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

Average Error: 0.0 → 0.0

Time: 10.6s

Precision: binary64

Cost: 576

Math

\[\frac{x - y}{2 - \left(x + y\right)} \]

↓

\[\frac{x - y}{2 - \left(x + y\right)} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

↓

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

↓

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

↓

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

↓

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

↓

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

↓

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)} \]

Derivation

1. Initial program 0.0

   \[\frac{x - y}{2 - \left(x + y\right)} \]

2. Final simplification 0.0

   \[\leadsto \frac{x - y}{2 - \left(x + y\right)} \]

Alternatives

Alternative 1
Error	25.3
Cost	1112

\[\begin{array}{l} t_0 := -1 + \frac{y}{x}\\ \mathbf{if}\;y \leq -3.6452425046897897 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8.93529700142645 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.1540490425263912 \cdot 10^{-122}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.8450445429284417 \cdot 10^{-296}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.049310988102626 \cdot 10^{-255}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.7596658380727143 \cdot 10^{-5}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2}{y}\\ \end{array} \]

Alternative 2
Error	18.0
Cost	1104

\[\begin{array}{l} \mathbf{if}\;y \leq -3.6452425046897897 \cdot 10^{+77}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{elif}\;y \leq -3.8304254605141083 \cdot 10^{-20}:\\ \;\;\;\;\frac{-1}{1 + \frac{y}{x}}\\ \mathbf{elif}\;y \leq -2.1540490425263912 \cdot 10^{-122}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.7596658380727143 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\left(2 - x\right) - x}{y}\\ \end{array} \]

Alternative 3
Error	18.1
Cost	976

\[\begin{array}{l} t_0 := 1 + \frac{x \cdot -2}{y}\\ \mathbf{if}\;y \leq -3.6452425046897897 \cdot 10^{+77}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.8304254605141083 \cdot 10^{-20}:\\ \;\;\;\;\frac{-1}{1 + \frac{y}{x}}\\ \mathbf{elif}\;y \leq -2.1540490425263912 \cdot 10^{-122}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.7596658380727143 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	18.1
Cost	912

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -3.6452425046897897 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8304254605141083 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.1540490425263912 \cdot 10^{-122}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.7596658380727143 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \end{array} \]

Alternative 5
Error	18.1
Cost	912

\[\begin{array}{l} \mathbf{if}\;y \leq -3.6452425046897897 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8304254605141083 \cdot 10^{-20}:\\ \;\;\;\;\frac{-1}{1 + \frac{y}{x}}\\ \mathbf{elif}\;y \leq -2.1540490425263912 \cdot 10^{-122}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.7596658380727143 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \end{array} \]

Alternative 6
Error	25.4
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -3.6452425046897897 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8.93529700142645 \cdot 10^{-12}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -2.1540490425263912 \cdot 10^{-122}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.8450445429284417 \cdot 10^{-296}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 6.049310988102626 \cdot 10^{-255}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.7596658380727143 \cdot 10^{-5}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	25.3
Cost	856

\[\begin{array}{l} t_0 := -1 + \frac{y}{x}\\ \mathbf{if}\;y \leq -3.6452425046897897 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8.93529700142645 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.1540490425263912 \cdot 10^{-122}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.8450445429284417 \cdot 10^{-296}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.049310988102626 \cdot 10^{-255}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.7596658380727143 \cdot 10^{-5}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	18.3
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -3.6452425046897897 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8304254605141083 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.1540490425263912 \cdot 10^{-122}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.7596658380727143 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2}{y}\\ \end{array} \]

Alternative 9
Error	26.0
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -5.891967999708948 \cdot 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 3.5042244519584246 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.3124289141001742 \cdot 10^{+97}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.567085650239426 \cdot 10^{+170}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 10
Error	24.6
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -3.6452425046897897 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.8450445429284417 \cdot 10^{-296}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 6.049310988102626 \cdot 10^{-255}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.7596658380727143 \cdot 10^{-5}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11
Error	39.9
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022316 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

  (/ (- x y) (- 2.0 (+ x y))))