diff --git a/src/HordeAd/Core/Ast.hs b/src/HordeAd/Core/Ast.hs
index db1b88365..0177a8ebd 100644
--- a/src/HordeAd/Core/Ast.hs
+++ b/src/HordeAd/Core/Ast.hs
@@ -40,9 +40,10 @@ import           Type.Reflection (Typeable, eqTypeRep, typeRep, (:~~:) (HRefl))
 
 import HordeAd.Core.HVector
 import HordeAd.Core.Types
-import HordeAd.Util.ShapedList (SizedListS (..), IndexS)
+import HordeAd.Internal.OrthotopeOrphanInstances
+  (IntegralF (..), RealFloatF (..))
+import HordeAd.Util.ShapedList (IndexS, SizedListS (..))
 import HordeAd.Util.SizedList
-import HordeAd.Internal.OrthotopeOrphanInstances (IntegralF(..))
 
 -- * Basic type family instances
 
@@ -142,10 +143,10 @@ varNameToAstVarId (AstVarName varId) = varId
 -- The reverse derivative artifact from step 6) of our full pipeline.
 -- The same type can also hold the forward derivative artifact.
 data AstArtifact = AstArtifact
-  { artVarsDt :: [AstDynamicVarName]
+  { artVarsDt     :: [AstDynamicVarName]
   , artVarsPrimal :: [AstDynamicVarName]
   , artDerivative :: HVectorOf (AstRaw PrimalSpan)
-  , artPrimal :: HVectorOf (AstRaw PrimalSpan)
+  , artPrimal     :: HVectorOf (AstRaw PrimalSpan)
   }
 
 -- | This is the (arbitrarily) chosen representation of terms denoting
@@ -688,15 +689,6 @@ instance (Num (OS.Array sh r), AstSpan s, OS.Shape sh)
     -- it's crucial that there is no AstConstant in fromInteger code
     -- so that we don't need 4 times the simplification rules
 
-instance (Real (OS.Array sh r), AstSpan s, OS.Shape sh)
-         => Real (AstShaped s r sh) where
-  toRational = undefined
-    -- very low priority, since these are all extremely not continuous
-
-instance Enum r => Enum (AstShaped s r n) where
-  toEnum = undefined
-  fromEnum = undefined  -- do we need to define our own Enum class for this?
-
 -- Warning: div and mod operations are very costly (simplifying them
 -- requires constructing conditionals, etc). If this error is removed,
 -- they are going to work, but slowly.
@@ -731,28 +723,9 @@ instance (Differentiable r, Floating (OS.Array sh r), AstSpan s, OS.Shape sh)
   acosh = AstR1S AcoshOp
   atanh = AstR1S AtanhOp
 
-instance (Differentiable r, RealFrac (OS.Array sh r), AstSpan s, OS.Shape sh)
-         => RealFrac (AstShaped s r sh) where
-  properFraction = undefined
-    -- The integral type doesn't have a Storable constraint,
-    -- so we can't implement this (nor RealFracB from Boolean package).
-
-instance (Differentiable r, RealFloat (OS.Array sh r), AstSpan s, OS.Shape sh)
-         => RealFloat (AstShaped s r sh) where
-  atan2 = AstR2S Atan2Op
-  -- We can be selective here and omit the other methods,
-  -- most of which don't even have a differentiable codomain.
-  floatRadix = undefined
-  floatDigits = undefined
-  floatRange = undefined
-  decodeFloat = undefined
-  encodeFloat = undefined
-  isNaN = undefined
-  isInfinite = undefined
-  isDenormalized = undefined
-  isNegativeZero = undefined
-  isIEEE = undefined
-
+instance (Differentiable r, Floating (OS.Array sh r), AstSpan s, OS.Shape sh)
+         => RealFloatF (AstShaped s r sh) where
+  atan2F = AstR2S Atan2Op
 
 -- * Unlawful instances of AST for bool; they are lawful modulo evaluation
 
diff --git a/src/HordeAd/Core/AstEnv.hs b/src/HordeAd/Core/AstEnv.hs
index b19fdc7ff..e027659ef 100644
--- a/src/HordeAd/Core/AstEnv.hs
+++ b/src/HordeAd/Core/AstEnv.hs
@@ -13,6 +13,7 @@ module HordeAd.Core.AstEnv
   , interpretLambdaHsH
     -- * Interpretation of arithmetic, boolean and relation operations
   , interpretAstN1, interpretAstN2, interpretAstR1, interpretAstR2
+  , interpretAstR2F
   , interpretAstI2, interpretAstI2F, interpretAstB2, interpretAstRelOp
   ) where
 
