diff --git a/README.md b/README.md
index f1fd935..84cb6ba 100644
--- a/README.md
+++ b/README.md
@@ -1,16 +1,25 @@
-# Quickstart Guide
+# Equation Tree
 
-You will need:
+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:
 
-- `python` 3.8 or greater: [https://www.python.org/downloads/](https://www.python.org/downloads/)
+- Equation sampling (including priors)
+- Feature Extraction from equation distributions
+- Distance metrics between equations
 
 
-```shell
-pip install -U equation-tree
-```
+## Getting Started
 
+Check out the documentation at 
+[https://autoresearch.github.io/equation-tree](https://autoresearch.github.io/equation-tree).
 
-Check your installation by running:
-```shell
-python -c "from equation_tree import EquationTree"
-```
+## About
+
+This project is in active development by
+the <a href="https://musslick.github.io/AER_website/Research.html">Autonomous Empirical Research
+Group</a>
+(package developer: <a href="https://younesstrittmatter.github.io/">Younes Strittmatter</a>,
+PI: <a href="https://smusslick.com/">Sebastian Musslick</a>. 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.
\ No newline at end of file
diff --git a/dev/burn.py b/dev/burn.py
new file mode 100644
index 0000000..7aea8fe
--- /dev/null
+++ b/dev/burn.py
@@ -0,0 +1,65 @@
+from equation_tree.sample import burn
+from equation_tree.defaults import DEFAULT_PRIOR
+
+prior_0 = {
+    '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}
+}
+
+
+
+prior_1 = {
+    '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}
+        }
+    },
+}
+
+# import random
+for _ in range(1, 5):
+    burn(DEFAULT_PRIOR,
+         _,
+         "../src/equation_tree/data/_hashed_probabilities.json",
+         10_000,
+         0.5,
+         )
+    burn(
+        prior_0,
+        2,
+        "../src/equation_tree/data/_hashed_probabilities.json",
+        10_000,
+        0.5,
+    )
+    burn(
+        prior_1,
+        2,
+        "../src/equation_tree/data/_hashed_probabilities.json",
+        10_000,
+        0.5,
+    )
\ No newline at end of file
diff --git a/docs/Additional Example.ipynb b/docs/Additional Example.ipynb
deleted file mode 100644
index b211083..0000000
--- a/docs/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": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 2
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython2",
-   "version": "2.7.6"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 0
-}
diff --git a/docs/Basic Usage.ipynb b/docs/Basic Usage.ipynb
index 1881b81..adc205b 100644
--- a/docs/Basic Usage.ipynb	
+++ b/docs/Basic Usage.ipynb	
@@ -7,37 +7,662 @@
     "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"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "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",
+      "Requirement already satisfied: tqdm in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from equation_tree) (4.66.1)\r\n",
+      "Requirement already satisfied: mpmath>=0.19 in /Users/younesstrittmatter/Documents/GitHub/AutoRA/equation-tree/venv/lib/python3.11/site-packages (from sympy->equation_tree) (1.3.0)\r\n",
+      "\r\n",
+      "\u001B[1m[\u001B[0m\u001B[34;49mnotice\u001B[0m\u001B[1;39;49m]\u001B[0m\u001B[39;49m A new release of pip is available: \u001B[0m\u001B[31;49m23.1.2\u001B[0m\u001B[39;49m -> \u001B[0m\u001B[32;49m23.3.1\u001B[0m\r\n",
+      "\u001B[1m[\u001B[0m\u001B[34;49mnotice\u001B[0m\u001B[1;39;49m]\u001B[0m\u001B[39;49m To update, run: \u001B[0m\u001B[32;49mpip install --upgrade pip\u001B[0m\r\n"
+     ]
+    }
+   ],
    "source": [
-    "from equation_tree import"
+    "import random\n",
+    "!pip install equation_tree"
    ]
   },
   {
    "cell_type": "markdown",
    "source": [
-    "Include inline mathematics like this: $4 < 5$\n",
+    "## Basic Functionality\n",
+    "\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",
+    "# 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",
+    "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",
+    "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",
-    "Include block mathematics like this (don't forget the empty lines above and below the block):\n",
+    "### Evaluating Equations\n",
     "\n",
-    "$$  \n",
-    "y + 1 = 4 \n",
-    "$$\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",
-    "... or this:\n",
+    "### Equation Complexity\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}"
+    "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
@@ -45,8 +670,108 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
-   "source": []
+   "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
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "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/docs/img/logo.png b/docs/img/logo.png
new file mode 100644
index 0000000..f4bd83c
Binary files /dev/null and b/docs/img/logo.png differ
diff --git a/docs/index.md b/docs/index.md
index d616bfa..ac76ca0 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -1,24 +1,31 @@
-# equation-tree
+# Equation Tree
 
