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

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

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: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - x \cdot y\\ \mathbf{if}\;x \leq -1 \cdot 10^{-22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-58}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-155}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (* x y))))
   (if (<= x -1e-22)
     t_0
     (if (<= x -6.6e-58) y (if (<= x -5.8e-155) t_0 (* y (- 1.0 x)))))))

C

double code(double x, double y) {
	double t_0 = x - (x * y);
	double tmp;
	if (x <= -1e-22) {
		tmp = t_0;
	} else if (x <= -6.6e-58) {
		tmp = y;
	} else if (x <= -5.8e-155) {
		tmp = t_0;
	} else {
		tmp = y * (1.0 - x);
	}
	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 - (x * y)
    if (x <= (-1d-22)) then
        tmp = t_0
    else if (x <= (-6.6d-58)) then
        tmp = y
    else if (x <= (-5.8d-155)) then
        tmp = t_0
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - (x * y);
	double tmp;
	if (x <= -1e-22) {
		tmp = t_0;
	} else if (x <= -6.6e-58) {
		tmp = y;
	} else if (x <= -5.8e-155) {
		tmp = t_0;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - (x * y)
	tmp = 0
	if x <= -1e-22:
		tmp = t_0
	elif x <= -6.6e-58:
		tmp = y
	elif x <= -5.8e-155:
		tmp = t_0
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(x * y))
	tmp = 0.0
	if (x <= -1e-22)
		tmp = t_0;
	elseif (x <= -6.6e-58)
		tmp = y;
	elseif (x <= -5.8e-155)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - (x * y);
	tmp = 0.0;
	if (x <= -1e-22)
		tmp = t_0;
	elseif (x <= -6.6e-58)
		tmp = y;
	elseif (x <= -5.8e-155)
		tmp = t_0;
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e-22], t$95$0, If[LessEqual[x, -6.6e-58], y, If[LessEqual[x, -5.8e-155], t$95$0, N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1e-22 or -6.60000000000000052e-58 < x < -5.80000000000000021e-155

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.3%

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

      1. *-commutative 86.3%

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

      2. distribute-rgt-out-- 86.3%

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

      3. *-lft-identity 86.3%

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

   4. Simplified 86.3%

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

   if -1e-22 < x < -6.60000000000000052e-58

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 83.8%

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

   if -5.80000000000000021e-155 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 70.5%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-22}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-58}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-155}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 3: 61.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+130}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= y -1.0) t_0 (if (<= y 2.4e-52) x (if (<= y 1.1e+130) y t_0)))))

C

double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 2.4e-52) {
		tmp = x;
	} else if (y <= 1.1e+130) {
		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 (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 2.4d-52) then
        tmp = x
    else if (y <= 1.1d+130) 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 (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 2.4e-52) {
		tmp = x;
	} else if (y <= 1.1e+130) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * -y
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 2.4e-52:
		tmp = x
	elif y <= 1.1e+130:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 2.4e-52)
		tmp = x;
	elseif (y <= 1.1e+130)
		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 (y <= -1.0)
		tmp = t_0;
	elseif (y <= 2.4e-52)
		tmp = x;
	elseif (y <= 1.1e+130)
		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[y, -1.0], t$95$0, If[LessEqual[y, 2.4e-52], x, If[LessEqual[y, 1.1e+130], y, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.09999999999999997e130 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.8%

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

   3. Taylor expanded in x around inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. distribute-rgt-neg-out 53.7%

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

   5. Simplified 53.7%

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

   if -1 < y < 2.4000000000000002e-52

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.2%

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

   if 2.4000000000000002e-52 < y < 1.09999999999999997e130

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 54.5%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+130}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 4: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (* x (- y)) (if (<= y 6.2e-54) x (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * -y;
	} else if (y <= 6.2e-54) {
		tmp = x;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = x * -y
    else if (y <= 6.2d-54) then
        tmp = x
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * -y;
	} else if (y <= 6.2e-54) {
		tmp = x;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x * -y
	elif y <= 6.2e-54:
		tmp = x
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(x * Float64(-y));
	elseif (y <= 6.2e-54)
		tmp = x;
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x * -y;
	elseif (y <= 6.2e-54)
		tmp = x;
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(x * (-y)), $MachinePrecision], If[LessEqual[y, 6.2e-54], x, N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.7%

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

   3. Taylor expanded in x around inf 46.1%

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

      1. mul-1-neg 46.1%

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

      2. distribute-rgt-neg-out 46.1%

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

   5. Simplified 46.1%

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

   if -1 < y < 6.20000000000000008e-54

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.2%

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

   if 6.20000000000000008e-54 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.0%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 50.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -5.2e-22) x y))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.2e-22) {
		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 <= (-5.2d-22)) 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 <= -5.2e-22) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.2e-22:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.2e-22)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.2e-22)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.2e-22], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -5.2e-22

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 52.6%

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

   if -5.2e-22 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 49.9%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

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. Taylor expanded in y around 0 37.4%

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

3. Final simplification 37.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))