x', 'y', 'z'])\n        &gt;&gt;&gt; tree.kind == NodeKind.VARIABLE\n        True\n        &gt;&gt;&gt; tree.attribute\n        'x'\n\n        # We can also use more elaborate tests depending. For example checking, weather the\n        # attribute contains an underscore\n        &gt;&gt;&gt; tree = node_from_prefix(\n        ...     prefix_notation=['sin', 'x_1'],\n        ...     function_test=lambda x: x in ['sin', 'cos'],\n        ...     variable_test=lambda x: '_' in x)\n        &gt;&gt;&gt; tree.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; tree.attribute\n        'sin'\n        &gt;&gt;&gt; tree.left.kind == NodeKind.VARIABLE\n        True\n        &gt;&gt;&gt; tree.left.attribute\n        'x_1'\n\n        # We can also pass other functions\n        &gt;&gt;&gt; def is_variable(x):\n        ...     return x == 'x' or x == 'y'\n        &gt;&gt;&gt; def is_operator(x):\n        ...     return not is_variable(x) and len(x) == 1\n        &gt;&gt;&gt; def is_function(x):\n        ...     return not is_variable(x) and not is_operator(x)\n        &gt;&gt;&gt; tree = node_from_prefix(\n        ...     prefix_notation=['+', 'sin', 'x', 'cos', 'y'],\n        ...     variable_test=is_variable,\n        ...     operator_test=is_operator,\n        ...     function_test=is_function\n        ...     )\n        &gt;&gt;&gt; tree.kind == NodeKind.OPERATOR\n        True\n        &gt;&gt;&gt; tree.attribute\n        '+'\n        &gt;&gt;&gt; tree.left.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; tree.left.attribute\n        'sin'\n        &gt;&gt;&gt; tree.left.left.kind == NodeKind.VARIABLE\n        True\n        &gt;&gt;&gt; tree.left.left.attribute\n        'x'\n        &gt;&gt;&gt; tree.right.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; tree.right.attribute\n        'cos'\n        &gt;&gt;&gt; tree.right.left.kind == NodeKind.VARIABLE\n        True\n        &gt;&gt;&gt; tree.right.left.attribute\n        'y'\n\n    \"\"\"\n    node, _ = _from_prefix_recursion(\n        prefix_notation, function_test, operator_test, variable_test, constant_test\n    )\n\n    return node\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full","title":"<code>sample_tree_full(prior, max_var_unique)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; np.random.seed(42)\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full--we-can-set-priors-for-features-functions-operators","title":"We can set priors for features, functions, operators","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full--and-also-conditionals-based-the-parent","title":"and also conditionals based the parent","text":"<pre><code>&gt;&gt;&gt; p = {\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .2, 'variables': .8},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': 1., '-': .0},\n...     'function_conditionals': {\n...                             'sin': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': 0., 'cos': 1.},\n...                                 'operators': {'+': 0., '-': 1.}\n...                             },\n...                             'cos': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'cos': 1., 'sin': 0.},\n...                                 'operators': {'+': 0., '-': 1.}\n...                             }\n...                         },\n...     'operator_conditionals': {\n...                             '+': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': 1., 'cos': 0.},\n...                                 'operators': {'+': 1., '-': 0.}\n...                             },\n...                             '-': {\n...                                 'features': {'constants': .3, 'variables': .7},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .9, '-': .1}\n...                             }\n...                         },\n... }\n&gt;&gt;&gt; sample = sample_tree_full(p, 3)\n&gt;&gt;&gt; sample.attribute\n'cos'\n&gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.left.attribute\n'cos'\n&gt;&gt;&gt; sample.left.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.right is None\nTrue\n&gt;&gt;&gt; sample = sample_tree_full(p, 3)\n&gt;&gt;&gt; sample.attribute\n'sin'\n&gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.left.attribute\n'cos'\n&gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.left.left.attribute\n'x_1'\n&gt;&gt;&gt; sample.left.left.kind == NodeKind.VARIABLE\nTrue\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full--if-we-dont-provide-priors-for-the-conditionals","title":"If we don't provide priors for the conditionals,","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full--the-fallback-is-the-unconditioned-priors","title":"the fallback is the unconditioned priors","text":"<pre><code>&gt;&gt;&gt; p = {'max_depth': 8,\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .2, 'variables': .8},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': .5, '-': .5},\n... }\n&gt;&gt;&gt; sample = sample_tree_full(p, 3)\n&gt;&gt;&gt; sample.attribute\n'-'\n&gt;&gt;&gt; sample.kind == NodeKind.OPERATOR\nTrue\n&gt;&gt;&gt; sample.right.attribute\n'x_1'\n&gt;&gt;&gt; sample.left.attribute\n'x_1'\n&gt;&gt;&gt; sample.left.kind == NodeKind.VARIABLE\nTrue\n</code></pre> Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>def sample_tree_full(prior, max_var_unique):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; np.random.seed(42)\n\n        # We can set priors for features, functions, operators\n        # and also conditionals based the parent\n        &gt;&gt;&gt; p = {\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .2, 'variables': .8},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': 1., '-': .0},\n        ...     'function_conditionals': {\n        ...                             'sin': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': 0., 'cos': 1.},\n        ...                                 'operators': {'+': 0., '-': 1.}\n        ...                             },\n        ...                             'cos': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'cos': 1., 'sin': 0.},\n        ...                                 'operators': {'+': 0., '-': 1.}\n        ...                             }\n        ...                         },\n        ...     'operator_conditionals': {\n        ...                             '+': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': 1., 'cos': 0.},\n        ...                                 