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

Average Error: 0.0 → 0.0

Time: 4.8s

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	16.5
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-43} \lor \neg \left(y \leq 2.6 \cdot 10^{-58}\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]

Alternative 2
Error	16.4
Cost	649

\[\begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-25} \lor \neg \left(y \leq 2.6 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]

Alternative 3
Error	16.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-23}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	16.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-21}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-55}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5
Error	17.0
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-40}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-53}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6
Error	31.9
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023073 
(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)))