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

Average Error: 0.0 → 0.0

Time: 6.6s

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	25.9
Cost	1244

\[\begin{array}{l} t_0 := 1 + \frac{2}{y}\\ \mathbf{if}\;y \leq -2000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{-168}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-293}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-200}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-159}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 360000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+98}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+107}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	26.2
Cost	1120

\[\begin{array}{l} \mathbf{if}\;y \leq -25000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-173}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-293}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-195}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-159}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5200:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+87}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+107}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	16.8
Cost	848

\[\begin{array}{l} t_0 := 1 + \frac{2}{y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1960000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 380000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+98}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	16.7
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1960000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-13}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+98}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+109}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	24.4
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -3400000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 380000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+98}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+107}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	39.4
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022340 
(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))))