Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A

Average Accuracy: 100.0% → 100.0%

Time: 2.8s

Precision: binary64

Cost: 448

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

\[\left(x + y\right) - x \cdot y \]

↓

\[x + \left(y - x \cdot y\right) \]

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(x + Float64(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[(x + N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]

2. Simplified 100.0%

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

   [Start] 100.0	\[ \left(x + y\right) - x \cdot y \]
   associate--l+ [=>] 100.0	\[ \color{blue}{x + \left(y - x \cdot y\right)} \]

3. Final simplification 100.0%

   \[\leadsto x + \left(y - x \cdot y\right) \]

Alternatives

Alternative 1
Accuracy	99.3%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-26}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \]

Alternative 2
Accuracy	98.6%
Cost	520

\[\begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 280000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3
Accuracy	88.0%
Cost	388

\[\begin{array}{l} \mathbf{if}\;x \leq 290000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 4
Accuracy	73.0%
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5
Accuracy	85.2%
Cost	192

\[x + y \]

Alternative 6
Accuracy	44.2%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023146 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))