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

Average Error: 0.0 → 0.0

Time: 28.6s

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

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

Alternatives

Alternative 1
Error	17.3
Cost	1304

\[\begin{array}{l} t_0 := \frac{y}{y - 2}\\ t_1 := 1 + \left(-\frac{x + x}{y}\right)\\ \mathbf{if}\;y \leq -270000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+53}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.76 \cdot 10^{+81}:\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+154}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	17.4
Cost	1240

\[\begin{array}{l} t_0 := \frac{y}{y - 2}\\ t_1 := \frac{-1}{y} \cdot \left(x - y\right)\\ \mathbf{if}\;y \leq -1550000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+55}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+80}:\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+154}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	17.4
Cost	980

\[\begin{array}{l} t_0 := \frac{y}{y - 2}\\ \mathbf{if}\;y \leq -1620000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+80}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+150}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+154}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	17.4
Cost	980

\[\begin{array}{l} t_0 := \frac{y}{y - 2}\\ \mathbf{if}\;y \leq -3100000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 4.55 \cdot 10^{+55}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+150}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+154}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	25.5
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -10000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-151}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-23}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+80}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+149}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+154}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	24.7
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -10000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{+82}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+150}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+154}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	16.8
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -1620000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+150}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+154}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	39.6
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023010 
(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))))