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

Average Error: 0.0 → 0.0

Time: 2.5s

Precision: binary64

Cost: 448

Math

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

↓

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

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(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 = (x + y) - (x * y);
end

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	19.8
Cost	848

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-116}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 2
Error	25.7
Cost	784

\[\begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	19.5
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{-136}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-117}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 4
Error	19.5
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{-135}:\\ \;\;\;\;x + x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-117}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5
Error	27.9
Cost	460

\[\begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-117}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6
Error	35.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023094 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))