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

Average Error: 0.0 → 0.0

Time: 16.9s

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	25.3
Cost	1376

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+79}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.85 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{+21}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-72}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+24}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+80}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+125}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 2
Error	17.4
Cost	1112

\[\begin{array}{l} t_0 := \frac{y}{y - 2}\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+90}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+23}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+85}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+125}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3
Error	25.0
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+24}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-45}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-73}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+24}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+80}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+125}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	16.9
Cost	848

\[\begin{array}{l} t_0 := \frac{y - x}{x}\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+84}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+125}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	24.7
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -4500000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+24}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+85}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+125}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6
Error	16.0
Cost	584

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 92000000000000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	39.9
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023074 
(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))))