'operators': {'+': 1., '-': 0.}\n        ...                             },\n        ...                             '-': {\n        ...                                 'features': {'constants': .3, 'variables': .7},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .9, '-': .1}\n        ...                             }\n        ...                         },\n        ... }\n        &gt;&gt;&gt; sample = sample_tree_full(p, 3)\n        &gt;&gt;&gt; sample.attribute\n        'cos'\n        &gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.left.attribute\n        'cos'\n        &gt;&gt;&gt; sample.left.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.right is None\n        True\n        &gt;&gt;&gt; sample = sample_tree_full(p, 3)\n        &gt;&gt;&gt; sample.attribute\n        'sin'\n        &gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.left.attribute\n        'cos'\n        &gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.left.left.attribute\n        'x_1'\n        &gt;&gt;&gt; sample.left.left.kind == NodeKind.VARIABLE\n        True\n\n        # If we don't provide priors for the conditionals,\n        # the fallback is the unconditioned priors\n        &gt;&gt;&gt; p = {'max_depth': 8,\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .2, 'variables': .8},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': .5, '-': .5},\n        ... }\n        &gt;&gt;&gt; sample = sample_tree_full(p, 3)\n        &gt;&gt;&gt; sample.attribute\n        '-'\n        &gt;&gt;&gt; sample.kind == NodeKind.OPERATOR\n        True\n        &gt;&gt;&gt; sample.right.attribute\n        'x_1'\n        &gt;&gt;&gt; sample.left.attribute\n        'x_1'\n        &gt;&gt;&gt; sample.left.kind == NodeKind.VARIABLE\n        True\n\n    \"\"\"\n    tree_structure = sample_tree_structure(prior[\"structures\"])\n    function_conditionals = None\n    operator_conditionals = None\n    if \"function_conditionals\" in prior.keys():\n        function_conditionals = prior[\"function_conditionals\"]\n    if \"operator_conditionals\" in prior.keys():\n        operator_conditionals = prior[\"operator_conditionals\"]\n\n    tree = sample_equation_tree_from_structure_with_conditionals(\n        tree_structure,\n        0,\n        prior[\"features\"],\n        prior[\"functions\"],\n        function_conditionals,\n        prior[\"operators\"],\n        operator_conditionals,\n    )\n    post(tree, max_var_unique)\n    return tree\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full_fast","title":"<code>sample_tree_full_fast(prior, tree_depth, max_var_unique)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; np.random.seed(42)\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full_fast--we-can-set-priors-for-features-functions-operators","title":"We can set priors for features, functions, operators","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full_fast--and-also-conditionals-based-the-parent","title":"and also conditionals based the parent","text":"<pre><code>&gt;&gt;&gt; p = {\n...     'features': {'constants': .2, 'variables': .8},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': 1., '-': .0},\n...     'function_conditionals': {\n...                             'sin': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': 0., 'cos': 1.},\n...                                 'operators': {'+': 0., '-': 1.}\n...                             },\n...                             'cos': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'cos': 1., 'sin': 0.},\n...                                 'operators': {'+': 0., '-': 1.}\n...                             }\n...                         },\n...     'operator_conditionals': {\n...                             '+': {\n...                                 'features': {'constants': 0., 'variables': 1.},\n...                                 'functions': {'sin': 1., 'cos': 0.},\n...                                 'operators': {'+': 1., '-': 0.}\n...                             },\n...                             '-': {\n...                                 'features': {'constants': .3, 'variables': .7},\n...                                 'functions': {'cos': .5, 'sin': .5},\n...                                 'operators': {'+': .9, '-': .1}\n...                             }\n...                         },\n... }\n&gt;&gt;&gt; sample = sample_tree_full_fast(p, 3, 2)\n&gt;&gt;&gt; sample.attribute\n'cos'\n&gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.left.attribute\n'cos'\n&gt;&gt;&gt; sample.left.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.right is None\nTrue\n&gt;&gt;&gt; sample = sample_tree_full_fast(p, 4, 3)\n&gt;&gt;&gt; sample.attribute\n'sin'\n&gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.left.attribute\n'-'\n&gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\nTrue\n&gt;&gt;&gt; sample.left.left.attribute\n'x_1'\n&gt;&gt;&gt; sample.left.left.kind == NodeKind.VARIABLE\nTrue\n</code></pre>"},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full_fast--if-we-dont-provide-priors-for-the-conditionals","title":"If we don't provide priors for the conditionals,","text":""},{"location":"reference/src/equation_tree/src/tree_node/#src.equation_tree.src.tree_node.sample_tree_full_fast--the-fallback-is-the-unconditioned-priors","title":"the fallback is the unconditioned priors","text":"<pre><code>&gt;&gt;&gt; p = {'max_depth': 8,\n...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n...     'features': {'constants': .2, 'variables': .8},\n...     'functions': {'sin': .5, 'cos': .5},\n...     'operators': {'+': .5, '-': .5},\n... }\n&gt;&gt;&gt; sample = sample_tree_full_fast(p, 5, 3)\n&gt;&gt;&gt; sample.attribute\n'-'\n&gt;&gt;&gt; sample.kind == NodeKind.OPERATOR\nTrue\n&gt;&gt;&gt; sample.right.attribute\n'cos'\n&gt;&gt;&gt; sample.left.attribute\n'sin'\n&gt;&gt;&gt; sample.left.kind == NodeKind.FUNCTION\nTrue\n</code></pre> Source code in <code>src/equation_tree/src/tree_node.py</code> <pre><code>def sample_tree_full_fast(prior, tree_depth, max_var_unique):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; np.random.seed(42)\n\n        # We can set priors for features, functions, operators\n        # and also conditionals based the parent\n        &gt;&gt;&gt; p = {\n        ...     'features': {'constants': .2, 'variables': .8},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': 1., '-': .0},\n        ...     