-Explain what your contribution is doing here
+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:
 
-You can include inline mathematics by wrapping LaTeX formatted math in `$` symbols: `$(3 < 4)$` will render as:  $(3 < 4)$
+- Equation sampling (including priors)
+- Feature Extraction from equation distributions
+- Distance metrics between equations
 
-To include block mathematics wrap the expression with double `$$`:
+## Equation Sampling
 
-```
-$$
-E(\mathbf{v}, \mathbf{h}) = -\sum_{i,j}w_{ij}v_i h_j - \sum_i b_i v_i - \sum_j c_j h_j
-$$
-```
+coming soon
 
-Will render as:
+## Feature Extraction
 
-$$
-E(\mathbf{v}, \mathbf{h}) = -\sum_{i,j}w_{ij}v_i h_j - \sum_i b_i v_i - \sum_j c_j h_j
-$$
+coming soon
 
+## Distance Metrics
 
-See more information on writing mathematical expressions [here](https://docs.github.com/en/get-started/writing-on-github/working-with-advanced-formatting/writing-mathematical-expressions). 
+coming soon
 
+## About
 
+This project is in active development by
+the <a href="https://musslick.github.io/AER_website/Research.html">Autonomous Empirical Research
+Group</a>
+(package developer: <a href="https://younesstrittmatter.github.io/">Younes Strittmatter</a>,
+PI: <a href="https://smusslick.com/">Sebastian Musslick</a>. 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.
\ No newline at end of file
diff --git a/docs/quickstart.md b/docs/quickstart.md
index 8771d5d..ac62c8f 100644
--- a/docs/quickstart.md
+++ b/docs/quickstart.md
@@ -7,11 +7,10 @@ You will need:
 
 ```shell
 pip install -U equation-tree
-"]
 ```
 
