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

Average Error: 0.0 → 0.0

Time: 4.9s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

↓

(FPCore (x y) :precision binary64 (/ (- y x) (+ x (+ y -2.0))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

↓

double code(double x, double y) {
	return (y - x) / (x + (y + -2.0));
}

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 = (y - x) / (x + (y + (-2.0d0)))
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 (y - x) / (x + (y + -2.0));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

↓

def code(x, y):
	return (y - x) / (x + (y + -2.0))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

↓

function code(x, y)
	return Float64(Float64(y - x) / Float64(x + Float64(y + -2.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

↓

function tmp = code(x, y)
	tmp = (y - x) / (x + (y + -2.0));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(y - x), $MachinePrecision] / N[(x + N[(y + -2.0), $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. Simplified 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	24.4
Cost	1120

\[\begin{array}{l} \mathbf{if}\;y \leq -16355550156891718000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.918615875692638 \cdot 10^{-37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -2.773410947853966 \cdot 10^{-93}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.0699897488965047 \cdot 10^{-254}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.741623447643691 \cdot 10^{-217}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.4553254199924398 \cdot 10^{-115}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.818163037642012 \cdot 10^{-101}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2007864049760.6697:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	24.5
Cost	1120

\[\begin{array}{l} \mathbf{if}\;y \leq -16355550156891718000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.918615875692638 \cdot 10^{-37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -2.773410947853966 \cdot 10^{-93}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.0699897488965047 \cdot 10^{-254}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.741623447643691 \cdot 10^{-217}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.4553254199924398 \cdot 10^{-115}:\\ \;\;\;\;-1 + \frac{-2}{x}\\ \mathbf{elif}\;y \leq 2.818163037642012 \cdot 10^{-101}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2007864049760.6697:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	16.2
Cost	648

\[\begin{array}{l} \mathbf{if}\;y \leq -16355550156891718000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.453985928303849 \cdot 10^{-12}:\\ \;\;\;\;\frac{-x}{x + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 4
Error	23.6
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -5.196111697622329 \cdot 10^{+21}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 8.671891842374942 \cdot 10^{-47}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.1420223754637673 \cdot 10^{-18}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 66765214.38599782:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5
Error	16.1
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -5.196111697622329 \cdot 10^{+21}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 8.671891842374942 \cdot 10^{-47}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq 2.1420223754637673 \cdot 10^{-18}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 66765214.38599782:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6
Error	23.6
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -5.196111697622329 \cdot 10^{+21}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 66765214.38599782:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7
Error	39.7
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022228 
(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))))