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

Average Error: 0.0 → 0.0

Time: 17.9s

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	24.8
Cost	1376

\[\begin{array}{l} t_0 := --0.5 \cdot x\\ t_1 := \frac{y}{x} - 1\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -0.0195:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-114}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-271}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-303}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	17.3
Cost	1176

\[\begin{array}{l} t_0 := -\frac{x}{x - 2}\\ t_1 := \frac{y}{y - 2}\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{y}{x} - 1\\ \mathbf{elif}\;x \leq -0.162:\\ \;\;\;\;\frac{y - x}{y}\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-143}:\\ \;\;\;\;--0.5 \cdot x\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	25.1
Cost	1120

\[\begin{array}{l} t_0 := --0.5 \cdot x\\ \mathbf{if}\;x \leq -1 \cdot 10^{+70}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -0.0195:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.52 \cdot 10^{-114}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-274}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-304}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	17.3
Cost	848

\[\begin{array}{l} t_0 := \frac{y}{x} - 1\\ t_1 := \frac{y}{y - 2}\\ \mathbf{if}\;x \leq -4.9 \cdot 10^{+60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-143}:\\ \;\;\;\;--0.5 \cdot x\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	24.4
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-271}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-303}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6
Error	24.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+32}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	39.8
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023075 
(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))))