 
 Check your installation by running:
 ```shell
-python -c "from autora.equation_tree.equation_tree import Example"
-```
+python -c "from equation_tree import EquationTree"
+```
\ No newline at end of file
diff --git a/docs/user-guide/equation-formats.md b/docs/user-guide/equation-formats.md
new file mode 100644
index 0000000..5b71620
--- /dev/null
+++ b/docs/user-guide/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/docs/user-guide/sampling.md b/docs/user-guide/sampling.md
new file mode 100644
index 0000000..faabcad
--- /dev/null
+++ b/docs/user-guide/sampling.md
@@ -0,0 +1,2 @@
+# Sampling Method
+coming soon
\ No newline at end of file
diff --git a/mkdocs.yml b/mkdocs.yml
index ac0dd82..430b315 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -1,12 +1,86 @@
-# yaml-language-server: $schema=https://squidfunk.github.io/mkdocs-material/schema.json
-INHERIT: mkdocs/base.yml  # use the shared AutoRA configuration by default
-
-site_name: AutoRA equation-tree
+site_name: AutoRA Equation Tree
 repo_url: 'https://github.com/AutoResearch/equation-tree'
 
+site_url: 'https://autoresearch.github.io/equation-tree/'
+edit_uri: 'blob/main/docs/'
+
+extra:
+  colab_base_url: 'https://colab.research.google.com/github/AutoResearch/equation-tree/blob/gh-pages/'
+  social:
+    - icon: fontawesome/brands/github-alt
+      link: https://github.com/AutoResearch
+
 nav:
-- Home: 'index.md'
-- Quickstart: 'quickstart.md'
-- Examples:
-  - Basic Usage: 'Basic Usage.ipynb'
-  - Additional Example: 'Additional Example.ipynb'
+  - Introduction: 'index.md'
+  - Quickstart: 'quickstart.md'
+  - User Guide:
+      - Sampling: 'user-guide/sampling.md'
+      - Equation Formats: 'user-guide/equation-formats.md'
+  - Tutorials:
+      - Equation Sampling: Equation Sampling.ipynb
+  - Code Reference: reference/
+
+theme:
+  name: material
+  features:
+
+  language: en
+  logo: img/logo.png
+  palette:
+    # Palette toggle for light mode
+    - scheme: default
+      primary: black
+      toggle:
+        icon: material/brightness-7
+        name: Switch to dark mode
+    - scheme: slate
+      primary: black
+      toggle:
+        icon: material/brightness-4
+        name: Switch to light mode
+  custom_dir: mkdocs/overrides
+
+
+
+
+
+
+watch:
+  - src/
+
+plugins:
+  - search
+  - gen-files:
+      scripts:
+        - mkdocs/gen_ref_pages.py
+  - literate-nav:
+      nav_file: SUMMARY/index.html
+  - section-index
+  - mkdocstrings:
+      handlers:
+        python:
+          import:
+            - https://scikit-learn.org/stable/objects.inv
+  - mkdocs-jupyter: # required to convert Jupyter notebooks
+      include_source: true
+      execute: false
+      ignore_h1_titles: true
+hooks:
+  - mkdocs/hooks.py
+
+markdown_extensions:
+  admonition: { }
+  pymdownx.details: { }
+  pymdownx.superfences: { }
+  pymdownx.arithmatex: # required for equation display
+    generic: true
+  pymdownx.snippets: { }
+  pymdownx.tabbed:
+    alternate_style: true
+
+extra_javascript: [
+  # requirements for pymdownx.arithmetex:
+  "javascripts/mathjax.js",
+  "https://polyfill.io/v3/polyfill.min.js?features=es6",
+  "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"
+]
\ No newline at end of file
diff --git a/mkdocs/base.yml b/mkdocs/base.yml
deleted file mode 100644
index 8676be1..0000000
--- a/mkdocs/base.yml
+++ /dev/null
@@ -1,25 +0,0 @@
