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

Average Error: 0.03% → 0.03%

Time: 5.4s

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	0.03%
Target	0.03%
Herbie	0.03%

\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)} \]

Derivation

1. Initial program 0.03

   \[\frac{x - y}{2 - \left(x + y\right)} \]

2. Final simplification 0.03

   \[\leadsto \frac{x - y}{2 - \left(x + y\right)} \]

Alternatives

Alternative 1
Error	40.43%
Cost	1252

\[\begin{array}{l} \mathbf{if}\;x \leq -2:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-40}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{-119}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-209}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-276}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-302}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-84}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 2
Error	27.77%
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -500000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-25}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+119}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	26.33%
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ t_1 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-38}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	37.69%
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -740000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-274}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-303}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5
Error	37.67%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -650000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6
Error	61.78%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023115 
(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))))