@@ -31,7 +32,8 @@ import           HordeAd.Core.HVector
 import           HordeAd.Core.HVectorOps
 import           HordeAd.Core.TensorClass
 import           HordeAd.Core.Types
-import           HordeAd.Internal.OrthotopeOrphanInstances (IntegralF (..))
+import           HordeAd.Internal.OrthotopeOrphanInstances
+  (IntegralF (..), RealFloatF (..))
 import           HordeAd.Util.ShapedList (IndexSh, IntSh)
 import qualified HordeAd.Util.ShapedList as ShapedList
 import           HordeAd.Util.SizedList
@@ -250,7 +252,7 @@ interpretAstN2 :: Num a
 interpretAstN2 MinusOp u v = u - v
 interpretAstN2 TimesOp u v = u * v
 
-interpretAstR1 :: RealFloat a
+interpretAstR1 :: Floating a
                => OpCode1 -> a -> a
 {-# INLINE interpretAstR1 #-}
 interpretAstR1 RecipOp u = recip u
@@ -278,6 +280,14 @@ interpretAstR2 PowerOp u v = u ** v
 interpretAstR2 LogBaseOp u v = logBase u v
 interpretAstR2 Atan2Op u v = atan2 u v
 
+interpretAstR2F :: RealFloatF a
+                => OpCode2 -> a -> a -> a
+{-# INLINE interpretAstR2F #-}
+interpretAstR2F DivideOp u v = u / v
+interpretAstR2F PowerOp u v = u ** v
+interpretAstR2F LogBaseOp u v = logBase u v
+interpretAstR2F Atan2Op u v = atan2F u v
+
 interpretAstI2 :: Integral a
                => OpCodeIntegral2 -> a -> a -> a
 {-# INLINE interpretAstI2 #-}
diff --git a/src/HordeAd/Core/AstInterpret.hs b/src/HordeAd/Core/AstInterpret.hs
index f07d12700..6098638cf 100644
--- a/src/HordeAd/Core/AstInterpret.hs
+++ b/src/HordeAd/Core/AstInterpret.hs
@@ -583,7 +583,7 @@ interpretAstS !env = \case
   AstR2S opCode u v ->
     let u2 = interpretAstS env u
         v2 = interpretAstS env v
-    in interpretAstR2 opCode u2 v2
+    in interpretAstR2F opCode u2 v2
   AstI2S opCode u v ->
     let u2 = interpretAstS env u
         v2 = interpretAstS env v
diff --git a/src/HordeAd/Core/DualNumber.hs b/src/HordeAd/Core/DualNumber.hs
index cb6303fd8..cd1b6b8e7 100644
--- a/src/HordeAd/Core/DualNumber.hs
+++ b/src/HordeAd/Core/DualNumber.hs
@@ -31,7 +31,8 @@ import           HordeAd.Core.HVector
 import           HordeAd.Core.IsPrimal
 import           HordeAd.Core.TensorClass
 import           HordeAd.Core.Types
-import           HordeAd.Internal.OrthotopeOrphanInstances (IntegralF (..))
+import           HordeAd.Internal.OrthotopeOrphanInstances
+  (IntegralF (..), RealFloatF (..))
 import           HordeAd.Util.ShapedList (IndexSh)
 import qualified HordeAd.Util.ShapedList as ShapedList
 import           HordeAd.Util.SizedList
@@ -397,6 +398,14 @@ instance (RealFrac (f r z), IsPrimal f r z)
     -- The integral type doesn't have a Storable constraint,
     -- so we can't implement this (nor RealFracB from Boolean package).
 
+instance (Fractional (f r z), RealFloatF (f r z), IsPrimal f r z)
+         => RealFloatF (ADVal f r z) where
+  atan2F (D ue u') (D ve v') =
+    let !u = sharePrimal ue in
+    let !v = sharePrimal ve in
+    let !t = sharePrimal (recip (u * u + v * v))
+    in dD (atan2F u v) (dAdd (dScale ((- u) * t) v') (dScale (v * t) u'))
+
 instance (RealFloat (f r z), IsPrimal f r z)
          => RealFloat (ADVal f r z) where
 {- TODO: this causes a cyclic dependency:
diff --git a/src/HordeAd/Core/TensorAst.hs b/src/HordeAd/Core/TensorAst.hs
index 6b2c6b2d0..41e3bf647 100644
--- a/src/HordeAd/Core/TensorAst.hs
+++ b/src/HordeAd/Core/TensorAst.hs
@@ -44,7 +44,8 @@ import           HordeAd.Core.TensorADVal (unADValHVector)
 import           HordeAd.Core.TensorClass
 import           HordeAd.Core.TensorConcrete ()
 import           HordeAd.Core.Types
-import           HordeAd.Internal.OrthotopeOrphanInstances (IntegralF (..))
+import           HordeAd.Internal.OrthotopeOrphanInstances
+  (IntegralF (..), RealFloatF (..))
 import           HordeAd.Util.ShapedList (IntSh)
 import qualified HordeAd.Util.ShapedList as ShapedList
 import           HordeAd.Util.SizedList
@@ -685,19 +686,14 @@ deriving instance AstSpan s => OrdF (AstRawS s)
 deriving instance Eq ((AstRawS s) r sh)
 deriving instance Ord ((AstRawS s) r sh)
 deriving instance Num (AstShaped s r sh) => Num (AstRawS s r sh)
-deriving instance (Real (AstShaped s r sh))
-                   => Real (AstRawS s r sh)
-deriving instance Enum (AstShaped s r sh) => Enum (AstRawS s r sh)
 deriving instance (IntegralF (AstShaped s r sh))
                   => IntegralF (AstRawS s r sh)
 deriving instance Fractional (AstShaped s r sh)
                   => Fractional (AstRawS s r sh)
 deriving instance Floating (AstShaped s r sh)
                   => Floating (AstRawS s r sh)
-deriving instance (RealFrac (AstShaped s r sh))
-                  => RealFrac (AstRawS s r sh)
-deriving instance (RealFloat (AstShaped s r sh))
-                  => RealFloat (AstRawS s r sh)
+deriving instance (RealFloatF (AstShaped s r sh))
+                  => RealFloatF (AstRawS s r sh)
 