-# yaml-language-server: $schema=https://squidfunk.github.io/mkdocs-material/schema.json
-# Shared configuration matching the rest of the AutoRA documentation.
-
-theme:
-  name: material
-
-plugins:
-  mkdocs-jupyter:  # required to convert Jupyter notebooks
-    include_source: true
-    execute: false
-    ignore_h1_titles: true
-
-markdown_extensions:
-  admonition: {}
-  pymdownx.details: {}
-  pymdownx.superfences: {}
-  pymdownx.arithmatex: # required for equation display
-    generic: true
-
-extra_javascript: [ 
-  # requirements for pymdownx.arithmetex:
-  "javascripts/mathjax.js",                                 
-  "https://polyfill.io/v3/polyfill.min.js?features=es6", 
-  "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"
-]
\ No newline at end of file
diff --git a/mkdocs/gen_ref_pages.py b/mkdocs/gen_ref_pages.py
new file mode 100644
index 0000000..68069d2
--- /dev/null
+++ b/mkdocs/gen_ref_pages.py
@@ -0,0 +1,39 @@
+"""Generate the code reference pages and navigation."""
+
+from pathlib import Path
+from typing import List
+
+import mkdocs_gen_files
+
+nav = mkdocs_gen_files.Nav()
+
+source_paths = sorted(Path("./src/equation_tree/").rglob("*.py"))
+
+
+special_paths: List[Path] = []  # [Path("./docs/docstrings.py")]
+
+for path in source_paths:
+    module_path = path.relative_to(".").with_suffix("")
+    doc_path = path.relative_to(".").with_suffix(".md")
+
+    full_doc_path = Path("reference", doc_path)
+
+
+    parts = tuple(module_path.parts)
+
+    if parts[-1] == "__init__":
+        parts = parts[:-1]
+        doc_path = doc_path.with_name("index.md")
+        full_doc_path = full_doc_path.with_name("index.md")
+    elif parts[-1] == "__main__":
+        continue
+
+    nav[parts] = doc_path.as_posix()
+
+    with mkdocs_gen_files.open(full_doc_path, "w") as fd:
+        ident = ".".join(parts)
+        fd.write(f"::: {ident}")
+    mkdocs_gen_files.set_edit_path(full_doc_path, path)
+
+with mkdocs_gen_files.open("reference/SUMMARY.md", "w") as nav_file:
+    nav_file.writelines(nav.build_literate_nav())
diff --git a/mkdocs/hooks.py b/mkdocs/hooks.py
new file mode 100644
index 0000000..9074dfe
--- /dev/null
+++ b/mkdocs/hooks.py
@@ -0,0 +1,12 @@
+import os
+from urllib.parse import quote
+
+
+def basename(path):
+    return os.path.basename(path)
+
+
+def on_env(env, config, files, **kwargs):
+    env.filters["basename"] = basename
+    env.filters["quote"] = quote
+    return env
\ No newline at end of file
diff --git a/mkdocs/overrides/main.html b/mkdocs/overrides/main.html
new file mode 100644
index 0000000..3a7b8a9
--- /dev/null
+++ b/mkdocs/overrides/main.html
@@ -0,0 +1,15 @@
+{% extends "base.html" %}
+
+{% block content %}
+{% if page.nb_url %}
+    <a href="{{ page.canonical_url }}{{ page.file.src_uri | basename | quote }}" title="Download Notebook"
+       class="md-content__button md-icon">
+        {% include ".icons/material/download.svg" %}
+    </a>
+    <a href="{{ config.extra.colab_base_url }}{{ page.url }}{{ page.file.src_uri | basename | quote }}"
+       title="Open Notebook in Google Colab" class="md-content__button md-icon">
+        <img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/>
+    </a>
+{% endif %}
+{{ super() }}
+{% endblock content %}
\ No newline at end of file
diff --git a/pyproject.toml b/pyproject.toml
index ce24738..cdacef4 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -21,6 +21,17 @@ dependencies = [
