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

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 4

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: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -2 \cdot 10^{-9} \lor \neg \left(x \cdot 2 \leq 4 \cdot 10^{-5}\right):\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (* x 2.0) -2e-9) (not (<= (* x 2.0) 4e-5))) (* 2.0 x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (((x * 2.0) <= -2e-9) || !((x * 2.0) <= 4e-5)) {
		tmp = 2.0 * x;
	} else {
		tmp = -y;
	}
	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) <= (-2d-9)) .or. (.not. ((x * 2.0d0) <= 4d-5))) then
        tmp = 2.0d0 * x
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x * 2.0) <= -2e-9) || !((x * 2.0) <= 4e-5)) {
		tmp = 2.0 * x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x * 2.0) <= -2e-9) or not ((x * 2.0) <= 4e-5):
		tmp = 2.0 * x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(x * 2.0) <= -2e-9) || !(Float64(x * 2.0) <= 4e-5))
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x * 2.0) <= -2e-9) || ~(((x * 2.0) <= 4e-5)))
		tmp = 2.0 * x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(x * 2.0), $MachinePrecision], -2e-9], N[Not[LessEqual[N[(x * 2.0), $MachinePrecision], 4e-5]], $MachinePrecision]], N[(2.0 * x), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < -2.00000000000000012e-9 or 4.00000000000000033e-5 < (*.f64 x #s(literal 2 binary64))

   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. lower-neg.f64 24.7

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

   5. Applied rewrites 24.7%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 76.6

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

   8. Applied rewrites 76.6%

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

   if -2.00000000000000012e-9 < (*.f64 x #s(literal 2 binary64)) < 4.00000000000000033e-5

   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. lower-neg.f64 79.8

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

   5. Applied rewrites 79.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -2 \cdot 10^{-9} \lor \neg \left(x \cdot 2 \leq 4 \cdot 10^{-5}\right):\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.1% 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. lower-neg.f64 53.1

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

5. Applied rewrites 53.1%

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

Alternative 4: 2.3% accurate, 9.0× 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 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. lower-neg.f64 53.1

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

5. Applied rewrites 53.1%

   \[\leadsto \color{blue}{-y} \]
6. Step-by-step derivation

7. Applied rewrites 2.4%

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

Reproduce

herbie shell --seed 2024318 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, C"
  :precision binary64
  (- (* x 2.0) y))