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

Average Error: 0.0 → 0.0

Time: 4.3s

Precision: binary64

Cost: 1600

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x - y}{x + y}\\ \frac{1}{t_0} \cdot \left(t_0 \cdot t_0\right) \end{array} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (+ x y)))) (* (/ 1.0 t_0) (* t_0 t_0))))

C

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

↓

double code(double x, double y) {
	double t_0 = (x - y) / (x + y);
	return (1.0 / t_0) * (t_0 * t_0);
}

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
    real(8) :: t_0
    t_0 = (x - y) / (x + y)
    code = (1.0d0 / t_0) * (t_0 * t_0)
end function

Java

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

↓

public static double code(double x, double y) {
	double t_0 = (x - y) / (x + y);
	return (1.0 / t_0) * (t_0 * t_0);
}

Python

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

↓

def code(x, y):
	t_0 = (x - y) / (x + y)
	return (1.0 / t_0) * (t_0 * t_0)

Julia

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

↓

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(x + y))
	return Float64(Float64(1.0 / t_0) * Float64(t_0 * t_0))
end

MATLAB

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

↓

function tmp = code(x, y)
	t_0 = (x - y) / (x + y);
	tmp = (1.0 / t_0) * (t_0 * t_0);
end

Wolfram

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

↓

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(1.0 / t$95$0), $MachinePrecision] * N[(t$95$0 * t$95$0), $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. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\frac{1}{\frac{x - y}{x + y}} \cdot \left(\frac{x - y}{x + y} \cdot \frac{x - y}{x + y}\right)} \]

3. Final simplification 0.0

   \[\leadsto \frac{1}{\frac{x - y}{x + y}} \cdot \left(\frac{x - y}{x + y} \cdot \frac{x - y}{x + y}\right) \]

Alternatives

Alternative 1
Error	17.4
Cost	976

\[\begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+77}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -27500000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	17.0
Cost	976

\[\begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ t_1 := 2 \cdot \frac{x}{y} - 1\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+77}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -20000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 330000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	17.8
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+80}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -200000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-78}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 30000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	0.0
Cost	448

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

Alternative 5
Error	32.0
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023088 
(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)))