 dev = [
 ]
 
+docs = [
+    "mkdocs-material",
+    "mkdocs-gen-files",
+    "mkdocs-literate-nav",
+    "mkdocs-section-index",
+    "mkdocs-multirepo-plugin",
+    "mkdocstrings-python",
+    "mkdocs-jupyter",
+    "pymdown-extensions",
+]
+
 [project.urls]
 homepage = "http://www.empiricalresearch.ai"
 repository = "https://github.com/AutoResearch/equation-tree"
diff --git a/src/equation_tree/__init__.py b/src/equation_tree/__init__.py
index eebaae9..2de8411 100644
--- a/src/equation_tree/__init__.py
+++ b/src/equation_tree/__init__.py
@@ -1,4 +1,4 @@
 from equation_tree.sample import burn, sample
-from equation_tree.tree import EquationTree
+from equation_tree.tree import EquationTree, instantiate_constants
 
-__all__ = ["EquationTree", "sample", "burn"]
+__all__ = ["EquationTree", "sample", "burn", "instantiate_constants"]
diff --git a/src/equation_tree/data/_hashed_probabilities.json b/src/equation_tree/data/_hashed_probabilities.json
index 243a582..20dd498 100644
--- a/src/equation_tree/data/_hashed_probabilities.json
+++ b/src/equation_tree/data/_hashed_probabilities.json
@@ -1 +1 @@
-{"{'features': {'constants': 0.4056818181818182, 'variables': 0.5943181818181819}, 'functions': {'cos': 0.24, 'exp': 0.13333333333333333, 'log': 0.013333333333333334, 'sin': 0.21333333333333335, 'sqrt': 0.38666666666666666, 'tan': 0.013333333333333334}, 'max_num_variables': 100, 'operators': {'*': 0.4480946123521682, '+': 0.07621550591327202, '-': 0.08409986859395532, '/': 0.19185282522996058, '^': 0.19973718791064388}, 'structures': {'[0, 1, 1, 2, 2, 3, 3]': 0.008403361344537815, '[0, 1, 1, 2, 2, 3, 4, 4, 3, 4]': 0.008403361344537815, '[0, 1, 1, 2, 2]': 0.008403361344537815, '[0, 1, 1, 2, 3, 3, 2, 3, 3]': 0.01680672268907563, '[0, 1, 1, 2, 3, 3, 2]': 0.008403361344537815, '[0, 1, 1, 2, 3, 3, 4, 2]': 0.008403361344537815, '[0, 1, 1, 2, 3, 3, 4, 5, 5, 4, 5, 5]': 0.01680672268907563, '[0, 1, 1, 2, 3, 3, 4, 5, 6, 6, 4, 2, 3, 4, 4]': 0.008403361344537815, '[0, 1, 1, 2, 3, 4, 4, 3, 2, 3, 3]': 0.008403361344537815, '[0, 1, 1, 2, 3, 4, 4, 3, 2, 3, 4, 5, 6, 6, 5, 6, 7, 8, 8, 7, 6, 7, 4, 5, 5]': 0.008403361344537815, '[0, 1, 1, 2, 3, 4, 4, 3, 2]': 0.01680672268907563, '[0, 1, 1, 2, 3, 4, 4, 5, 5, 6, 3, 4, 5, 5, 4, 2]': 0.008403361344537815, '[0, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 3, 4, 5, 5, 4, 3]': 0.008403361344537815, '[0, 1, 1, 2, 3, 4, 5, 5, 4, 5, 5, 2, 3, 4, 5, 6, 6, 5, 4, 5, 5]': 0.008403361344537815, '[0, 1, 1, 2, 3, 4, 5, 5, 4, 5, 5, 2]': 0.008403361344537815, '[0, 1, 1, 2, 3, 4, 5, 5, 4, 5, 5, 3, 2]': 0.008403361344537815, '[0, 1, 1, 2, 3, 4, 5, 5, 4, 5, 5, 3, 4, 4]': 0.008403361344537815, '[0, 1, 1, 2, 3, 4, 5, 5, 4, 5, 6, 7, 7, 6, 5, 2]': 0.008403361344537815, '[0, 1, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 4, 4]': 0.008403361344537815, '[0, 1, 1]': 0.03361344537815126, '[0, 1, 2, 1, 2, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 7, 6, 7, 7, 3]': 0.008403361344537815, '[0, 1, 2, 2, 1, 2, 2, 3, 3]': 0.008403361344537815, '[0, 1, 2, 2, 1, 2, 2, 3, 4, 4, 3, 4, 4]': 0.008403361344537815, '[0, 1, 2, 2, 1, 2, 2, 3, 4, 4]': 0.008403361344537815, '[0, 1, 2, 2, 1, 2, 2]': 0.04201680672268908, 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0.027777777777777776, '[0, 1, 2, 2, 1]': 0.027777777777777776, '[0, 1, 2, 2, 3, 1]': 0.027777777777777776, '[0, 1, 2, 2, 3, 3]': 