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

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

Alternatives: 7

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: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+135} \lor \neg \left(y \leq 6.8 \cdot 10^{+255}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -1.0)
     t_0
     (if (<= y 1.9e-36)
       x
       (if (<= y 3e+75)
         y
         (if (or (<= y 2.5e+135) (not (<= y 6.8e+255))) t_0 y))))))

C

double code(double x, double y) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1.9e-36) {
		tmp = x;
	} else if (y <= 3e+75) {
		tmp = y;
	} else if ((y <= 2.5e+135) || !(y <= 6.8e+255)) {
		tmp = t_0;
	} else {
		tmp = y;
	}
	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 = y * -x
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 1.9d-36) then
        tmp = x
    else if (y <= 3d+75) then
        tmp = y
    else if ((y <= 2.5d+135) .or. (.not. (y <= 6.8d+255))) then
        tmp = t_0
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1.9e-36) {
		tmp = x;
	} else if (y <= 3e+75) {
		tmp = y;
	} else if ((y <= 2.5e+135) || !(y <= 6.8e+255)) {
		tmp = t_0;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * -x
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 1.9e-36:
		tmp = x
	elif y <= 3e+75:
		tmp = y
	elif (y <= 2.5e+135) or not (y <= 6.8e+255):
		tmp = t_0
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 1.9e-36)
		tmp = x;
	elseif (y <= 3e+75)
		tmp = y;
	elseif ((y <= 2.5e+135) || !(y <= 6.8e+255))
		tmp = t_0;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * -x;
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 1.9e-36)
		tmp = x;
	elseif (y <= 3e+75)
		tmp = y;
	elseif ((y <= 2.5e+135) || ~((y <= 6.8e+255)))
		tmp = t_0;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 1.9e-36], x, If[LessEqual[y, 3e+75], y, If[Or[LessEqual[y, 2.5e+135], N[Not[LessEqual[y, 6.8e+255]], $MachinePrecision]], t$95$0, y]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 3e75 < y < 2.50000000000000015e135 or 6.7999999999999997e255 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 50.7%

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

   3. Taylor expanded in y around inf 50.7%

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

      1. mul-1-neg 50.7%

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

      2. distribute-rgt-neg-out 50.7%

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

   5. Simplified 50.7%

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

   if -1 < y < 1.89999999999999985e-36

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.2%

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

   if 1.89999999999999985e-36 < y < 3e75 or 2.50000000000000015e135 < y < 6.7999999999999997e255

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 57.1%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+135} \lor \neg \left(y \leq 6.8 \cdot 10^{+255}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;x \leq -2.45 \cdot 10^{-18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-46}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-85}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 y))))
   (if (<= x -2.45e-18)
     t_0
     (if (<= x -7.2e-46)
       y
       (if (<= x -4.5e-85) t_0 (if (<= x 1.0) y (* y (- x))))))))

C

double code(double x, double y) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (x <= -2.45e-18) {
		tmp = t_0;
	} else if (x <= -7.2e-46) {
		tmp = y;
	} else if (x <= -4.5e-85) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = y * -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 * (1.0d0 - y)
    if (x <= (-2.45d-18)) then
        tmp = t_0
    else if (x <= (-7.2d-46)) then
        tmp = y
    else if (x <= (-4.5d-85)) then
        tmp = t_0
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (x <= -2.45e-18) {
		tmp = t_0;
	} else if (x <= -7.2e-46) {
		tmp = y;
	} else if (x <= -4.5e-85) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (1.0 - y)
	tmp = 0
	if x <= -2.45e-18:
		tmp = t_0
	elif x <= -7.2e-46:
		tmp = y
	elif x <= -4.5e-85:
		tmp = t_0
	elif x <= 1.0:
		tmp = y
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (x <= -2.45e-18)
		tmp = t_0;
	elseif (x <= -7.2e-46)
		tmp = y;
	elseif (x <= -4.5e-85)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (1.0 - y);
	tmp = 0.0;
	if (x <= -2.45e-18)
		tmp = t_0;
	elseif (x <= -7.2e-46)
		tmp = y;
	elseif (x <= -4.5e-85)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.45e-18], t$95$0, If[LessEqual[x, -7.2e-46], y, If[LessEqual[x, -4.5e-85], t$95$0, If[LessEqual[x, 1.0], y, N[(y * (-x)), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4500000000000001e-18 or -7.2e-46 < x < -4.50000000000000004e-85

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 92.5%

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

   if -2.4500000000000001e-18 < x < -7.2e-46 or -4.50000000000000004e-85 < x < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.1%

