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

Average Error: 0.0 → 0.0

Time: 8.6s

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	23.7
Cost	1112

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1600000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-69}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-43}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+16}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+53}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+74}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	16.2
Cost	976

\[\begin{array}{l} \mathbf{if}\;y \leq -1350000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+53}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-1}{y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+70}:\\ \;\;\;\;-1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 3
Error	16.4
Cost	976

\[\begin{array}{l} t_0 := 1 + -2 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -700000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+53}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+87}:\\ \;\;\;\;-1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	23.9
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -1150000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-69}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-41}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+14}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+74}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	16.2
Cost	848

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1600000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+53}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+77}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	16.2
Cost	848

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1350000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+53}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+72}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	16.2
Cost	848

\[\begin{array}{l} \mathbf{if}\;y \leq -1600000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+53}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-1}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+74}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 8
Error	23.9
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -1600000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+78}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9
Error	39.3
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022325 
(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))))