0.027777777777777776, '[0, 1, 2, 2, 3, 4]': 0.027777777777777776, '[0, 1, 2, 2, 3]': 0.027777777777777776, '[0, 1, 2, 2]': 0.027777777777777776, '[0, 1, 2, 3, 1, 2]': 0.027777777777777776, '[0, 1, 2, 3, 1]': 0.027777777777777776, '[0, 1, 2, 3, 2, 1]': 0.027777777777777776, '[0, 1, 2, 3, 2, 3]': 0.027777777777777776, '[0, 1, 2, 3, 2]': 0.027777777777777776, '[0, 1, 2, 3, 3, 1]': 0.027777777777777776, '[0, 1, 2, 3, 3, 2]': 0.027777777777777776, '[0, 1, 2, 3, 3, 4]': 0.027777777777777776, '[0, 1, 2, 3, 3]': 0.027777777777777776, '[0, 1, 2, 3, 4, 1]': 0.027777777777777776, '[0, 1, 2, 3, 4, 2]': 0.027777777777777776, '[0, 1, 2, 3, 4, 3]': 0.027777777777777776, '[0, 1, 2, 3, 4, 4]': 0.027777777777777776, '[0, 1, 2, 3, 4, 5]': 0.027777777777777776, '[0, 1, 2, 3, 4]': 0.027777777777777776, '[0, 1, 2, 3]': 0.027777777777777776, '[0, 1, 2]': 0.027777777777777776}}": {"structures": {"[0, 1, 2, 3]": 0.023266666666666665, "[0, 1, 2, 3, 1]": 0.03311666666666666, "[0, 1, 2, 3, 4, 5]": 0.029416666666666664, "[0, 1, 2]": 0.021566666666666665, "[0, 1, 2, 1]": 0.025216666666666665, "[0, 1, 2, 3, 3, 4]": 0.028766666666666663, "[0, 1, 1, 2]": 0.018366666666666663, "[0, 1, 2, 3, 3, 1]": 0.03356666666666666, "[0, 1, 2, 2, 3, 4]": 0.026366666666666663, "[0, 1, 2, 3, 2, 1]": 0.03506666666666666, "[0, 1, 1, 2, 2, 3]": 0.033666666666666664, "[0, 1, 2, 1, 2, 2]": 0.029416666666666664, "[0, 1, 2, 3, 4, 2]": 0.033466666666666665, "[0, 1, 2, 2, 3, 1]": 0.030766666666666664, "[0, 1, 2, 3, 2, 3]": 0.03256666666666666, "[0, 1, 1, 2, 2]": 0.026016666666666664, "[0, 1, 2, 2]": 0.014916666666666665, "[0, 1, 2, 3, 1, 2]": 0.034216666666666666, "[0, 1, 2, 3, 4, 1]": 0.032516666666666666, "[0, 1, 1, 2, 3]": 0.026966666666666667, "[0, 1, 2, 1, 2, 3]": 0.033666666666666664, "[0, 1, 2, 3, 3, 2]": 0.029266666666666663, "[0, 1, 1]": 0.012866666666666665, "[0, 1, 2, 3, 3]": 0.021866666666666663, "[0, 1, 2, 3, 2]": 0.030616666666666664, "[0, 1, 2, 3, 4, 3]": 0.032016666666666665, "[0, 1, 2, 1, 2]": 0.03281666666666666, "[0, 1, 2, 2, 3]": 0.026566666666666662, "[0, 1, 2, 3, 4]": 0.028466666666666664, "[0, 1, 2, 2, 1]": 0.026866666666666664, "[0, 1, 1, 2, 3, 3]": 0.021866666666666663, "[0, 1, 1, 2, 3, 2]": 0.031466666666666664, "[0, 1, 1, 2, 3, 4]": 0.028766666666666663, "[0, 1, 2, 2, 3, 3]": 0.024866666666666665, "[0, 1, 2, 3, 4, 4]": 0.023266666666666665, "[0, 1, 2, 2, 1, 2]": 0.025516666666666663}, "functions": {"log": 0.11468674789410348, "exp": 0.11322014139590852, "sqrt": 0.11070998796630566, "abs": 0.11206377858002406, "acos": 0.1089895457280385, "sin": 0.11082280385078218, "cos": 0.1097510529482551, "asin": 0.11133047533092658, "tan": 0.10842546630565583}, "operators": {"^": 0.11614890979362648, "max": 0.15966601035513744, "*": 0.13720557135564793, "-": 0.13894965847492646, "/": 0.14490507790660928, "min": 0.159878703906269, "+": 0.14324606820778335}, "features": {"constants": 0.5949710398087709, "variables": 0.4050289601912292}}}
\ No newline at end of file
diff --git a/src/equation_tree/defaults.py b/src/equation_tree/defaults.py
index dd8fc48..a2a9237 100644
--- a/src/equation_tree/defaults.py
+++ b/src/equation_tree/defaults.py
@@ -11,9 +11,17 @@
 function_space = DEFAULT_FUNCTION_SPACE
 operators_prior = DEFAULT_PRIOR_OPERATORS
 functions_prior = DEFAULT_PRIOR_FUNCTIONS
+features_prior = {'constants': 0.5, 'variables': 0.5}
 structure_prior_from_depth = structure_prior_from_depth