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

   if 1 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 97.7%

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

   3. Taylor expanded in y around inf 61.2%

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

      1. mul-1-neg 61.2%

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

      2. distribute-rgt-neg-out 61.2%

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

   5. Simplified 61.2%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-46}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 4: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-23}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-45}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.2e-23)
   (- x (* x y))
   (if (<= x -2.25e-45)
     y
     (if (<= x -9.6e-83) (* x (- 1.0 y)) (if (<= x 1.0) y (* y (- x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.2e-23) {
		tmp = x - (x * y);
	} else if (x <= -2.25e-45) {
		tmp = y;
	} else if (x <= -9.6e-83) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = y * -x;
	}
	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-23)) then
        tmp = x - (x * y)
    else if (x <= (-2.25d-45)) then
        tmp = y
    else if (x <= (-9.6d-83)) then
        tmp = x * (1.0d0 - y)
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5.2e-23) {
		tmp = x - (x * y);
	} else if (x <= -2.25e-45) {
		tmp = y;
	} else if (x <= -9.6e-83) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.2e-23:
		tmp = x - (x * y)
	elif x <= -2.25e-45:
		tmp = y
	elif x <= -9.6e-83:
		tmp = x * (1.0 - y)
	elif x <= 1.0:
		tmp = y
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.2e-23)
		tmp = Float64(x - Float64(x * y));
	elseif (x <= -2.25e-45)
		tmp = y;
	elseif (x <= -9.6e-83)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.2e-23)
		tmp = x - (x * y);
	elseif (x <= -2.25e-45)
		tmp = y;
	elseif (x <= -9.6e-83)
		tmp = x * (1.0 - y);
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.2e-23], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.25e-45], y, If[LessEqual[x, -9.6e-83], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], y, N[(y * (-x)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.2e-23

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 95.5%

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

      1. *-commutative 95.5%

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

      2. distribute-rgt-out-- 95.5%

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

      3. *-lft-identity 95.5%

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

   4. Simplified 95.5%

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

   if -5.2e-23 < x < -2.2499999999999999e-45 or -9.6000000000000003e-83 < x < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.4%

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

   if -2.2499999999999999e-45 < x < -9.6000000000000003e-83

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 58.6%

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

   if 1 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 97.7%

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

   3. Taylor expanded in y around inf 61.2%

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

      1. mul-1-neg 61.2%

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

      2. distribute-rgt-neg-out 61.2%

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

   5. Simplified 61.2%

      \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-23}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-45}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 5: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-17}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-45}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4e-17)
   (- x (* x y))
   (if (<= x -5.3e-45) y (if (<= x -1.35e-80) (* x (- 1.0 y)) (- y (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4e-17) {
		tmp = x - (x * y);
	} else if (x <= -5.3e-45) {
		tmp = y;
	} else if (x <= -1.35e-80) {
		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 <= (-4d-17)) then
        tmp = x - (x * y)
    else if (x <= (-5.3d-45)) then
        tmp = y
    else if (x <= (-1.35d-80)) 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 <= -4e-17) {
		tmp = x - (x * y);
	} else if (x <= -5.3e-45) {
		tmp = y;
	} else if (x <= -1.35e-80) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4e-17:
		tmp = x - (x * y)
	elif x <= -5.3e-45:
		tmp = y
	elif x <= -1.35e-80:
		tmp = x * (1.0 - y)
	else:
		tmp = y - (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4e-17)
		tmp = Float64(x - Float64(x * y));
	elseif (x <= -5.3e-45)
		tmp = y;
	elseif (x <= -1.35e-80)
		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 <= -4e-17)
		tmp = x - (x * y);
	elseif (x <= -5.3e-45)
		tmp = y;
	elseif (x <= -1.35e-80)
		tmp = x * (1.0 - y);
	else
		tmp = y - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4e-17], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.3e-45], y, If[LessEqual[x, -1.35e-80], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.00000000000000029e-17

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 96.6%

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

      1. *-commutative 96.6%

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

      2. distribute-rgt-out-- 96.6%

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

      3. *-lft-identity 96.6%

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

   4. Simplified 96.6%

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

   if -4.00000000000000029e-17 < x < -5.2999999999999997e-45

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 85.4%

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

   if -5.2999999999999997e-45 < x < -1.3500000000000001e-80

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.1%

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

   if -1.3500000000000001e-80 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 74.5%

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

      1. distribute-lft-out-- 74.5%

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

      2. *-rgt-identity 74.5%

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

   4. Simplified 74.5%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-17}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-45}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \]

Alternative 6: 50.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 4.5e-35) x y))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.5e-35) {
		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 (y <= 4.5d-35) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 4.5e-35) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.5e-35:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.5e-35)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4.5e-35)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.5e-35], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 4.5000000000000001e-35

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 51.5%

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

   if 4.5000000000000001e-35 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 48.1%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7: 38.4% 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 37.1%

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

3. Final simplification 37.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))