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

Average Error: 0.0 → 0.0

Time: 12.6s

Precision: binary64

Cost: 448

Math

\[\frac{x - y}{x + y} \]

↓

\[\frac{x - y}{x + y} \]

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (x + y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (x + y)
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\frac{x}{x + y} - \frac{y}{x + y} \]

Derivation

1. Initial program 0.0

   \[\frac{x - y}{x + y} \]

2. Final simplification 0.0

   \[\leadsto \frac{x - y}{x + y} \]

Alternatives

Alternative 1
Error	17.7
Cost	976

\[\begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+87}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-48}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-30}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 2
Error	17.4
Cost	976

\[\begin{array}{l} t_0 := 2 \cdot \frac{x}{y} - 1\\ t_1 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	17.5
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -95000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 10^{-113}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{-47}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-28}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	31.9
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023075 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

  (/ (- x y) (+ x y)))