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

Average Error: 0.0 → 0.0

Time: 6.7s

Precision: binary64

Cost: 320

Math

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

↓

\[x - y \cdot x \]

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 * 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. Taylor expanded in x around 0 0.0

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

5. Simplified 0.0

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

   [Start] 0.0	\[ \left(1 + -1 \cdot y\right) \cdot x \]
   rational.json-simplify-2 [=>] 0.0	\[ \color{blue}{x \cdot \left(1 + -1 \cdot y\right)} \]
   rational.json-simplify-2 [=>] 0.0	\[ x \cdot \left(1 + \color{blue}{y \cdot -1}\right) \]
   rational.json-simplify-8 [<=] 0.0	\[ x \cdot \left(1 + \color{blue}{\left(-y\right)}\right) \]
   rational.json-simplify-17 [=>] 0.0	\[ x \cdot \color{blue}{\left(\left(-y\right) - -1\right)} \]
   rational.json-simplify-12 [=>] 0.0	\[ x \cdot \left(\color{blue}{\left(0 - y\right)} - -1\right) \]
   rational.json-simplify-42 [=>] 0.0	\[ x \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)} \]
   metadata-eval [=>] 0.0	\[ x \cdot \left(\color{blue}{1} - y\right) \]
   rational.json-simplify-52 [<=] 0.0	\[ \color{blue}{x \cdot 1 - y \cdot x} \]
   rational.json-simplify-2 [=>] 0.0	\[ \color{blue}{1 \cdot x} - y \cdot x \]
   rational.json-simplify-6 [=>] 0.0	\[ \color{blue}{x} - y \cdot x \]

6. Final simplification 0.0

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

Alternatives

Alternative 1
Error	1.6
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	27.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023075 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H"
  :precision binary64
  (* x (- 1.0 y)))