'function_conditionals': {\n        ...                             'sin': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': 0., 'cos': 1.},\n        ...                                 'operators': {'+': 0., '-': 1.}\n        ...                             },\n        ...                             'cos': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'cos': 1., 'sin': 0.},\n        ...                                 'operators': {'+': 0., '-': 1.}\n        ...                             }\n        ...                         },\n        ...     'operator_conditionals': {\n        ...                             '+': {\n        ...                                 'features': {'constants': 0., 'variables': 1.},\n        ...                                 'functions': {'sin': 1., 'cos': 0.},\n        ...                                 'operators': {'+': 1., '-': 0.}\n        ...                             },\n        ...                             '-': {\n        ...                                 'features': {'constants': .3, 'variables': .7},\n        ...                                 'functions': {'cos': .5, 'sin': .5},\n        ...                                 'operators': {'+': .9, '-': .1}\n        ...                             }\n        ...                         },\n        ... }\n        &gt;&gt;&gt; sample = sample_tree_full_fast(p, 3, 2)\n        &gt;&gt;&gt; sample.attribute\n        'cos'\n        &gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.left.attribute\n        'cos'\n        &gt;&gt;&gt; sample.left.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.right is None\n        True\n        &gt;&gt;&gt; sample = sample_tree_full_fast(p, 4, 3)\n        &gt;&gt;&gt; sample.attribute\n        'sin'\n        &gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.left.attribute\n        '-'\n        &gt;&gt;&gt; sample.kind == NodeKind.FUNCTION\n        True\n        &gt;&gt;&gt; sample.left.left.attribute\n        'x_1'\n        &gt;&gt;&gt; sample.left.left.kind == NodeKind.VARIABLE\n        True\n\n        # If we don't provide priors for the conditionals,\n        # the fallback is the unconditioned priors\n        &gt;&gt;&gt; p = {'max_depth': 8,\n        ...     'structures': {'[0, 1, 1]': .3, '[0, 1, 2]': .3, '[0, 1, 2, 3, 2, 3, 1]': .4},\n        ...     'features': {'constants': .2, 'variables': .8},\n        ...     'functions': {'sin': .5, 'cos': .5},\n        ...     'operators': {'+': .5, '-': .5},\n        ... }\n        &gt;&gt;&gt; sample = sample_tree_full_fast(p, 5, 3)\n        &gt;&gt;&gt; sample.attribute\n        '-'\n        &gt;&gt;&gt; sample.kind == NodeKind.OPERATOR\n        True\n        &gt;&gt;&gt; sample.right.attribute\n        'cos'\n        &gt;&gt;&gt; sample.left.attribute\n        'sin'\n        &gt;&gt;&gt; sample.left.kind == NodeKind.FUNCTION\n        True\n\n    \"\"\"\n    tree_structure = sample_tree_structure_fast(tree_depth)\n    function_conditionals = None\n    operator_conditionals = None\n    if \"function_conditionals\" in prior.keys():\n        function_conditionals = prior[\"function_conditionals\"]\n    if \"operator_conditionals\" in prior.keys():\n        operator_conditionals = prior[\"operator_conditionals\"]\n\n    tree = sample_equation_tree_from_structure_with_conditionals(\n        tree_structure,\n        0,\n        prior[\"features\"],\n        prior[\"functions\"],\n        function_conditionals,\n        prior[\"operators\"],\n        operator_conditionals,\n    )\n    post(tree, max_var_unique)\n    return tree\n</code></pre>"},{"location":"reference/src/equation_tree/util/","title":"Util","text":""},{"location":"reference/src/equation_tree/util/conversions/","title":"Conversions","text":""},{"location":"reference/src/equation_tree/util/conversions/#src.equation_tree.util.conversions.func_to_op_const","title":"<code>func_to_op_const(expr)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; e_1 = 'x_1*cubed(x_1*3-squared(c_1/x_1*2)-x_3)-squared(x)'\n&gt;&gt;&gt; func_to_op_const(e_1)\n'x_1*(x_1*3-(c_1/x_1*2)**2-x_3)**3-(x)**2'\n&gt;&gt;&gt; func_to_op_const('cubed(x_1)')\n'(x_1)**3'\n</code></pre> Source code in <code>src/equation_tree/util/conversions.py</code> <pre><code>def func_to_op_const(expr):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; e_1 = 'x_1*cubed(x_1*3-squared(c_1/x_1*2)-x_3)-squared(x)'\n        &gt;&gt;&gt; func_to_op_const(e_1)\n        'x_1*(x_1*3-(c_1/x_1*2)**2-x_3)**3-(x)**2'\n        &gt;&gt;&gt; func_to_op_const('cubed(x_1)')\n        '(x_1)**3'\n    \"\"\"\n    for key, el in CONVERSIONS_FUNC_OP_CONST.items():\n        expr = _func_op_const_rec(expr, key, el)\n    return expr\n</code></pre>"},{"location":"reference/src/equation_tree/util/conversions/#src.equation_tree.util.conversions.infix_to_prefix","title":"<code>infix_to_prefix(infix, function_test, operator_test)</code>","text":"<p>Transforms prefix notation to infix notation</p> Example <p>is_function = lambda x: x in ['sin', 'cos'] is_operator = lambda x : x in ['+', '-', '*', '/'] infix_to_prefix('x_2-x_1', is_function, is_operator) ['-', 'x_2', 'x_1']</p> <p>infix_to_prefix('x_1-(x_2+x_4)', is_function, is_operator) ['-', 'x_1', '+', 'x_2', 'x_4']</p> <p>infix_to_prefix('x_1cos(c_1+x_2)', is_function, is_operator) ['', 'x_1', 'cos', '+', 'c_1', 'x_2']</p> <p>is_function = lambda x: x in ['sin', 'cos', 'e'] is_operator = lambda x: x in ['+', '-', '', '^', 'max', '*', '/'] infix_to_prefix('x_1 + max(x_2, x_3)', is_function, is_operator) ['+', 'x_1', 'max', 'x_2', 'x_3']</p> <p>infix_to_prefix('x_1-(x_2/(x_3-x_4))',is_function, is_operator) ['-', 'x_1', '/', 'x_2', '-', 'x_3', 'x_4']</p> <p>infix_to_prefix('x_1^(sin(x_2)/x_3)', is_function, is_operator) ['^', 'x_1', '/', 'sin', 'x_2', 'x_3']</p> <p>infix_to_prefix('sin(x_1)-x_2', is_function, is_operator) ['-', 'sin', 'x_1', 'x_2']</p> Source code in <code>src/equation_tree/util/conversions.py</code> <pre><code>def infix_to_prefix(infix, function_test, operator_test):\n    \"\"\"\n    Transforms prefix notation to infix notation\n\n    Example:\n        &gt;&gt;&gt; is_function = lambda x: x in ['sin', 'cos']\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '-', '*', '/']\n        &gt;&gt;&gt; infix_to_prefix('x_2-x_1', is_function, is_operator)\n        ['-', 'x_2', 'x_1']\n\n        &gt;&gt;&gt; infix_to_prefix('x_1-(x_2+x_4)', is_function, is_operator)\n        ['-', 'x_1', '+', 'x_2', 'x_4']\n\n        &gt;&gt;&gt; infix_to_prefix('x_1*cos(c_1+x_2)', is_function, is_operator)\n        ['*', 'x_1', 'cos', '+', 'c_1', 'x_2']\n\n        &gt;&gt;&gt; is_function = lambda x: x in ['sin', 'cos', 'e']\n        &gt;&gt;&gt; is_operator = lambda x: x in ['+', '-', '*', '^', 'max', '**', '/']\n        &gt;&gt;&gt; infix_to_prefix('x_1 + max(x_2, x_3)', is_function, is_operator)\n        ['+', 'x_1', 'max', 'x_2', 'x_3']\n\n        &gt;&gt;&gt; infix_to_prefix('x_1-(x_2/(x_3-x_4))',is_function, is_operator)\n        ['-', 'x_1', '/', 'x_2', '-', 'x_3', 'x_4']\n\n        &gt;&gt;&gt; infix_to_prefix('x_1^(sin(x_2)/x_3)', is_function, is_operator)\n        ['^', 'x_1', '/', 'sin', 'x_2', 'x_3']\n\n        &gt;&gt;&gt; infix_to_prefix('sin(x_1)-x_2', is_function, is_operator)\n        ['-', 'sin', 'x_1', 'x_2']\n    \"\"\"\n\n    # n = len(infix)\n\n    # infix = list(infix[::-1].lower())\n    #\n    # for i in range(n):\n    #     if infix[i] == \"(\":\n    #         infix[i] = \")\"\n    #     elif infix[i] == \")\":\n    #         infix[i] = \"(\"\n    #\n    # infix = \"\".join(infix)\n    postfix = _infix_to_postfix(infix, function_test, operator_test)\n    prefix = postfix[::-1]\n\n    return prefix\n</code></pre>"},{"location":"reference/src/equation_tree/util/conversions/#src.equation_tree.util.conversions.op_const_to_func","title":"<code>op_const_to_func(expr)</code>","text":"<p>Known operators with constants to functions. For exampl, e2-&gt;squared Examples:     &gt;&gt;&gt; op_const_to_func('x_1(x_13-(c_1/x_1*2)2-x_3)3-(x)2')     'x_1cubed(x_13-squared(c_1/x_12)-x_3)-squared(x)'     &gt;&gt;&gt; op_const_to_func('(x_1)3')     'cubed(x_1)'     &gt;&gt;&gt; op_const_to_func('x2')     'squared(x)'     &gt;&gt;&gt; op_const_to_func('c_13')     'cubed(c_1)'     &gt;&gt;&gt; op_const_to_func('(x_2*2)')     'squared(x_2)'</p> Source code in <code>src/equation_tree/util/conversions.py</code> <pre><code>def op_const_to_func(expr):\n    \"\"\"\n    Known operators with constants to functions. For exampl, e**2-&gt;squared\n    Examples:\n        &gt;&gt;&gt; op_const_to_func('x_1*(x_1*3-(c_1/x_1*2)**2-x_3)**3-(x)**2')\n        'x_1*cubed(x_1*3-squared(c_1/x_1*2)-x_3)-squared(x)'\n        &gt;&gt;&gt; op_const_to_func('(x_1)**3')\n        'cubed(x_1)'\n        &gt;&gt;&gt; op_const_to_func('x**2')\n        'squared(x)'\n        &gt;&gt;&gt; op_const_to_func('c_1**3')\n        'cubed(c_1)'\n        &gt;&gt;&gt; op_const_to_func('(x_2**2)')\n        'squared(x_2)'\n    \"\"\"\n\n    for key, el in CONVERSION_OP_CONST_FUNC.items():\n        expr = _op_const_func_rec(expr, key, el)\n    expr = _remove_unnecessary_parentheses(expr)\n\n    return expr\n</code></pre>"},{"location":"reference/src/equation_tree/util/conversions/#src.equation_tree.util.conversions.prefix_to_infix","title":"<code>prefix_to_infix(prefix, function_test=lambda : False, operator_test=lambda : False)</code>","text":"<p>Transforms prefix notation to infix notation</p> Example <p>is_function = lambda x: x in ['sin', 'cos'] is_operator = lambda x : x in ['+', '-', '', 'max', '*'] prefix_to_infix(['-', 'x_1', 'x_2'], is_function, is_operator) '(x_1-x_2)'</p> <p>prefix_to_infix( ...     ['', 'x', 'cos', '+', 'y', 'z'], is_function, is_operator) '(xcos((y+z)))'</p> <p>prefix_to_infix(['max', 'x_1', 'x_2'], is_function, is_operator) 'max(x_1,x_2)'</p> <p>prefix_to_infix(['', 'x_1', 'x_2'], is_function, is_operator) '(x_1x_2)'</p> Source code in <code>src/equation_tree/util/conversions.py</code> <pre><code>def prefix_to_infix(\n    prefix, function_test=lambda _: False, operator_test=lambda _: False\n):\n    \"\"\"\n    Transforms prefix notation to infix notation\n\n    Example:\n        &gt;&gt;&gt; is_function = lambda x: x in ['sin', 'cos']\n        &gt;&gt;&gt; is_operator = lambda x : x in ['+', '-', '*', 'max', '**']\n        &gt;&gt;&gt; prefix_to_infix(['-', 'x_1', 'x_2'], is_function, is_operator)\n        '(x_1-x_2)'\n\n        &gt;&gt;&gt; prefix_to_infix(\n        ...     ['*', 'x', 'cos', '+', 'y', 'z'], is_function, is_operator)\n        '(x*cos((y+z)))'\n\n        &gt;&gt;&gt; prefix_to_infix(['max', 'x_1', 'x_2'], is_function, is_operator)\n        'max(x_1,x_2)'\n\n        &gt;&gt;&gt; prefix_to_infix(['**', 'x_1', 'x_2'], is_function, is_operator)\n        '(x_1**x_2)'\n\n    \"\"\"\n    stack = []\n    for i in range(len(prefix) - 1, -1, -1):\n        if function_test(prefix[i]):\n            # symbol in unary operator\n            stack.append(prefix[i] + \"(\" + stack.pop() + \")\")\n        elif (operator_test(prefix[i]) or prefix[i] == \"**\") and prefix[i] in [\n            \"+\",\n            \"-\",\n            \"/\",\n            \"^\",\n            \"*\",\n            \"**\",\n        ]:\n            # symbol is binary operator\n            str = \"(\" + stack.pop() + prefix[i] + stack.pop() + \")\"\n            stack.append(str)\n        elif operator_test(prefix[i]):\n            str = prefix[i] + \"(\" + stack.pop() + \",\" + stack.pop() + \")\"\n            stack.append(str)\n        else:\n            # symbol is operand\n            stack.append(prefix[i])\n    return stack.pop()\n</code></pre>"},{"location":"reference/src/equation_tree/util/conversions/#src.equation_tree.util.conversions.standardize_sympy","title":"<code>standardize_sympy(sympy_expr, variable_test=lambda : False, constant_test=lambda : False)</code>","text":"<p>replace all variables and constants with standards</p> Example <p>from sympy import sympify expr = sympify('x + A * cos(z+y)') expr A*cos(y + z) + x</p> <p>is_variable = lambda x : x in ['x', 'y', 'z'] is_constant = lambda x : x in ['A'] standardize_sympy(expr, is_variable, is_constant) c_1*cos(x_2 + x_3) + x_1</p> <p>expr = sympify('x_a+By') expr By + x_a is_variable = lambda x : '_' in x or x in ['y'] is_constant = lambda x : x == 'B' standardize_sympy(expr, is_variable, is_constant) c_1*x_2 + x_1</p> <p>expr = sympify('x ** x') expr xx is_variable = lambda x: x in ['x'] standardize_sympy(expr, is_variable) x_1x_1</p> <p>expr = sympify('sin(Cx) + cos(Cx)') expr sin(Cx) + cos(Cx)</p> <p>is_variable = lambda x: x == 'x' is_constant = lambda x: x == 'C' standardize_sympy(expr, is_variable, is_constant) sin(c_1x_1) + cos(c_1x_1)</p> Source code in <code>src/equation_tree/util/conversions.py</code> <pre><code>def standardize_sympy(\n    sympy_expr, variable_test=lambda _: