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

Average Error: 0.0 → 0.0

Time: 11.5s

Precision: binary64

Cost: 704

Math

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

↓

\[0.5 \cdot \frac{2}{\frac{x + y}{x - y}} \]

FPCore

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

↓

(FPCore (x y) :precision binary64 (* 0.5 (/ 2.0 (/ (+ x y) (- x y)))))

C

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

↓

double code(double x, double y) {
	return 0.5 * (2.0 / ((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 = 0.5d0 * (2.0d0 / ((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 0.5 * (2.0 / ((x + y) / (x - y)));
}

Python

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

↓

def code(x, y):
	return 0.5 * (2.0 / ((x + y) / (x - y)))

Julia

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

↓

function code(x, y)
	return Float64(0.5 * Float64(2.0 / 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 = 0.5 * (2.0 / ((x + y) / (x - y)));
end

Wolfram

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

↓

code[x_, y_] := N[(0.5 * N[(2.0 / N[(N[(x + y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $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 0.2

   \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(\frac{2}{x + y} \cdot 0.5\right)} \]

3. Simplified 0.0

   \[\leadsto \color{blue}{0.5 \cdot \frac{2}{\frac{x + y}{x - y}}} \]
   Proof

   [Start] 0.2	\[ \left(x - y\right) \cdot \left(\frac{2}{x + y} \cdot 0.5\right) \]
   rational.json-simplify-43 [<=] 0.2	\[ \color{blue}{0.5 \cdot \left(\left(x - y\right) \cdot \frac{2}{x + y}\right)} \]
   rational.json-simplify-2 [=>] 0.2	\[ 0.5 \cdot \color{blue}{\left(\frac{2}{x + y} \cdot \left(x - y\right)\right)} \]
   rational.json-simplify-7 [<=] 0.2	\[ 0.5 \cdot \left(\frac{2}{x + y} \cdot \color{blue}{\frac{x - y}{1}}\right) \]
   rational.json-simplify-35 [=>] 0.2	\[ 0.5 \cdot \left(\frac{2}{x + y} \cdot \color{blue}{\frac{\left(x - y\right) + \left(x - y\right)}{1 + 1}}\right) \]
   metadata-eval [=>] 0.2	\[ 0.5 \cdot \left(\frac{2}{x + y} \cdot \frac{\left(x - y\right) + \left(x - y\right)}{\color{blue}{2}}\right) \]
   rational.json-simplify-55 [=>] 0.1	\[ 0.5 \cdot \color{blue}{\frac{\frac{\left(x - y\right) + \left(x - y\right)}{2}}{\frac{x + y}{2}}} \]
   metadata-eval [<=] 0.1	\[ 0.5 \cdot \frac{\frac{\left(x - y\right) + \left(x - y\right)}{\color{blue}{1 + 1}}}{\frac{x + y}{2}} \]
   rational.json-simplify-35 [<=] 0.0	\[ 0.5 \cdot \frac{\color{blue}{\frac{x - y}{1}}}{\frac{x + y}{2}} \]
   rational.json-simplify-7 [=>] 0.0	\[ 0.5 \cdot \frac{\color{blue}{x - y}}{\frac{x + y}{2}} \]
   rational.json-simplify-61 [<=] 0.0	\[ 0.5 \cdot \color{blue}{\frac{2}{\frac{x + y}{x - y}}} \]

4. Final simplification 0.0

   \[\leadsto 0.5 \cdot \frac{2}{\frac{x + y}{x - y}} \]

Alternatives

Alternative 1
Error	17.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-87}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+51}:\\ \;\;\;\;2 \cdot \frac{x}{y} - 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

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

Alternative 3
Error	17.7
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-113}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-11}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	32.4
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023064 
(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)))