 type instance BoolOf (AstNoVectorize s) = AstBool
 
@@ -729,19 +725,14 @@ deriving instance AstSpan s => OrdF (AstNoVectorizeS s)
 deriving instance Eq ((AstNoVectorizeS s) r sh)
 deriving instance Ord ((AstNoVectorizeS s) r sh)
 deriving instance Num (AstShaped s r sh) => Num (AstNoVectorizeS s r sh)
-deriving instance (Real (AstShaped s r sh))
-                   => Real (AstNoVectorizeS s r sh)
-deriving instance Enum (AstShaped s r sh) => Enum (AstNoVectorizeS s r sh)
 deriving instance (IntegralF (AstShaped s r sh))
                   => IntegralF (AstNoVectorizeS s r sh)
 deriving instance Fractional (AstShaped s r sh)
                   => Fractional (AstNoVectorizeS s r sh)
 deriving instance Floating (AstShaped s r sh)
                   => Floating (AstNoVectorizeS s r sh)
-deriving instance (RealFrac (AstShaped s r sh))
-                  => RealFrac (AstNoVectorizeS s r sh)
-deriving instance (RealFloat (AstShaped s r sh))
-                  => RealFloat (AstNoVectorizeS s r sh)
+deriving instance (RealFloatF (AstShaped s r sh))
+                  => RealFloatF (AstNoVectorizeS s r sh)
 
 type instance BoolOf (AstNoSimplify s) = AstBool
 
@@ -773,19 +764,14 @@ deriving instance AstSpan s => OrdF (AstNoSimplifyS s)
 deriving instance Eq (AstNoSimplifyS s r sh)
 deriving instance Ord (AstNoSimplifyS s r sh)
 deriving instance Num (AstShaped s r sh) => Num (AstNoSimplifyS s r sh)
-deriving instance (Real (AstShaped s r sh))
-                  => Real (AstNoSimplifyS s r sh)
-deriving instance Enum (AstShaped s r sh) => Enum (AstNoSimplifyS s r sh)
 deriving instance (IntegralF (AstShaped s r sh))
                   => IntegralF (AstNoSimplifyS s r sh)
 deriving instance Fractional (AstShaped s r sh)
                   => Fractional (AstNoSimplifyS s r sh)
 deriving instance Floating (AstShaped s r sh)
                   => Floating (AstNoSimplifyS s r sh)
-deriving instance (RealFrac (AstShaped s r sh))
-                  => RealFrac (AstNoSimplifyS s r sh)
-deriving instance (RealFloat (AstShaped s r sh))
-                  => RealFloat (AstNoSimplifyS s r sh)
+deriving instance (RealFloatF (AstShaped s r sh))
+                  => RealFloatF (AstNoSimplifyS s r sh)
 
 instance AstSpan s => RankedTensor (AstRaw s) where
   rlet a f = AstRaw $ astLetFunRaw (unAstRaw a) (unAstRaw . f . AstRaw)
diff --git a/src/HordeAd/Core/TensorClass.hs b/src/HordeAd/Core/TensorClass.hs
index 205c7f13d..87233fa8b 100644
--- a/src/HordeAd/Core/TensorClass.hs
+++ b/src/HordeAd/Core/TensorClass.hs
@@ -37,7 +37,8 @@ import           Unsafe.Coerce (unsafeCoerce)
 
 import           HordeAd.Core.HVector
 import           HordeAd.Core.Types
-import           HordeAd.Internal.OrthotopeOrphanInstances (IntegralF (..))
+import           HordeAd.Internal.OrthotopeOrphanInstances
+  (IntegralF (..), RealFloatF (..))
 import           HordeAd.Util.ShapedList
   (IndexSh, IntSh, ShapeIntS, consIndex, pattern (:.$), pattern ZIS)
 import qualified HordeAd.Util.ShapedList as ShapedList
@@ -336,7 +337,9 @@ class ( Integral (IntOf ranked), CRanked ranked Num
 -- * Shaped tensor class definition
 