 structure_prior_from_leaves = structure_prior_from_max_depth
 
+DEFAULT_PRIOR = {
+    'structures': structure_prior_from_max_depth(6),
+    'functions': functions_prior,
+    'operators': operators_prior,
+    'features': features_prior
+}
+
 
 def is_operator(a):
     return a.lower() in operator_space
diff --git a/src/equation_tree/prior.py b/src/equation_tree/prior.py
index df14878..5f8a9a3 100644
--- a/src/equation_tree/prior.py
+++ b/src/equation_tree/prior.py
@@ -23,6 +23,8 @@
 DEFAULT_PRIOR_OPERATORS = priors_from_space(DEFAULT_OPERATOR_SPACE)
 
 
+
+
 def prior_from_space(space):
     """
     Uniform prior from a list of strings
diff --git a/src/equation_tree/sample.py b/src/equation_tree/sample.py
index 976227d..cf58355 100644
--- a/src/equation_tree/sample.py
+++ b/src/equation_tree/sample.py
@@ -1,3 +1,4 @@
+import copy
 from typing import Dict, List, Optional, Union
 
 from tqdm import tqdm
@@ -19,6 +20,9 @@
 from equation_tree.util.priors import priors_from_space
 from equation_tree.util.type_check import is_constant_formatted, is_variable_formatted
 
+from equation_tree.defaults import DEFAULT_PRIOR, structure_prior_from_max_depth, \
+    structure_prior_from_depth
+
 PriorType = Union[List, Dict]
 
 MAX_ITER = 10_000
@@ -29,8 +33,21 @@ def sample_fast(n, prior, tree_depth, max_num_variables, file=None):
     return sample_trees_fast(n, adjusted_prior, tree_depth, max_num_variables)
 
 
-def sample(n, prior, max_num_variables, file=None):
-    adjusted_prior = load(prior, max_num_variables, file)
+def sample(n=1,
+           prior=DEFAULT_PRIOR,
+           max_num_variables=1,
+           file=None,
+           max_depth=None,
+           depth=None):
+    _prior = copy.deepcopy(prior)
+    if max_depth is not None and depth is not None:
+        raise Exception("Both depth and max depth are defined. Please only define one of both")
+    elif max_depth is not None:
+        _prior['structures'] = structure_prior_from_max_depth(max_depth)
+    elif depth is not None:
+        _prior['structures'] = structure_prior_from_depth(depth)
+
+    adjusted_prior = load(_prior, max_num_variables, file)
     return sample_trees(n, adjusted_prior, max_num_variables)
 
 
diff --git a/src/equation_tree/src/__init__.py b/src/equation_tree/src/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/src/equation_tree/tree.py b/src/equation_tree/tree.py
index 6b0dfde..6e4e8f5 100644
--- a/src/equation_tree/tree.py
+++ b/src/equation_tree/tree.py
@@ -186,6 +186,9 @@ def __init__(self, node: TreeNode):
 
         self._build()
 
+    def __repr__(self):
+        return str(self.sympy_expr)
+
     @classmethod
     def from_prefix(
         cls,
@@ -350,6 +353,8 @@ def from_prior(cls, prior: Dict, max_variables_unique: int):
         root = sample_tree_full(prior, max_variables_unique)
         return cls(root)
 
+
+
     @classmethod
     def from_priors(
         cls,
@@ -625,6 +630,14 @@ def has_valid_value(self):
         ev = self.evaluation[0, :]
         return np.any(np.isfinite(ev) & ~np.isnan(ev))
 
+    @property
+    def depth(self):
+        return max(self.structure)
+
+    @property
+    def n_nodes(self):
+        return len(self.structure)
+
     @property
     def info(self):
         """
diff --git a/src/equation_tree/util/__init__.py b/src/equation_tree/util/__init__.py
new file mode 100644
index 0000000..e69de29