Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 2.9s

Alternatives: 3

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot 2 - y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* x 2.0) y))

C

double code(double x, double y) {
	return (x * 2.0) - y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 2.0d0) - y
end function

Java

public static double code(double x, double y) {
	return (x * 2.0) - y;
}

Python

def code(x, y):
	return (x * 2.0) - y

Julia

function code(x, y)
	return Float64(Float64(x * 2.0) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 2.0) - y;
end

Wolfram

code[x_, y_] := N[(N[(x * 2.0), $MachinePrecision] - y), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 2 - y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* x 2.0) y))

C

double code(double x, double y) {
	return (x * 2.0) - y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 2.0d0) - y
end function

Java

public static double code(double x, double y) {
	return (x * 2.0) - y;
}

Python

def code(x, y):
	return (x * 2.0) - y

Julia

function code(x, y)
	return Float64(Float64(x * 2.0) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 2.0) - y;
end

Wolfram

code[x_, y_] := N[(N[(x * 2.0), $MachinePrecision] - y), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 2 - y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* x 2.0) y))

C

double code(double x, double y) {
	return (x * 2.0) - y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 2.0d0) - y
end function

Java

public static double code(double x, double y) {
	return (x * 2.0) - y;
}

Python

def code(x, y):
	return (x * 2.0) - y

Julia

function code(x, y)
	return Float64(Float64(x * 2.0) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 2.0) - y;
end

Wolfram

code[x_, y_] := N[(N[(x * 2.0), $MachinePrecision] - y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot 2 - y \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 74.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -210000000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 \leq 5.1 \cdot 10^{-53}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* x 2.0) -210000000000.0)
   (* x 2.0)
   (if (<= (* x 2.0) 5.1e-53) (- y) (* x 2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x * 2.0) <= -210000000000.0) {
		tmp = x * 2.0;
	} else if ((x * 2.0) <= 5.1e-53) {
		tmp = -y;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x * 2.0d0) <= (-210000000000.0d0)) then
        tmp = x * 2.0d0
    else if ((x * 2.0d0) <= 5.1d-53) then
        tmp = -y
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x * 2.0) <= -210000000000.0) {
		tmp = x * 2.0;
	} else if ((x * 2.0) <= 5.1e-53) {
		tmp = -y;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x * 2.0) <= -210000000000.0:
		tmp = x * 2.0
	elif (x * 2.0) <= 5.1e-53:
		tmp = -y
	else:
		tmp = x * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x * 2.0) <= -210000000000.0)
		tmp = Float64(x * 2.0);
	elseif (Float64(x * 2.0) <= 5.1e-53)
		tmp = Float64(-y);
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x * 2.0) <= -210000000000.0)
		tmp = x * 2.0;
	elseif ((x * 2.0) <= 5.1e-53)
		tmp = -y;
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x * 2.0), $MachinePrecision], -210000000000.0], N[(x * 2.0), $MachinePrecision], If[LessEqual[N[(x * 2.0), $MachinePrecision], 5.1e-53], (-y), N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < -2.1e11 or 5.10000000000000045e-53 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 100.0%

      \[x \cdot 2 - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \color{blue}{\left(2 \cdot 1\right)} \cdot x \]

      2. *-inverses N/A

         \[\leadsto \left(2 \cdot \color{blue}{\frac{y}{y}}\right) \cdot x \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\frac{2 \cdot y}{y}} \cdot x \]

      4. associate-*l/ N/A

         \[\leadsto \color{blue}{\left(\frac{2}{y} \cdot y\right)} \cdot x \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \left(\frac{2}{y} \cdot y\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\frac{2}{y} \cdot y\right)} \]

      7. associate-*l/ N/A

         \[\leadsto x \cdot \color{blue}{\frac{2 \cdot y}{y}} \]

      8. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\left(2 \cdot \frac{y}{y}\right)} \]

      9. *-inverses N/A

         \[\leadsto x \cdot \left(2 \cdot \color{blue}{1}\right) \]

      10. metadata-eval 79.9

          \[\leadsto x \cdot \color{blue}{2} \]

   5. Simplified 79.9%

      \[\leadsto \color{blue}{x \cdot 2} \]

   if -2.1e11 < (*.f64 x #s(literal 2 binary64)) < 5.10000000000000045e-53

   1. Initial program 100.0%

      \[x \cdot 2 - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 82.8

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

   5. Simplified 82.8%

      \[\leadsto \color{blue}{-y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 50.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ -y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -y

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := (-y)

Derivation

1. Initial program 100.0%

   \[x \cdot 2 - y \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

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

   2. neg-lowering-neg.f64 50.1

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

5. Simplified 50.1%

   \[\leadsto \color{blue}{-y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024205 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, C"
  :precision binary64
  (- (* x 2.0) y))