Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H

Average Error: 0.0 → 0.0

Time: 2.8s

Precision: binary64

Cost: 320

Math

\[x \cdot \left(1 - y\right) \]

↓

\[x - x \cdot y \]

FPCore

(FPCore (x y) :precision binary64 (* x (- 1.0 y)))

↓

(FPCore (x y) :precision binary64 (- x (* x y)))

C

double code(double x, double y) {
	return x * (1.0 - y);
}

↓

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (1.0d0 - y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - (x * y)
end function

Java

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

↓

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

Python

def code(x, y):
	return x * (1.0 - y)

↓

def code(x, y):
	return x - (x * y)

Julia

function code(x, y)
	return Float64(x * Float64(1.0 - y))
end

↓

function code(x, y)
	return Float64(x - Float64(x * y))
end

MATLAB

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

↓

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

Wolfram

code[x_, y_] := N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]

↓

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

Derivation

1. Initial program 0.0

   \[x \cdot \left(1 - y\right) \]

2. Taylor expanded in x around 0 0.0

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

3. Simplified 0.0

   \[\leadsto \color{blue}{x - y \cdot x} \]
   Proof

   [Start] 0.0	\[ \left(1 - y\right) \cdot x \]
   *-commutative [<=] 0.0	\[ \color{blue}{x \cdot \left(1 - y\right)} \]
   distribute-rgt-out-- [<=] 0.0	\[ \color{blue}{1 \cdot x - y \cdot x} \]
   *-lft-identity [=>] 0.0	\[ \color{blue}{x} - y \cdot x \]

4. Final simplification 0.0

   \[\leadsto x - x \cdot y \]

Alternatives

Alternative 1
Error	1.5
Cost	521

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

Alternative 2
Error	0.0
Cost	320

\[x \cdot \left(1 - y\right) \]

Alternative 3
Error	27.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023073 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H"
  :precision binary64
  (* x (- 1.0 y)))