 class ( Integral (IntOf shaped), CShaped shaped Num
-      , TensorSupports RealFloat shaped, TensorSupports2 Integral IntegralF shaped )
+      , TensorSupports2 RealFloat Floating shaped
+      , TensorSupports2 RealFloat RealFloatF shaped
+      , TensorSupports2 Integral IntegralF shaped )
       => ShapedTensor (shaped :: ShapedTensorType) where
 
   slet :: (KnownShape sh, KnownShape sh2, GoodScalar r, GoodScalar r2)
diff --git a/src/HordeAd/Internal/OrthotopeOrphanInstances.hs b/src/HordeAd/Internal/OrthotopeOrphanInstances.hs
index 3d3e372dd..44dffed31 100644
--- a/src/HordeAd/Internal/OrthotopeOrphanInstances.hs
+++ b/src/HordeAd/Internal/OrthotopeOrphanInstances.hs
@@ -10,7 +10,7 @@ module HordeAd.Internal.OrthotopeOrphanInstances
   , Dict(..)
   , -- * Numeric instances for tensors
     liftVR, liftVR2, liftVS, liftVS2
-  , IntegralF(..)
+  , IntegralF(..), RealFloatF(..)
   , -- * Assorted orphans and additions
     MapSucc, trustMeThisIsAPermutation
   ) where
@@ -416,10 +416,6 @@ instance (Real (Vector r), KnownNat n, Numeric r, Show r, Ord r)
          => Real (OR.Array n r) where
   toRational = undefined  -- TODO
 
-instance (Real (Vector r), KnownShape2 sh, OS.Shape sh, Numeric r, Ord r)
-         => Real (OS.Array sh r) where
-  toRational = undefined  -- TODO
-
 instance ( RealFrac (Vector r), KnownNat n, Numeric r, Show r, Fractional r
          , Ord r )
          => RealFrac (OR.Array n r) where
@@ -427,10 +423,6 @@ instance ( RealFrac (Vector r), KnownNat n, Numeric r, Show r, Fractional r
     -- The integral type doesn't have a Storable constraint,
     -- so we can't implement this (nor even RealFracB from Boolean package).
 
-instance (RealFrac (Vector r), KnownShape2 sh, OS.Shape sh, Numeric r, Fractional r, Ord r)
-         => RealFrac (OS.Array sh r) where
-  properFraction = error "OS.properFraction: can't be implemented"
-
 instance ( RealFloat (Vector r), KnownNat n, Numeric r, Show r, Floating r
          , Ord r )
          => RealFloat (OR.Array n r) where
@@ -446,19 +438,12 @@ instance ( RealFloat (Vector r), KnownNat n, Numeric r, Show r, Floating r
   isNegativeZero = undefined
   isIEEE = undefined
 
-instance (RealFloat (Vector r), KnownShape2 sh, OS.Shape sh, Numeric r, Floating r, Ord r)
-         => RealFloat (OS.Array sh r) where
-  atan2 = liftVS2NoAdapt atan2
-  floatRadix = undefined  -- TODO (and below)
-  floatDigits = undefined
-  floatRange = undefined
-  decodeFloat = undefined
-  encodeFloat = undefined
-  isNaN = undefined
-  isInfinite = undefined
-  isDenormalized = undefined
-  isNegativeZero = undefined
-  isIEEE = undefined
+class Floating a => RealFloatF a where
+  atan2F :: a -> a -> a
+
+instance (Floating r, RealFloat (Vector r), KnownShape2 sh, Numeric r)
+         => RealFloatF (OS.Array sh r) where
+  atan2F = liftVS2NoAdapt atan2
 
 deriving instance Num (f a b) => Num (Flip f b a)
 
@@ -476,6 +461,8 @@ deriving instance Real (f a b) => Real (Flip f b a)
 
 deriving instance RealFrac (f a b) => RealFrac (Flip f b a)
 
+deriving instance RealFloatF (f a b) => RealFloatF (Flip f b a)
+
 deriving instance RealFloat (f a b) => RealFloat (Flip f b a)
 
 deriving instance NFData (f a b) => NFData (Flip f b a)
diff --git a/test/simplified/TestAdaptorSimplified.hs b/test/simplified/TestAdaptorSimplified.hs
index f5aa7a0e8..c0428749f 100644
--- a/test/simplified/TestAdaptorSimplified.hs
+++ b/test/simplified/TestAdaptorSimplified.hs
@@ -25,6 +25,7 @@ import HordeAd
 import HordeAd.Core.AstEnv
 import HordeAd.Core.AstFreshId (funToAstR, funToAstS, resetVarCounter)
 import HordeAd.Core.IsPrimal (resetIdCounter)
+import HordeAd.Internal.OrthotopeOrphanInstances (RealFloatF (..))
 
