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

Average Error: 0.0 → 0.0

Time: 8.0s

Precision: binary64

Cost: 576

Math

\[\frac{x - y}{2 - \left(x + y\right)} \]

↓

\[\frac{x - y}{\left(2 - x\right) - y} \]

FPCore

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

↓

(FPCore (x y) :precision binary64 (/ (- x y) (- (- 2.0 x) y)))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

↓

double code(double x, double y) {
	return (x - y) / ((2.0 - x) - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / ((2.0d0 - x) - y)
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

↓

public static double code(double x, double y) {
	return (x - y) / ((2.0 - x) - y);
}

Python

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

↓

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

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

↓

function code(x, y)
	return Float64(Float64(x - y) / Float64(Float64(2.0 - x) - y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

↓

function tmp = code(x, y)
	tmp = (x - y) / ((2.0 - x) - y);
end

Wolfram

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

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)} \]

Derivation

1. Initial program 0.0

   \[\frac{x - y}{2 - \left(x + y\right)} \]

2. Simplified 0.0

   \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]
   Proof
   (/.f64 (-.f64 x y) (-.f64 (-.f64 2 x) y)): 0 points increase in error, 0 points decrease in error
   (/.f64 (-.f64 x y) (Rewrite<= associate--r+_binary64 (-.f64 2 (+.f64 x y)))): 0 points increase in error, 0 points decrease in error

3. Final simplification 0.0

   \[\leadsto \frac{x - y}{\left(2 - x\right) - y} \]

Alternatives

Alternative 1
Error	25.3
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3331169617255747 \cdot 10^{+38}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.3726830097278183 \cdot 10^{-104}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.295156052286724 \cdot 10^{-170}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.2114677715770131 \cdot 10^{-206}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.4947595255381554 \cdot 10^{-291}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.304110283995504 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 2
Error	25.7
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -6.953982642352497 \cdot 10^{+78}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.3726830097278183 \cdot 10^{-104}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq -5.295156052286724 \cdot 10^{-170}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.2114677715770131 \cdot 10^{-206}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.4947595255381554 \cdot 10^{-291}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.304110283995504 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3
Error	24.6
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3331169617255747 \cdot 10^{+38}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.3726830097278183 \cdot 10^{-104}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.295156052286724 \cdot 10^{-170}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 4.304110283995504 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	16.4
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2611519542071663 \cdot 10^{+82}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.538231839633215 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	23.6
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3331169617255747 \cdot 10^{+38}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 4.304110283995504 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6
Error	39.6
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022295 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

  (/ (- x y) (- 2.0 (+ x y))))