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

Percentage Accurate: 100.0% → 100.0%

Time: 1.8s

Alternatives: 3

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 98.0% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0))) (- (* x y)) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = -(x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = -(x * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = -(x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.0):
		tmp = -(x * y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(-Float64(x * y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = -(x * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], (-N[(x * y), $MachinePrecision]), x]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot x\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 99.6%

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

      2. distribute-rgt-neg-in 99.6%

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

   4. Simplified 99.6%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

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

Alternative 3: 51.4% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0 46.3%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 46.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023196 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H"
  :precision binary64
  (* x (- 1.0 y)))