Data.Colour.RGB:hslsv from colour-2.3.3, D

Average Accuracy: 100.0% → 100.0%

Time: 7.3s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	73.2%
Cost	1112

\[\begin{array}{l} t_0 := 1 - \frac{y}{x}\\ \mathbf{if}\;x \leq -5 \cdot 10^{-40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-96}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-124}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-149}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-26}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Accuracy	73.8%
Cost	976

\[\begin{array}{l} t_0 := 1 - \frac{y}{x}\\ t_1 := 2 \cdot \frac{x}{y} + -1\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{-32}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-124}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Accuracy	72.7%
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-94}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-124}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-149}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{-43}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Accuracy	49.6%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023129 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

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

  (/ (- x y) (+ x y)))