 import CrossTesting
 import EqEpsilon
@@ -235,19 +236,19 @@ testZero3S :: Assertion
 testZero3S =
   assertEqualUpToEpsilon 1e-9
     (Flip $ OS.fromList @'[33, 2] (replicate 66 3.6174114266850617))
-    (crev (\x -> bar @(ADVal (Flip OS.Array) Double '[33, 2]) (x, x)) 1)
+    (crev (\x -> barF @(ADVal (Flip OS.Array) Double '[33, 2]) (x, x)) 1)
 
 testCFwdZero3S :: Assertion
 testCFwdZero3S =
   assertEqualUpToEpsilon 1e-9
     (Flip $ OS.fromList @'[33, 2] (replicate 66 3.9791525693535674))
-    (cfwd (\x -> bar @(ADVal (Flip OS.Array) Double '[33, 2]) (x, x)) 1 1.1)
+    (cfwd (\x -> barF @(ADVal (Flip OS.Array) Double '[33, 2]) (x, x)) 1 1.1)
 
 testFwdZero3S :: Assertion
 testFwdZero3S =
   assertEqualUpToEpsilon 1e-9
     (Flip $ OS.fromList @'[33, 2] (replicate 66 3.9791525693535674))
-    (fwd (\x -> bar @(AstShaped FullSpan Double '[33, 2]) (x, x)) 1 1.1)
+    (fwd (\x -> barF @(AstShaped FullSpan Double '[33, 2]) (x, x)) 1 1.1)
 
 testZero4S :: Assertion
 testZero4S =
@@ -271,7 +272,7 @@ testZero6S =
   assertEqualUpToEpsilon 1e-9
     (Flip $ OS.fromList @'[2, 2, 2, 2, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 2, 2, 2, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,111,1,1,1,1, 2, 2, 2, 2] (replicate (product ([2, 2, 2, 2, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 2, 2, 2, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,111,1,1,1,1, 2, 2, 2, 2] :: [Int])) 3.6174114266850617))
     (rev @Double @'[2, 2, 2, 2, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 2, 2, 2, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,111,1,1,1,1, 2, 2, 2, 2]
-         @(AstShaped FullSpan) (\x -> bar (x, x)) 1)
+         @(AstShaped FullSpan) (\x -> barF (x, x)) 1)
 
 testZero7S :: Assertion
 testZero7S =
@@ -500,6 +501,11 @@ foo (x, y, z) =
   let w = x * sin y
   in atan2 z w + z * w
 
+fooF :: RealFloatF a => (a, a, a) -> a
+fooF (x, y, z) =
+  let w = x * sin y
+  in atan2F z w + z * w
+
 testFoo :: Assertion
 testFoo = do
   assertEqualUpToEpsilon 1e-10
@@ -510,14 +516,14 @@ testFooS :: Assertion
 testFooS = do
   assertEqualUpToEpsilon 1e-10
     (2.4396285219055063, -1.953374825727421, 0.9654825811012627)
-    (rev @Double @'[3, 534, 3] @(AstShaped FullSpan) foo (1.1, 2.2, 3.3))
+    (rev @Double @'[3, 534, 3] @(AstShaped FullSpan) fooF (1.1, 2.2, 3.3))
 
 testFooSToFloat :: Assertion
 testFooSToFloat = do
   assertEqualUpToEpsilon 1e-10
     (2.4396285219055063, -1.953374825727421, 0.9654825811012627)
     (rev @Float @'[3, 534, 3] @(AstShaped FullSpan)
-         (scast . foo)
+         (scast . fooF)
          (1.1 :: Flip OS.Array Double '[3, 534, 3], 2.2, 3.3))
 
 testFooSBoth :: Assertion
@@ -525,7 +531,7 @@ testFooSBoth = do
   assertEqualUpToEpsilon 1e-10
     (2.439628436155373, -1.9533749, 0.9654825479484146)
     (rev @Float @'[3, 534, 3] @(AstShaped FullSpan)
-         (scast . foo . (\(d, f, d2) -> (d, scast f, d2)))
+         (scast . fooF . (\(d, f, d2) -> (d, scast f, d2)))
          ( 1.1 :: Flip OS.Array Double '[3, 534, 3]
          , 2.2 :: Flip OS.Array Float '[3, 534, 3]
          , 3.3 ))
@@ -1201,6 +1207,11 @@ bar (x, y) =
   let w = foo (x, y, x) * sin y
   in atan2 x w + y * w
 
+barF :: forall a. RealFloatF a => (a, a) -> a
+barF (x, y) =
+  let w = fooF (x, y, x) * sin y
+  in atan2F x w + y * w
+
 testBar :: Assertion
 testBar =
   assertEqualUpToEpsilon 1e-9
@@ -1211,13 +1222,13 @@ testBarS :: Assertion
 testBarS =
   assertEqualUpToEpsilon 1e-9
     (3.1435239435581166,-1.1053869545195814)
-    (crev (bar @(ADVal (Flip OS.Array) Double '[])) (1.1, 2.2))
+    (crev (barF @(ADVal (Flip OS.Array) Double '[])) (1.1, 2.2))
 
