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

Average Error: 0.04% → 0.04%

Time: 7.9s

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	0.04%
Target	0.03%
Herbie	0.04%

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

Derivation

1. Initial program 0.04

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

2. Final simplification 0.04

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

Alternatives

Alternative 1
Error	25.71%
Cost	978

\[\begin{array}{l} \mathbf{if}\;x \leq -0.0005 \lor \neg \left(x \leq 8.2 \cdot 10^{-61} \lor \neg \left(x \leq 8.4 \cdot 10^{-33}\right) \land x \leq 0.0022\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 2
Error	25.31%
Cost	977

\[\begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{-7}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-61}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-33} \lor \neg \left(x \leq 4.5 \cdot 10^{-8}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3
Error	25.66%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -0.00022:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-6}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	50.46%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023115 
(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)))