False, constant_test=lambda _: False\n):\n    \"\"\"\n    replace all variables and constants with standards\n\n    Example:\n        &gt;&gt;&gt; from sympy import sympify\n        &gt;&gt;&gt; expr = sympify('x + A * cos(z+y)')\n        &gt;&gt;&gt; expr\n        A*cos(y + z) + x\n\n        &gt;&gt;&gt; is_variable = lambda x : x in ['x', 'y', 'z']\n        &gt;&gt;&gt; is_constant = lambda x : x in ['A']\n        &gt;&gt;&gt; standardize_sympy(expr, is_variable, is_constant)\n        c_1*cos(x_2 + x_3) + x_1\n\n        &gt;&gt;&gt; expr = sympify('x_a+B*y')\n        &gt;&gt;&gt; expr\n        B*y + x_a\n        &gt;&gt;&gt; is_variable = lambda x : '_' in x or x in ['y']\n        &gt;&gt;&gt; is_constant = lambda x : x == 'B'\n        &gt;&gt;&gt; standardize_sympy(expr, is_variable, is_constant)\n        c_1*x_2 + x_1\n\n        &gt;&gt;&gt; expr = sympify('x ** x')\n        &gt;&gt;&gt; expr\n        x**x\n        &gt;&gt;&gt; is_variable = lambda x: x in ['x']\n        &gt;&gt;&gt; standardize_sympy(expr, is_variable)\n        x_1**x_1\n\n        &gt;&gt;&gt; expr = sympify('sin(C*x) + cos(C*x)')\n        &gt;&gt;&gt; expr\n        sin(C*x) + cos(C*x)\n\n        &gt;&gt;&gt; is_variable = lambda x: x == 'x'\n        &gt;&gt;&gt; is_constant = lambda x: x == 'C'\n        &gt;&gt;&gt; standardize_sympy(expr, is_variable, is_constant)\n        sin(c_1*x_1) + cos(c_1*x_1)\n    \"\"\"\n    variable_count = 0\n    constant_count = 0\n    variables = {}\n    constants = {}\n\n    def replace_symbols(node):\n        nonlocal variable_count, constant_count, variables, constants\n        if variable_test(str(node)):\n            if not str(node) in variables.keys():\n                variable_count += 1\n                new_symbol = symbols(f\"x_{variable_count}\")\n                variables[str(node)] = new_symbol\n            else:\n                new_symbol = variables[str(node)]\n            return new_symbol\n        elif constant_test(str(node)) and not is_numeric(str(node)):\n            if not str(node) in constants.keys():\n                constant_count += 1\n                new_symbol = symbols(f\"c_{constant_count}\")\n                constants[str(node)] = new_symbol\n            else:\n                new_symbol = constants[str(node)]\n            return new_symbol\n        else:\n            return node\n\n    def recursive_replace(node):\n        if node.is_Function or node.is_Add or node.is_Mul or node.is_Pow:\n            return node.func(*[recursive_replace(arg) for arg in node.args])\n        return replace_symbols(node)\n\n    new_expression = recursive_replace(sympy_expr)\n    return new_expression\n</code></pre>"},{"location":"reference/src/equation_tree/util/conversions/#src.equation_tree.util.conversions.unary_minus_to_binary","title":"<code>unary_minus_to_binary(expr, operator_test)</code>","text":"<p>replace unary minus with binary</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; o = lambda x: x in ['+', '-', '*', '/', '^']\n&gt;&gt;&gt; unary_minus_to_binary('-x_1+x_2', o)\n'x_2-x_1'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('x_1-x_2', o)\n'x_1-x_2'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('x_1+(-x_2+x_3)', o)\n'x_1+(x_3-x_2)'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('-tan(x_1-exp(x_2))', o)\n'(0-tan(x_1-exp(x_2)))'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('-x_2', o)\n'(0-x_2)'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('exp(-x_1)*log(x_2)', o)\n'exp((0-x_1))*log(x_2)'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('(c_1 + x_2)*(-c_2 + x_3)', o)\n'(c_1+x_2)*(x_3-c_2)'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('-(c_1 - x_1)^2', o)\n'(0-(c_1-x_1))^2'\n</code></pre> <pre><code>&gt;&gt;&gt; unary_minus_to_binary('-(c_1 - x_2)*(x_1 + x_2)', o)\n'(0-(c_1-x_2))*(x_1+x_2)'\n</code></pre> Source code in <code>src/equation_tree/util/conversions.py</code> <pre><code>def unary_minus_to_binary(expr, operator_test):\n    \"\"\"\n    replace unary minus with binary\n\n    Examples:\n        &gt;&gt;&gt; o = lambda x: x in ['+', '-', '*', '/', '^']\n        &gt;&gt;&gt; unary_minus_to_binary('-x_1+x_2', o)\n        'x_2-x_1'\n\n        &gt;&gt;&gt; unary_minus_to_binary('x_1-x_2', o)\n        'x_1-x_2'\n\n        &gt;&gt;&gt; unary_minus_to_binary('x_1+(-x_2+x_3)', o)\n        'x_1+(x_3-x_2)'\n\n        &gt;&gt;&gt; unary_minus_to_binary('-tan(x_1-exp(x_2))', o)\n        '(0-tan(x_1-exp(x_2)))'\n\n        &gt;&gt;&gt; unary_minus_to_binary('-x_2', o)\n        '(0-x_2)'\n\n        &gt;&gt;&gt; unary_minus_to_binary('exp(-x_1)*log(x_2)', o)\n        'exp((0-x_1))*log(x_2)'\n\n        &gt;&gt;&gt; unary_minus_to_binary('(c_1 + x_2)*(-c_2 + x_3)', o)\n        '(c_1+x_2)*(x_3-c_2)'\n\n        &gt;&gt;&gt; unary_minus_to_binary('-(c_1 - x_1)^2', o)\n        '(0-(c_1-x_1))^2'\n\n        &gt;&gt;&gt; unary_minus_to_binary('-(c_1 - x_2)*(x_1 + x_2)', o)\n        '(0-(c_1-x_2))*(x_1+x_2)'\n\n    \"\"\"\n    _temp = _find_unary(\"-\", str(expr), operator_test)\n    while \"#\" in _temp:\n        _temp = _move_placeholder(_temp, operator_test)\n    _temp = _find_unary(\"+\", _temp, operator_test)\n    _temp = __remove_character_from_string(_temp, \"#\")\n    _temp = _find_unary(\"-\", _temp, operator_test)\n    while \"#\" in _temp:\n        _temp = _replace_with_zero_minus(_temp, operator_test)\n    return _temp\n</code></pre>"},{"location":"reference/src/equation_tree/util/io/","title":"Io","text":""},{"location":"reference/src/equation_tree/util/priors/","title":"Priors","text":""},{"location":"reference/src/equation_tree/util/priors/#src.equation_tree.util.priors.normalized_dict","title":"<code>normalized_dict(d)</code>","text":"<p>Examples:</p> <pre><code>&gt;&gt;&gt; t_d = {'a': 1, 'b': 3}\n&gt;&gt;&gt; t_d = normalized_dict(t_d)\n&gt;&gt;&gt; t_d\n{'a': 0.25, 'b': 0.75}\n&gt;&gt;&gt; t_d = {'c': 0, 'd': 0}\n&gt;&gt;&gt; t_d = normalized_dict(t_d)\n&gt;&gt;&gt; t_d\n{'c': 0, 'd': 0}\n</code></pre> Source code in <code>src/equation_tree/util/priors.py</code> <pre><code>def normalized_dict(d):\n    \"\"\"\n    Examples:\n        &gt;&gt;&gt; t_d = {'a': 1, 'b': 3}\n        &gt;&gt;&gt; t_d = normalized_dict(t_d)\n        &gt;&gt;&gt; t_d\n        {'a': 0.25, 'b': 0.75}\n        &gt;&gt;&gt; t_d = {'c': 0, 'd': 0}\n        &gt;&gt;&gt; t_d = normalized_dict(t_d)\n        &gt;&gt;&gt; t_d\n        {'c': 0, 'd': 0}\n    \"\"\"\n    n = sum(d.values())\n    if