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

Percentage Accurate: 100.0% → 100.0%

Time: 2.3s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{+246}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+210}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -5e+246)
     x
     (if (<= x -5.2e+210) t_0 (if (<= x -4.2e-85) x (if (<= x 1.0) y t_0))))))

C

double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -5e+246) {
		tmp = x;
	} else if (x <= -5.2e+210) {
		tmp = t_0;
	} else if (x <= -4.2e-85) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} 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 (x <= (-5d+246)) then
        tmp = x
    else if (x <= (-5.2d+210)) then
        tmp = t_0
    else if (x <= (-4.2d-85)) then
        tmp = x
    else if (x <= 1.0d0) then
        tmp = y
    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 (x <= -5e+246) {
		tmp = x;
	} else if (x <= -5.2e+210) {
		tmp = t_0;
	} else if (x <= -4.2e-85) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * -y
	tmp = 0
	if x <= -5e+246:
		tmp = x
	elif x <= -5.2e+210:
		tmp = t_0
	elif x <= -4.2e-85:
		tmp = x
	elif x <= 1.0:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (x <= -5e+246)
		tmp = x;
	elseif (x <= -5.2e+210)
		tmp = t_0;
	elseif (x <= -4.2e-85)
		tmp = x;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * -y;
	tmp = 0.0;
	if (x <= -5e+246)
		tmp = x;
	elseif (x <= -5.2e+210)
		tmp = t_0;
	elseif (x <= -4.2e-85)
		tmp = x;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[x, -5e+246], x, If[LessEqual[x, -5.2e+210], t$95$0, If[LessEqual[x, -4.2e-85], x, If[LessEqual[x, 1.0], y, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.99999999999999976e246 or -5.1999999999999998e210 < x < -4.2e-85

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 58.9%

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

   if -4.99999999999999976e246 < x < -5.1999999999999998e210 or 1 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 98.1%

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

   3. Taylor expanded in y around inf 55.1%

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

      1. mul-1-neg 55.1%

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

      2. distribute-rgt-neg-out 55.1%

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

   5. Simplified 55.1%

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

   if -4.2e-85 < x < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+246}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+210}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-85} \lor \neg \left(x \leq 0.028\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.3e-85) (not (<= x 0.028))) (* x (- 1.0 y)) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.3e-85) || !(x <= 0.028)) {
		tmp = x * (1.0 - y);
	} 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 <= (-4.3d-85)) .or. (.not. (x <= 0.028d0))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.3e-85) || !(x <= 0.028)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.3e-85) or not (x <= 0.028):
		tmp = x * (1.0 - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.3e-85) || !(x <= 0.028))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.3e-85) || ~((x <= 0.028)))
		tmp = x * (1.0 - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.3e-85], N[Not[LessEqual[x, 0.028]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -4.29999999999999999e-85 or 0.0280000000000000006 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 96.9%

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

   if -4.29999999999999999e-85 < x < 0.0280000000000000006

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.8%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-85} \lor \neg \left(x \leq 0.028\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.2e-85) (* x (- 1.0 y)) (- y (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.2e-85) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y - (x * 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 <= (-4.2d-85)) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y - (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.2e-85) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.2e-85:
		tmp = x * (1.0 - y)
	else:
		tmp = y - (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.2e-85)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.2e-85)
		tmp = x * (1.0 - y);
	else
		tmp = y - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.2e-85], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2e-85

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 97.3%

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

   if -4.2e-85 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 69.4%

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

      1. distribute-lft-out-- 69.4%

         \[\leadsto \color{blue}{y \cdot 1 - y \cdot x} \]

      2. *-rgt-identity 69.4%

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

   4. Simplified 69.4%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \]

Alternative 5: 49.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -1.25e-85) x y))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.25e-85) {
		tmp = 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 <= (-1.25d-85)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.25e-85) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.25e-85:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.25e-85)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.25e-85)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.25e-85], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e-85

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 55.6%

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

   if -1.25e-85 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 49.5%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6: 38.9% accurate, 7.0× 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%

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

2. Taylor expanded in y around 0 39.2%

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

3. Final simplification 39.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023242 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))