Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.5% → 96.4%

Time: 8.6s

Precision: binary64

Cost: 448

Math

\[\frac{x \cdot \left(y + z\right)}{z} \]

↓

\[\frac{x}{\frac{z}{z + y}} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))

↓

(FPCore (x y z) :precision binary64 (/ x (/ z (+ z y))))

C

double code(double x, double y, double z) {
	return (x * (y + z)) / z;
}

↓

double code(double x, double y, double z) {
	return x / (z / (z + y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y + z)) / z
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x / (z / (z + y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) / z;
}

↓

public static double code(double x, double y, double z) {
	return x / (z / (z + y));
}

Python

def code(x, y, z):
	return (x * (y + z)) / z

↓

def code(x, y, z):
	return x / (z / (z + y))

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) / z)
end

↓

function code(x, y, z)
	return Float64(x / Float64(z / Float64(z + y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) / z;
end

↓

function tmp = code(x, y, z)
	tmp = x / (z / (z + y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

↓

code[x_, y_, z_] := N[(x / N[(z / N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	84.5%
Target	96.4%
Herbie	96.4%

\[\frac{x}{\frac{z}{y + z}} \]

Derivation

1. Initial program 84.8%

   \[\frac{x \cdot \left(y + z\right)}{z} \]

2. Simplified 81.0%

   \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]
   Step-by-step derivation

   [Start] 84.8%	\[ \frac{x \cdot \left(y + z\right)}{z} \]
   associate-*l/ [<=] 81.0%	\[ \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

3. Applied egg-rr 96.5%

   \[\leadsto \color{blue}{\frac{x}{\frac{z}{z + y}}} \]
   Step-by-step derivation

   [Start] 81.0%	\[ \frac{x}{z} \cdot \left(y + z\right) \]
   associate-/r/ [<=] 96.5%	\[ \color{blue}{\frac{x}{\frac{z}{y + z}}} \]
   +-commutative [=>] 96.5%	\[ \frac{x}{\frac{z}{\color{blue}{z + y}}} \]

4. Final simplification 96.5%

   \[\leadsto \frac{x}{\frac{z}{z + y}} \]

Alternatives

Alternative 1
Accuracy	96.4%
Cost	448

\[\frac{x}{\frac{z}{z + y}} \]

Alternative 2
Accuracy	89.6%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+199}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+135}:\\ \;\;\;\;\frac{x}{z} \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	71.1%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Accuracy	72.9%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Accuracy	73.0%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	50.8%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023263 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))