n == 0:\n        return d\n    else:\n        return {key: value / n for key, value in d.items()}\n</code></pre>"},{"location":"reference/src/equation_tree/util/priors/#src.equation_tree.util.priors.set_priors","title":"<code>set_priors(priors=None, space=None)</code>","text":"<p>Utility function to set priors without setting all probabilities of the space</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; default_priors = set_priors(space=['a', 'b', 'c', 'd'])\n&gt;&gt;&gt; default_priors\n{'a': 0.25, 'b': 0.25, 'c': 0.25, 'd': 0.25}\n</code></pre> <pre><code>&gt;&gt;&gt; custom_priors_full = set_priors({'a' : .3, 'b': .7}, ['a', 'b'])\n&gt;&gt;&gt; custom_priors_full\n{'a': 0.3, 'b': 0.7}\n</code></pre> <pre><code>&gt;&gt;&gt; custom_priors_partial = set_priors({'a' : .5}, ['a', 'b', 'c'])\n&gt;&gt;&gt; custom_priors_partial\n{'a': 0.5, 'b': 0.25, 'c': 0.25}\n</code></pre> Source code in <code>src/equation_tree/util/priors.py</code> <pre><code>def set_priors(priors=None, space=None):\n    \"\"\"\n    Utility function to set priors without setting all probabilities of the space\n\n    Examples:\n        &gt;&gt;&gt; default_priors = set_priors(space=['a', 'b', 'c', 'd'])\n        &gt;&gt;&gt; default_priors\n        {'a': 0.25, 'b': 0.25, 'c': 0.25, 'd': 0.25}\n\n        &gt;&gt;&gt; custom_priors_full = set_priors({'a' : .3, 'b': .7}, ['a', 'b'])\n        &gt;&gt;&gt; custom_priors_full\n        {'a': 0.3, 'b': 0.7}\n\n        &gt;&gt;&gt; custom_priors_partial = set_priors({'a' : .5}, ['a', 'b', 'c'])\n        &gt;&gt;&gt; custom_priors_partial\n        {'a': 0.5, 'b': 0.25, 'c': 0.25}\n    \"\"\"\n    if space is None:\n        space = []\n    if priors is None:\n        priors = {}\n\n    n = len(space)\n    default_prior = 1 / n\n\n    # Set all to default to begin with\n    _priors = {el: default_prior for el in space}\n\n    # If the user provides priors\n    if priors:\n        if not set(priors.keys()).issubset(set(space)):\n            raise Exception(f\"Priors {priors} are not subset of space {space}\")\n        total_custom_prior = sum(math.floor(p * 100) / 100 for p in (priors.values()))\n        if total_custom_prior &gt; 1:\n            raise ValueError(f\"Sum of custom priors {priors} is greater than 1\")\n\n        # Update the priors dict with custom values\n        for key, value in priors.items():\n            _priors[key] = value\n\n        # Adjust the other priors\n        remaining_probability = 1 - total_custom_prior\n        num_unset_possibilities = n - len(priors)\n        for key in _priors:\n            if key not in priors:\n                _priors[key] = remaining_probability / num_unset_possibilities\n    return _normalize(_priors)\n</code></pre>"},{"location":"reference/src/equation_tree/util/type_check/","title":"Type check","text":""},{"location":"reference/src/equation_tree/util/type_check/#src.equation_tree.util.type_check.check_functions","title":"<code>check_functions(expression, function_test)</code>","text":"Example <p>from sympy import sympify expr = sympify('sin(x)') check_functions(expr, lambda x: x in ['sin']) True</p> <p>expr = sympify('x + y') check_functions(expr, lambda x: x in ['sin']) True</p> <p>expr = sympify('sin(x) + cos(y)') check_functions(expr, lambda x: x in ['sin', 'cos']) True</p> <p>check_functions(expr, lambda x: x in ['sin']) False</p> Source code in <code>src/equation_tree/util/type_check.py</code> <pre><code>def check_functions(expression, function_test):\n    \"\"\"\n    Example:\n        &gt;&gt;&gt; from sympy import sympify\n        &gt;&gt;&gt; expr = sympify('sin(x)')\n        &gt;&gt;&gt; check_functions(expr, lambda x: x in ['sin'])\n        True\n\n        &gt;&gt;&gt; expr = sympify('x + y')\n        &gt;&gt;&gt; check_functions(expr, lambda x: x in ['sin'])\n        True\n\n        &gt;&gt;&gt; expr = sympify('sin(x) + cos(y)')\n        &gt;&gt;&gt; check_functions(expr, lambda x: x in ['sin', 'cos'])\n        True\n\n        &gt;&gt;&gt; check_functions(expr, lambda x: x in ['sin'])\n        False\n\n    \"\"\"\n\n    def apply_test(node):\n        if isinstance(node, Function):\n            return function_test(str(node.func).lower()) or str(node.func) == \"re\"\n        elif isinstance(node, (Add, Mul, Pow)):\n            return all(apply_test(arg) or str(node.func) == \"re\" for arg in node.args)\n        return True\n\n    return apply_test(expression)\n</code></pre>"},{"location":"reference/src/equation_tree/util/type_check/#src.equation_tree.util.type_check.is_constant_formatted","title":"<code>is_constant_formatted(s)</code>","text":"<p>Tests weather the input is in standard format for a constant</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; is_constant_formatted('c_4')\nTrue\n&gt;&gt;&gt; is_constant_formatted('c_42')\nTrue\n&gt;&gt;&gt; is_constant_formatted('c_a')\nFalse\n&gt;&gt;&gt; is_constant_formatted('abc')\nFalse\n&gt;&gt;&gt; is_constant_formatted('x_3')\nFalse\n</code></pre> Source code in <code>src/equation_tree/util/type_check.py</code> <pre><code>def is_constant_formatted(s: str):\n    \"\"\"\n    Tests weather the input is in standard format for a constant\n\n    Examples:\n        &gt;&gt;&gt; is_constant_formatted('c_4')\n        True\n        &gt;&gt;&gt; is_constant_formatted('c_42')\n        True\n        &gt;&gt;&gt; is_constant_formatted('c_a')\n        False\n        &gt;&gt;&gt; is_constant_formatted('abc')\n        False\n        &gt;&gt;&gt; is_constant_formatted('x_3')\n        False\n    \"\"\"\n    pattern = r\"^c_\\d+$\"\n    return re.match(pattern, s) is not None\n</code></pre>"},{"location":"reference/src/equation_tree/util/type_check/#src.equation_tree.util.type_check.is_numeric","title":"<code>is_numeric(s)</code>","text":"<p>Tests weather the input is a number</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; is_numeric('0')\nTrue\n&gt;&gt;&gt; is_numeric('10')\nTrue\n&gt;&gt;&gt; is_numeric('hallo')\nFalse\n&gt;&gt;&gt; is_numeric('.1')\nTrue\n&gt;&gt;&gt; is_numeric('+.1')\nFalse\n</code></pre> Source code in <code>src/equation_tree/util/type_check.py</code> <pre><code>def is_numeric(s):\n    \"\"\"\n    Tests weather the input is a number\n\n    Examples:\n        &gt;&gt;&gt; is_numeric('0')\n        True\n        &gt;&gt;&gt; is_numeric('10')\n        True\n        &gt;&gt;&gt; is_numeric('hallo')\n        False\n        &gt;&gt;&gt; is_numeric('.1')\n        True\n        &gt;&gt;&gt; is_numeric('+.1')\n        False\n\n    \"\"\"\n    if isinstance(s, str) and (not s[0].isnumeric() and s[0] != \".