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

Average Error: 0.0 → 0.0

Time: 25.5s

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	17.2
Cost	1112

\[\begin{array}{l} t_0 := --0.5 \cdot x\\ t_1 := \frac{y}{x} - 1\\ t_2 := \frac{y}{y - 2}\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-49}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+83}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	17.2
Cost	1112

\[\begin{array}{l} t_0 := --0.5 \cdot x\\ t_1 := \frac{y}{y - 2}\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+41}:\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.85 \cdot 10^{-46}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+88}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} - 1\\ \end{array} \]

Alternative 3
Error	17.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+85}:\\ \;\;\;\;-\frac{x}{x - 2}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y} \cdot -2\\ \end{array} \]

Alternative 4
Error	24.8
Cost	652

\[\begin{array}{l} \mathbf{if}\;y \leq -7100000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-265}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-275}:\\ \;\;\;\;--0.5 \cdot x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+85}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	24.7
Cost	652

\[\begin{array}{l} \mathbf{if}\;y \leq -2000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-260}:\\ \;\;\;\;\frac{y}{x} - 1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-275}:\\ \;\;\;\;--0.5 \cdot x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+85}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	17.0
Cost	648

\[\begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+86}:\\ \;\;\;\;-\frac{x}{x - 2}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	24.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -510000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+85}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	39.2
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023064 
(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))))