Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Average Error: 12.4 → 3.0

Time: 59.3s

Precision: binary64

Cost: 708

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y + z \ne 0:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (if (!= (+ y z) 0.0) (/ x (/ z (+ y z))) (/ (* x (+ y z)) z)))

C

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

↓

double code(double x, double y, double z) {
	double tmp;
	if ((y + z) != 0.0) {
		tmp = x / (z / (y + z));
	} else {
		tmp = (x * (y + z)) / z;
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((y + z) /= 0.0d0) then
        tmp = x / (z / (y + z))
    else
        tmp = (x * (y + z)) / z
    end if
    code = tmp
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) {
	double tmp;
	if ((y + z) != 0.0) {
		tmp = x / (z / (y + z));
	} else {
		tmp = (x * (y + z)) / z;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	tmp = 0
	if (y + z) != 0.0:
		tmp = x / (z / (y + z))
	else:
		tmp = (x * (y + z)) / z
	return tmp

Julia

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

↓

function code(x, y, z)
	tmp = 0.0
	if (Float64(y + z) != 0.0)
		tmp = Float64(x / Float64(z / Float64(y + z)));
	else
		tmp = Float64(Float64(x * Float64(y + z)) / z);
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y + z) ~= 0.0)
		tmp = x / (z / (y + z));
	else
		tmp = (x * (y + z)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := If[Unequal[N[(y + z), $MachinePrecision], 0.0], N[(x / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Target

Original	12.4
Target	3.0
Herbie	3.0

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

Derivation

1. Initial program 12.4

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

2. Applied egg-rr 3.0

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;y + z \ne 0:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ } \end{array}} \]

Alternatives

Alternative 1
Error	20.1
Cost	1112

\[\begin{array}{l} t_0 := \frac{x}{z} \cdot y\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.26:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+159}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	20.0
Cost	1112

\[\begin{array}{l} t_0 := \frac{x}{z} \cdot y\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.34:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-48}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+159}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	20.0
Cost	1112

\[\begin{array}{l} t_0 := \frac{x}{z} \cdot y\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+92}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq -0.27:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-48}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+159}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	8.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+224}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	3.3
Cost	448

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

Alternative 6
Error	25.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023033 
(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))