\"):\n        return False\n    try:\n        float(s)\n        return True\n    except ValueError:\n        return False\n</code></pre>"},{"location":"reference/src/equation_tree/util/type_check/#src.equation_tree.util.type_check.is_variable_formatted","title":"<code>is_variable_formatted(s)</code>","text":"<p>Tests weather the input is in standard format for a variable</p> <p>Examples:</p> <pre><code>&gt;&gt;&gt; is_variable_formatted('x_1')\nTrue\n&gt;&gt;&gt; is_variable_formatted('x_42')\nTrue\n&gt;&gt;&gt; is_variable_formatted('x_a')\nFalse\n&gt;&gt;&gt; is_variable_formatted('abc')\nFalse\n&gt;&gt;&gt; is_variable_formatted('c_3')\nFalse\n</code></pre> Source code in <code>src/equation_tree/util/type_check.py</code> <pre><code>def is_variable_formatted(s: str):\n    \"\"\"\n    Tests weather the input is in standard format for a variable\n\n    Examples:\n        &gt;&gt;&gt; is_variable_formatted('x_1')\n        True\n        &gt;&gt;&gt; is_variable_formatted('x_42')\n        True\n        &gt;&gt;&gt; is_variable_formatted('x_a')\n        False\n        &gt;&gt;&gt; is_variable_formatted('abc')\n        False\n        &gt;&gt;&gt; is_variable_formatted('c_3')\n        False\n    \"\"\"\n    pattern = r\"^x_\\d+$\"\n    return re.match(pattern, s) is not None\n</code></pre>"},{"location":"reference/src/equation_tree/util/type_check/#src.equation_tree.util.type_check.parse_string_list_int","title":"<code>parse_string_list_int(lst)</code>","text":"Example <p>a = '[1, 2, 3, 4]' parse_string_list_int(a) [1, 2, 3, 4] b = '[10, 2, 3]' parse_string_list_int(b) [10, 2, 3]</p> Source code in <code>src/equation_tree/util/type_check.py</code> <pre><code>def parse_string_list_int(lst):\n    \"\"\"\n    Example:\n        &gt;&gt;&gt; a = '[1, 2, 3, 4]'\n        &gt;&gt;&gt; parse_string_list_int(a)\n        [1, 2, 3, 4]\n        &gt;&gt;&gt; b = '[10, 2, 3]'\n        &gt;&gt;&gt; parse_string_list_int(b)\n        [10, 2, 3]\n    \"\"\"\n    res = []\n    i = 0\n    while i &lt; len(lst) - 1:\n        start = i\n        end = i\n        while is_numeric(lst[i]):\n            end += 1\n            i += 1\n        if start != end:\n            i = end\n            res.append(int(lst[start:end]))\n        i += 1\n    return res\n</code></pre>"},{"location":"user-guide/equation-formats/","title":"Equation Formats","text":"<p>Equations can be represented in multiple formats. Depending on the use case, some of these formats might be more useful than others. While the underlying format of the Equation Tree is a incomplete binary tree, it supports multiple formats as initialisation and output.</p>"},{"location":"user-guide/equation-formats/#tree-representation","title":"Tree Representation","text":""},{"location":"user-guide/equation-formats/#tree-structure","title":"Tree Structure","text":"<p>coming soon</p>"},{"location":"user-guide/equation-formats/#string-representation","title":"String Representation","text":"<p>coming soon</p>"},{"location":"user-guide/equation-formats/#prefix-notation","title":"Prefix Notation","text":"<p>coming soon</p>"},{"location":"user-guide/sampling/","title":"Sampling Method","text":"<p>coming soon</p>"}]}
\ No newline at end of file
diff --git a/sitemap.xml b/sitemap.xml
index cb40a77..b3e3422 100644
--- a/sitemap.xml
+++ b/sitemap.xml
@@ -5,11 +5,6 @@
          <lastmod>2023-11-02</lastmod>
          <changefreq>daily</changefreq>
     </url>
-    <url>
-         <loc>https://autoresearch.github.io/equation-tree/Additional%20Example/</loc>
-         <lastmod>2023-11-02</lastmod>
-         <changefreq>daily</changefreq>
-    </url>
     <url>
          <loc>https://autoresearch.github.io/equation-tree/Basic%20Usage/</loc>
          <lastmod>2023-11-02</lastmod>
@@ -95,4 +90,14 @@
          <lastmod>2023-11-02</lastmod>
          <changefreq>daily</changefreq>
     </url>
+    <url>
+         <loc>https://autoresearch.github.io/equation-tree/user-guide/equation-formats/</loc>
+         <lastmod>2023-11-02</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://autoresearch.github.io/equation-tree/user-guide/sampling/</loc>
+         <lastmod>2023-11-02</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
 </urlset>
\ No newline at end of file
diff --git a/sitemap.xml.gz b/sitemap.xml.gz
index c2a45deec7ea9e8eb5841054884714cf43ee4fe7..12d62dac048b563f364940926055c3a06950e05b 100644
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diff --git a/user-guide/equation-formats/equation-formats.md b/user-guide/equation-formats/equation-formats.md
new file mode 100644
index 0000000..5b71620
--- /dev/null
+++ b/user-guide/equation-formats/equation-formats.md
@@ -0,0 +1,16 @@
+# Equation Formats
+Equations can be represented in multiple formats. Depending on the use case, some of these formats might be more useful than others. While the underlying format of the Equation Tree is a incomplete binary tree, it supports multiple formats as initialisation and output.
+
+## Tree Representation
+### Tree Structure 
+coming soon
+
+
+## String Representation
+coming soon
+
+## Prefix Notation
+coming soon
+
+
+
diff --git a/user-guide/equation-formats/index.html b/user-guide/equation-formats/index.html
new file mode 100644
index 0000000..79b7537
--- /dev/null
+++ b/user-guide/equation-formats/index.html
@@ -0,0 +1,1136 @@
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+    String Representation
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+            <a href="../../reference/src/equation_tree/" class="md-nav__link ">
+              
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+  <span class="md-ellipsis">
+    Equation tree
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+          <label class="md-nav__title" for="__nav_5_1_1">
+            <span class="md-nav__icon md-icon"></span>
+            Equation tree
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../reference/src/equation_tree/analysis/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    Analysis
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+              
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+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../reference/src/equation_tree/defaults/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    Defaults
+  </span>
+  
