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

Average Error: 0.0 → 0.0

Time: 8.8s

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	26.5
Cost	1112

\[\begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -1.16 \cdot 10^{+109}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-297}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-143}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+45}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	18.3
Cost	976

\[\begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+108}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-19}:\\ \;\;\;\;-2 \cdot \frac{x}{y} + 1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{x}{x - y}}\\ \end{array} \]

Alternative 3
Error	26.6
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+108}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-298}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-143}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	18.2
Cost	848

\[\begin{array}{l} t_0 := \frac{y}{x} + -1\\ t_1 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	18.2
Cost	848

\[\begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-18}:\\ \;\;\;\;-2 \cdot \frac{x}{y} + 1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	9.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+107}:\\ \;\;\;\;\frac{y - x}{x + -2}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{y} + 1\\ \end{array} \]

Alternative 7
Error	26.1
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+108}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-299}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-143}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 10^{+41}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8
Error	17.3
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-14}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+107}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9
Error	25.3
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+107}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10
Error	39.1
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023031 
(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))))