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

Average Error: 0.04% → 0.04%

Time: 4.1s

Precision: binary64

Cost: 576

Math

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

↓

\[\frac{1}{\frac{x + y}{x - y}} \]

FPCore

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

↓

(FPCore (x y) :precision binary64 (/ 1.0 (/ (+ x y) (- x y))))

C

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

↓

double code(double x, double y) {
	return 1.0 / ((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 = 1.0d0 / ((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 1.0 / ((x + y) / (x - y));
}

Python

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

↓

def code(x, y):
	return 1.0 / ((x + y) / (x - y))

Julia

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

↓

function code(x, y)
	return Float64(1.0 / 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 = 1.0 / ((x + y) / (x - y));
end

Wolfram

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

↓

code[x_, y_] := N[(1.0 / N[(N[(x + y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $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. Applied egg-rr 0.03

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

3. Applied egg-rr 0.04

   \[\leadsto \color{blue}{\frac{1}{\frac{x + y}{x - y}}} \]

4. Final simplification 0.04

   \[\leadsto \frac{1}{\frac{x + y}{x - y}} \]

Alternatives

Alternative 1
Error	26.32%
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-95}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-71}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 500000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+56}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+85}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	25.82%
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+45}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-95}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-71}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 340000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+56}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+83}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	0.04%
Cost	448

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

Alternative 4
Error	49.47%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023093 
(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)))