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

Percentage Accurate: 100.0% → 100.0%

Time: 4.0s

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+250}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -1.4e+250) t_0 (if (<= x -4.5e-66) x (if (<= x 1.0) y t_0)))))

C

double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -1.4e+250) {
		tmp = t_0;
	} else if (x <= -4.5e-66) {
		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 <= (-1.4d+250)) then
        tmp = t_0
    else if (x <= (-4.5d-66)) 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 <= -1.4e+250) {
		tmp = t_0;
	} else if (x <= -4.5e-66) {
		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 <= -1.4e+250:
		tmp = t_0
	elif x <= -4.5e-66:
		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 <= -1.4e+250)
		tmp = t_0;
	elseif (x <= -4.5e-66)
		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 <= -1.4e+250)
		tmp = t_0;
	elseif (x <= -4.5e-66)
		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, -1.4e+250], t$95$0, If[LessEqual[x, -4.5e-66], x, If[LessEqual[x, 1.0], y, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.40000000000000005e250 or 1 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in y around inf 57.7%

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

      1. associate-*r* 57.7%

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

      2. neg-mul-1 57.7%

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

      3. *-commutative 57.7%

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

   6. Simplified 57.7%

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

   if -1.40000000000000005e250 < x < -4.4999999999999998e-66

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 97.1%

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

   4. Taylor expanded in y around 0 57.5%

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

   if -4.4999999999999998e-66 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.7%

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

   4. Taylor expanded in x around 0 83.2%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+250}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-66}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.8e-66) (- x (* x y)) (if (<= x 1.0) y (* x (- y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.8e-66) {
		tmp = x - (x * y);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = 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 <= (-6.8d-66)) then
        tmp = x - (x * y)
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.8e-66) {
		tmp = x - (x * y);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.8e-66:
		tmp = x - (x * y)
	elif x <= 1.0:
		tmp = y
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.8e-66)
		tmp = Float64(x - Float64(x * y));
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.8e-66)
		tmp = x - (x * y);
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.8e-66], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], y, N[(x * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.79999999999999994e-66

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.0%

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

   if -6.79999999999999994e-66 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.7%

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

   4. Taylor expanded in x around 0 83.2%

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

   if 1 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in y around inf 55.1%

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

      1. associate-*r* 55.1%

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

      2. neg-mul-1 55.1%

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

      3. *-commutative 55.1%

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

   6. Simplified 55.1%

      \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-66}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-65}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7e-65) (- x (* x y)) (- y (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7e-65) {
		tmp = x - (x * 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 <= (-7d-65)) then
        tmp = x - (x * 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 <= -7e-65) {
		tmp = x - (x * y);
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7e-65:
		tmp = x - (x * y)
	else:
		tmp = y - (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7e-65)
		tmp = Float64(x - Float64(x * y));
	else
		tmp = Float64(y - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7e-65)
		tmp = x - (x * y);
	else
		tmp = y - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7e-65], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.00000000000000009e-65

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.0%

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

   if -7.00000000000000009e-65 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.9%

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

Alternative 5: 49.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -2.3e-65) x y))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3e-65) {
		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 <= (-2.3d-65)) 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 <= -2.3e-65) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3e-65:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3e-65)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3e-65)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3e-65], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e-65

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 97.6%

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

   4. Taylor expanded in y around 0 52.9%

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

   if -2.3e-65 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.8%

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

   4. Taylor expanded in x around 0 56.7%

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

Alternative 6: 38.6% 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. Add Preprocessing

3. Taylor expanded in x around inf 85.7%

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

4. Taylor expanded in y around 0 34.1%

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

Reproduce

herbie shell --seed 2024165 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))