 testBar2S :: Assertion
 testBar2S =
   assertEqualUpToEpsilon 1e-9
     (3.1435239435581166,-1.1053869545195814)
-    (rev (bar @(AstShaped FullSpan Double '[52, 2, 2, 1, 1, 3])) (1.1, 2.2))
+    (rev (barF @(AstShaped FullSpan Double '[52, 2, 2, 1, 1, 3])) (1.1, 2.2))
 
 testBarCFwd :: Assertion
 testBarCFwd =
@@ -1526,9 +1537,9 @@ reluMaxS = smap0N (maxF 0)
 
 barReluMaxS
   :: ( ADReadyS shaped, GoodScalar r, KnownShape sh, KnownNat (Sh.Rank sh)
-     , RealFloat (shaped r sh) )
+     , RealFloatF (shaped r sh) )
   => shaped r sh -> shaped r sh
-barReluMaxS x = reluMaxS $ bar (x, reluMaxS x)
+barReluMaxS x = reluMaxS $ barF (x, reluMaxS x)
 
 -- Previously the shape of FromListR[ZeroR] couldn't be determined
 -- in buildDerivative, so this was needed. See below that it now works fine.
diff --git a/test/simplified/TestHighRankSimplified.hs b/test/simplified/TestHighRankSimplified.hs
index 72b0a2450..cf2b0d588 100644
--- a/test/simplified/TestHighRankSimplified.hs
+++ b/test/simplified/TestHighRankSimplified.hs
@@ -18,6 +18,7 @@ import           Test.Tasty.HUnit hiding (assert)
 
 import HordeAd
 import HordeAd.Core.AstFreshId (funToAstR, resetVarCounter)
+import HordeAd.Internal.OrthotopeOrphanInstances (RealFloatF (..))
 
 import CrossTesting
 import EqEpsilon
@@ -77,6 +78,11 @@ foo (x,y,z) =
   let w = x * sin y
   in atan2 z w + z * w
 
+fooF :: RealFloatF a => (a,a,a) -> a
+fooF (x,y,z) =
+  let w = x * sin y
+  in atan2F z w + z * w
+
 testFoo :: Assertion
 testFoo =
   assertEqualUpToEpsilon 1e-3
@@ -88,6 +94,11 @@ bar (x, y) =
   let w = foo (x, y, x) * sin y
   in atan2 x w + y * w
 
+barF :: forall a. RealFloatF a => (a, a) -> a
+barF (x, y) =
+  let w = fooF (x, y, x) * sin y
+  in atan2F x w + y * w
+
 testBar :: Assertion
 testBar =
   assertEqualUpToEpsilon 1e-5
@@ -98,7 +109,7 @@ testBarS :: Assertion
 testBarS =
   assertEqualUpToEpsilon 1e-5
     (Flip $ OS.fromList @'[3, 1, 2, 2, 1, 2, 2] [304.13867,914.9335,823.0187,1464.4688,5264.3306,1790.0055,1535.4309,3541.6572,304.13867,914.9335,823.0187,1464.4688,6632.4355,6047.113,1535.4309,1346.6815,45.92141,6.4903135,5.5406737,1.4242969,6.4903135,1.1458766,4.6446533,2.3550234,88.783676,27.467598,125.27507,18.177452,647.1917,0.3878851,2177.6152,786.1792,6.4903135,6.4903135,6.4903135,6.4903135,2.3550234,2.3550234,2.3550234,2.3550234,21.783596,2.3550234,2.3550234,2.3550234,21.783596,21.783596,21.783596,21.783596], Flip $ OS.fromList @'[3, 1, 2, 2, 1, 2, 2] [-5728.7617,24965.113,32825.07,-63505.953,-42592.203,145994.88,-500082.5,-202480.06,-5728.7617,24965.113,32825.07,-63505.953,49494.473,-2446.7632,-500082.5,-125885.58,-43.092484,-1.9601002,-98.97709,2.1931143,-1.9601002,1.8243169,-4.0434446,-1.5266153,2020.9731,-538.0603,-84.28137,62.963814,-34987.0,-9.917454,135.30023,17741.998,-1.9601002,-1.9601002,-1.9601002,-1.9601002,-1.5266153,-1.5266153,-1.5266153,-1.5266153,-4029.1775,-1.5266153,-1.5266153,-1.5266153,-4029.1775,-4029.1775,-4029.1775,-4029.1775])
-    (crev (bar @(ADVal (Flip OS.Array) Float '[3, 1, 2, 2, 1, 2, 2])) (sfromR t48, sfromR t48))
+    (crev (barF @(ADVal (Flip OS.Array) Float '[3, 1, 2, 2, 1, 2, 2])) (sfromR t48, sfromR t48))
 
