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

Average Error: 0.0 → 0.0

Time: 8.4s

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	0.0
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	26.0
Cost	1112

\[\begin{array}{l} t_0 := 1 + \frac{2}{y}\\ \mathbf{if}\;x \leq -7 \cdot 10^{-15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-261}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-279}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-11}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 2
Error	16.1
Cost	976

\[\begin{array}{l} t_0 := 1 + \frac{x \cdot -2}{y}\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 4600:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+44}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	25.9
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-263}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-280}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-13}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	16.4
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+76}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+67}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	25.2
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-262}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-279}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 10^{+18}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6
Error	16.3
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+76}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	24.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8
Error	39.3
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022338 
(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))))