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+  
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+              
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+  
+  
+    <li class="md-nav__item">
+      <a href="../../reference/src/equation_tree/prior/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
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+              
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+    <li class="md-nav__item">
+      <a href="../../reference/src/equation_tree/sample/" class="md-nav__link">
+        
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+              
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+    <li class="md-nav__item">
+      <a href="../../reference/src/equation_tree/tree/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    Tree
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+  
+  
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+      <a href="../../reference/src/equation_tree/src/sample_tree_structure/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    Sample tree structure
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../reference/src/equation_tree/src/tree_node/" class="md-nav__link">
+        
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+  
+
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+    </li>
+  
+
+              
+            
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+        </nav>
+      
+    </li>
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+            <a href="../../reference/src/equation_tree/util/" class="md-nav__link ">
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+  <span class="md-ellipsis">
+    Util
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+            
+              
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+    <li class="md-nav__item">
+      <a href="../../reference/src/equation_tree/util/conversions/" class="md-nav__link">
+        
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+    Conversions
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+  
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+              
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+                
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+  
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+    <li class="md-nav__item">
+      <a href="../../reference/src/equation_tree/util/io/" class="md-nav__link">
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+              
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+                
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+  
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+      <a href="../../reference/src/equation_tree/util/priors/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    Priors
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../reference/src/equation_tree/util/type_check/" class="md-nav__link">
+        
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+    Type check
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+      
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+  
+
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+  
+
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+</nav>
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+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="Table of contents">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      Table of contents
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#tree-representation" class="md-nav__link">
+    Tree Representation
+  </a>
+  
+    <nav class="md-nav" aria-label="Tree Representation">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#tree-structure" class="md-nav__link">
+    Tree Structure
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#string-representation" class="md-nav__link">
+    String Representation
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
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+    Prefix Notation
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+</li>
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+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+
+
+                  
+
+  
+  
+
+
+<h1 id="equation-formats">Equation Formats</h1>
+<p>Equations can be represented in multiple formats. Depending on the use case, some of these formats might be more useful than others. While the underlying format of the Equation Tree is a incomplete binary tree, it supports multiple formats as initialisation and output.</p>
+<h2 id="tree-representation">Tree Representation</h2>
+<h3 id="tree-structure">Tree Structure</h3>
+<p>coming soon</p>
+<h2 id="string-representation">String Representation</h2>
+<p>coming soon</p>
+<h2 id="prefix-notation">Prefix Notation</h2>
+<p>coming soon</p>
+
+
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diff --git a/user-guide/sampling/index.html b/user-guide/sampling/index.html
new file mode 100644
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+    <script id="__config" type="application/json">{"base": "../..", "features": [], "search": "../../assets/javascripts/workers/search.f886a092.min.js", "translations": {"clipboard.copied": "Copied to clipboard", "clipboard.copy": "Copy to clipboard", "search.result.more.one": "1 more on this page", "search.result.more.other": "# more on this page", "search.result.none": "No matching documents", "search.result.one": "1 matching document", "search.result.other": "# matching documents", "search.result.placeholder": "Type to start searching", "search.result.term.missing": "Missing", "select.version": "Select version"}}</script>
+    
+    
+      <script src="../../assets/javascripts/bundle.aecac24b.min.js"></script>
+      
+        <script src="../../javascripts/mathjax.js"></script>
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+        <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
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+        <script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>
+      
+    
+  </body>
+</html>
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diff --git a/user-guide/sampling/sampling.md b/user-guide/sampling/sampling.md
new file mode 100644
index 0000000..faabcad
--- /dev/null
+++ b/user-guide/sampling/sampling.md
@@ -0,0 +1,2 @@
+# Sampling Method
+coming soon
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