 -- A dual-number and list-based version of a function that goes
 -- from `R^3` to `R`.
diff --git a/test/simplified/TestRevFwdFold.hs b/test/simplified/TestRevFwdFold.hs
index 081e801ba..bae4b7b50 100644
--- a/test/simplified/TestRevFwdFold.hs
+++ b/test/simplified/TestRevFwdFold.hs
@@ -20,6 +20,7 @@ import           Test.Tasty.HUnit hiding (assert)
 
 import HordeAd
 import HordeAd.Core.AstFreshId (resetVarCounter)
+import HordeAd.Internal.OrthotopeOrphanInstances (RealFloatF (..))
 import HordeAd.Util.ShapedList (pattern (:.$), pattern ZIS)
 
 import CrossTesting
@@ -635,7 +636,7 @@ testSin0Fold4S = do
   assertEqualUpToEpsilon' 1e-10
     (-0.7053476446727861 :: OR.Array 0 Double)
     (rev' (let f :: forall f. ADReadyS f => f Double '[] -> f Double '[]
-               f a0 = sfold (\x a -> atan2 (sin x) (sin a))
+               f a0 = sfold (\x a -> atan2F (sin x) (sin a))
                         (2 * a0) (sreplicate @f @3 a0)
            in rfromS . f . sfromR) 1.1)
 
