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

Average Error: 0.0 → 0.0

Time: 4.9s

Precision: binary64

Cost: 384

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 + (y * -x)
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 + (y * -x);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Taylor expanded in y around 0 0.0

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

3. Simplified 0.0

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

   [Start] 0.0	\[ -1 \cdot \left(y \cdot x\right) + x \]
   rational.json-simplify-1 [=>] 0.0	\[ \color{blue}{x + -1 \cdot \left(y \cdot x\right)} \]
   rational.json-simplify-43 [=>] 0.0	\[ x + \color{blue}{y \cdot \left(x \cdot -1\right)} \]
   rational.json-simplify-9 [=>] 0.0	\[ x + y \cdot \color{blue}{\left(-x\right)} \]

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	1.4
Cost	520

\[\begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.0
Cost	320

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

Alternative 3
Error	26.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023068 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H"
  :precision binary64
  (* x (- 1.0 y)))