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

Average Error: 0.0 → 0.0

Time: 11.9s

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	0.0
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	18.5
Cost	1240

\[\begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+44}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-105}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-187}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-151}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 0.036:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 2
Error	18.0
Cost	1240

\[\begin{array}{l} t_0 := 2 \cdot \frac{x}{y} - 1\\ t_1 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-105}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-151}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 0.054:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	18.8
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+43}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-105}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-187}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-151}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 0.122:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	32.1
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023077 
(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)))