@@ -648,9 +649,9 @@ testSin0Fold5S = do
                                    => f2 Double '[] -> f2 Double '[2, 5]
                                    -> f2 Double '[]
                                  g x a = ssum
-                                   $ atan2 (sin $ sreplicate @f2 @5 x)
-                                         (ssum $ sin $ ssum
-                                          $ str $ sreplicate @f2 @7 a)
+                                   $ atan2F (sin $ sreplicate @f2 @5 x)
+                                            (ssum $ sin $ ssum
+                                             $ str $ sreplicate @f2 @7 a)
                              in g)
                         (2 * a0)
                         (sreplicate @f @3
@@ -689,9 +690,9 @@ testSin0Fold8S = do
     (rev' (let f :: forall f. ADReadyS f => f Double '[] -> f Double '[2, 5]
                f a0 = sfold @_ @f @Double @Double @'[2, 5] @'[] @3
                         (\x a -> str $ sreplicate @_ @5
-                                 $ atan2 (ssum (str $ sin x))
-                                         (sreplicate @_ @2
-                                          $ sin (ssum $ sreplicate @_ @7 a)))
+                                 $ atan2F (ssum (str $ sin x))
+                                          (sreplicate @_ @2
+                                           $ sin (ssum $ sreplicate @_ @7 a)))
                         (sreplicate @_ @2 (sreplicate @_ @5 (2 * a0)))
                         (sreplicate @_ @3 a0)
            in rfromS . f . sfromR) 1.1)
@@ -728,9 +729,9 @@ testSin0Fold8Srev = do
     (rrev1 (let f :: forall f. ADReadyS f => f Double '[] -> f Double '[2, 5]
                 f a0 = sfold @_ @f @Double @Double @'[2, 5] @'[] @3
                         (\x a -> str $ sreplicate @_ @5
-                                 $ atan2 (ssum (str $ sin x))
-                                         (sreplicate @_ @2
-                                          $ sin (ssum $ sreplicate @_ @7 a)))
+                                 $ atan2F (ssum (str $ sin x))
+                                          (sreplicate @_ @2
+                                           $ sin (ssum $ sreplicate @_ @7 a)))
                         (sreplicate @_ @2 (sreplicate @_ @5 (2 * a0)))
                         (sreplicate @_ @3 a0)
             in rfromS . f . sfromR) 1.1)
@@ -742,9 +743,9 @@ testSin0Fold8Srev2 = do
                        => f Double '[] -> f Double '[2, 5]
                      f a0 = sfold @_ @f @Double @Double @'[2, 5] @'[] @3
                         (\x a -> str $ sreplicate @_ @5
-                                 $ atan2 (ssum (str $ sin x))
-                                         (sreplicate @_ @2
-                                          $ sin (ssum $ sreplicate @_ @7 a)))
+                                 $ atan2F (ssum (str $ sin x))
+                                          (sreplicate @_ @2
+                                           $ sin (ssum $ sreplicate @_ @7 a)))
                         (sreplicate @_ @2 (sreplicate @_ @5 (2 * a0)))
                         (sreplicate @_ @3 a0)
                  in f)
@@ -758,9 +759,9 @@ testSin0Fold182SrevPP = do
   let a1 = rrev1 @(AstRanked FullSpan)
            (let f :: forall f. ADReadyS f => f Double '[] -> f Double '[5]
                 f a0 = sfold @_ @f @Double @Double @'[5] @'[] @1
-                        (\_x a -> atan2 (sreplicate @_ @5 a)
-                                        (sreplicate @_ @5
-                                         $ sin (ssum $ sreplicate @_ @7 a)))
+                        (\_x a -> atan2F (sreplicate @_ @5 a)
+                                         (sreplicate @_ @5
+                                          $ sin (ssum $ sreplicate @_ @7 a)))
                         (sreplicate @_ @5 a0)
                         (sreplicate @_ @1 a0)
             in rfromS . f . sfromR) 1.1
@@ -774,9 +775,9 @@ testSin0Fold18Srev = do
     (rrev1 (let f :: forall f. ADReadyS f => f Double '[] -> f Double '[2, 5]
                 f a0 = sfold @_ @f @Double @Double @'[2, 5] @'[] @2
                         (\x a -> str $ sreplicate @_ @5
-                                 $ atan2 (ssum (str $ sin x))
-                                         (sreplicate @_ @2
-                                          $ sin (ssum $ sreplicate @_ @7 a)))
+                                 $ atan2F (ssum (str $ sin x))
+                                          (sreplicate @_ @2
+                                           $ sin (ssum $ sreplicate @_ @7 a)))
                         (sreplicate @_ @2 (sreplicate @_ @5 (2 * a0)))
                         (sreplicate @_ @2 a0)
             in rfromS . f . sfromR) 1.1)
@@ -813,9 +814,9 @@ testSin0Fold8Sfwd = do
     (rfwd1 (let f :: forall f. ADReadyS f => f Double '[] -> f Double '[2, 5]
                 f a0 = sfold @_ @f @Double @Double @'[2, 5] @'[] @3
                         (\x a -> str $ sreplicate @_ @5
-                                 $ atan2 (ssum (str $ sin x))
-                                         (sreplicate @_ @2
-                                          $ sin (ssum $ sreplicate @_ @7 a)))
+                                 $ atan2F (ssum (str $ sin x))
+                                          (sreplicate @_ @2
+                                           $ sin (ssum $ sreplicate @_ @7 a)))
                         (sreplicate @_ @2 (sreplicate @_ @5 (2 * a0)))
                         (sreplicate @_ @3 a0)
             in rfromS . f . sfromR) 1.1)
@@ -827,9 +828,9 @@ testSin0Fold8Sfwd2 = do
                        => f Double '[] -> f Double '[2, 5]
                      f a0 = sfold @_ @f @Double @Double @'[2, 5] @'[] @3
                         (\x a -> str $ sreplicate @_ @5
-                                 $ atan2 (ssum (str $ sin x))
-                                         (sreplicate @_ @2
-                                          $ sin (ssum $ sreplicate @_ @7 a)))
+                                 $ atan2F (ssum (str $ sin x))
+                                          (sreplicate @_ @2
+                                           $ sin (ssum $ sreplicate @_ @7 a)))
                         (sreplicate @_ @2 (sreplicate @_ @5 (2 * a0)))
                         (sreplicate @_ @3 a0)
                  in rfromS . f . sfromR)
@@ -846,9 +847,9 @@ testSin0Fold5Sfwd = do
                                    => f2 Double '[] -> f2 Double '[2, 5]
                                    -> f2 Double '[]
                                  g x a = ssum
-                                   $ atan2 (sin $ sreplicate @f2 @5 x)
-                                         (ssum $ sin $ ssum
-                                          $ str $ sreplicate @f2 @7 a)
+                                   $ atan2F (sin $ sreplicate @f2 @5 x)
+                                            (ssum $ sin $ ssum
+                                             $ str $ sreplicate @f2 @7 a)
                              in g)
                         (2 * a0)
                         (sreplicate @f @3
@@ -865,9 +866,9 @@ testSin0Fold5Sfwds = do
                                    => f2 Double '[] -> f2 Double '[2, 5]
                                    -> f2 Double '[]
                                  g x a = ssum
-                                   $ atan2 (sin $ sreplicate @f2 @5 x)
-                                         (ssum $ sin $ ssum
-                                          $ str $ sreplicate @f2 @7 a)
+                                   $ atan2F (sin $ sreplicate @f2 @5 x)
+                                            (ssum $ sin $ ssum
+                                             $ str $ sreplicate @f2 @7 a)
                              in g)
                         (2 * a0)
                         (sreplicate @f @3
@@ -2716,7 +2717,7 @@ testSin0rmapAccumRD01SN6 = do
                                    $ V.fromList
                                        [ DynamicShaped
                                          $ sin x
-                                           `atan2` smaxIndex
+                                           `atan2F` smaxIndex
                                                @_ @Double @Double @'[] @2
                                                (sfromD (a V.! 1))
                                        , DynamicShaped
@@ -2889,7 +2890,7 @@ testSin0ScanD51S = do
                           -> f2 Double '[1,1,1,1]
                         g x a =
                           ssum
-                          $ atan2 (sin $ sreplicate @f2 @5 x)
+                          $ atan2F (sin $ sreplicate @f2 @5 x)
                                   (ssum $ sin $ ssum
                                    $ str $ sreplicate @f2 @7
                                    $ sreplicate @f2 @2 $ sreplicate @f2 @5
@@ -4012,7 +4013,7 @@ testSin0FoldNestedSi = do
   assertEqualUpToEpsilon' 1e-10
     (-0.20775612781643243 :: OR.Array 0 Double)
     (rev' (let f :: forall f. ADReadyS f => f Double '[] -> f Double '[3]
-               f a0 = sfold (\x a -> atan2
+               f a0 = sfold (\x a -> atan2F
                                        (sscan (+) (ssum x)
                                           (sscan (*) 2
                                                  (sreplicate @_ @1 a)))