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

Percentage Accurate: 100.0% → 100.0%

Time: 4.0s

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 97.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -x \cdot y\\ \mathbf{if}\;1 - y \leq -4000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - y \leq 2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (* x y))))
   (if (<= (- 1.0 y) -4000.0) t_0 (if (<= (- 1.0 y) 2.0) x t_0))))

C

double code(double x, double y) {
	double t_0 = -(x * y);
	double tmp;
	if ((1.0 - y) <= -4000.0) {
		tmp = t_0;
	} else if ((1.0 - y) <= 2.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -(x * y)
    if ((1.0d0 - y) <= (-4000.0d0)) then
        tmp = t_0
    else if ((1.0d0 - y) <= 2.0d0) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = -(x * y);
	double tmp;
	if ((1.0 - y) <= -4000.0) {
		tmp = t_0;
	} else if ((1.0 - y) <= 2.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -(x * y)
	tmp = 0
	if (1.0 - y) <= -4000.0:
		tmp = t_0
	elif (1.0 - y) <= 2.0:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-Float64(x * y))
	tmp = 0.0
	if (Float64(1.0 - y) <= -4000.0)
		tmp = t_0;
	elseif (Float64(1.0 - y) <= 2.0)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -(x * y);
	tmp = 0.0;
	if ((1.0 - y) <= -4000.0)
		tmp = t_0;
	elseif ((1.0 - y) <= 2.0)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = (-N[(x * y), $MachinePrecision])}, If[LessEqual[N[(1.0 - y), $MachinePrecision], -4000.0], t$95$0, If[LessEqual[N[(1.0 - y), $MachinePrecision], 2.0], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -4e3 or 2 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 100.0%

      \[x \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 98.1

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

   5. Applied rewrites 98.1%

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

   if -4e3 < (-.f64 #s(literal 1 binary64) y) < 2

   1. Initial program 100.0%

      \[x \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto x \cdot \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.2%

      \[\leadsto x \cdot \color{blue}{1} \]
   6. Step-by-step derivation

      1. *-rgt-identity 98.2

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

   7. Applied rewrites 98.2%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -4000:\\ \;\;\;\;-x \cdot y\\ \mathbf{elif}\;1 - y \leq 2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.8% accurate, 9.0× 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. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto x \cdot \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 55.5%

   \[\leadsto x \cdot \color{blue}{1} \]
6. Step-by-step derivation

   1. *-rgt-identity 55.5

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

7. Applied rewrites 55.5%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024219 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H"
  :precision binary64
  (* x (- 1.0 y)))