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

Percentage Accurate: 100.0% → 100.0%

Time: 4.0s

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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 61.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-72}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+120} \lor \neg \left(y \leq 4.8 \cdot 10^{+146}\right) \land y \leq 1.5 \cdot 10^{+243}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= y -1.0)
     t_0
     (if (<= y 5.2e-84)
       x
       (if (<= y 2.5e-72)
         y
         (if (<= y 6e-50)
           x
           (if (or (<= y 6.5e+120) (and (not (<= y 4.8e+146)) (<= y 1.5e+243)))
             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 <= 5.2e-84) {
		tmp = x;
	} else if (y <= 2.5e-72) {
		tmp = y;
	} else if (y <= 6e-50) {
		tmp = x;
	} else if ((y <= 6.5e+120) || (!(y <= 4.8e+146) && (y <= 1.5e+243))) {
		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 <= 5.2d-84) then
        tmp = x
    else if (y <= 2.5d-72) then
        tmp = y
    else if (y <= 6d-50) then
        tmp = x
    else if ((y <= 6.5d+120) .or. (.not. (y <= 4.8d+146)) .and. (y <= 1.5d+243)) 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 <= 5.2e-84) {
		tmp = x;
	} else if (y <= 2.5e-72) {
		tmp = y;
	} else if (y <= 6e-50) {
		tmp = x;
	} else if ((y <= 6.5e+120) || (!(y <= 4.8e+146) && (y <= 1.5e+243))) {
		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 <= 5.2e-84:
		tmp = x
	elif y <= 2.5e-72:
		tmp = y
	elif y <= 6e-50:
		tmp = x
	elif (y <= 6.5e+120) or (not (y <= 4.8e+146) and (y <= 1.5e+243)):
		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 <= 5.2e-84)
		tmp = x;
	elseif (y <= 2.5e-72)
		tmp = y;
	elseif (y <= 6e-50)
		tmp = x;
	elseif ((y <= 6.5e+120) || (!(y <= 4.8e+146) && (y <= 1.5e+243)))
		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 <= 5.2e-84)
		tmp = x;
	elseif (y <= 2.5e-72)
		tmp = y;
	elseif (y <= 6e-50)
		tmp = x;
	elseif ((y <= 6.5e+120) || (~((y <= 4.8e+146)) && (y <= 1.5e+243)))
		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, 5.2e-84], x, If[LessEqual[y, 2.5e-72], y, If[LessEqual[y, 6e-50], x, If[Or[LessEqual[y, 6.5e+120], And[N[Not[LessEqual[y, 4.8e+146]], $MachinePrecision], LessEqual[y, 1.5e+243]]], y, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 6.4999999999999997e120 < y < 4.8000000000000004e146 or 1.49999999999999992e243 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 58.4%

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

   4. Taylor expanded in y around inf 58.3%

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

      1. mul-1-neg 58.3%

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

      2. distribute-lft-neg-out 58.3%

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

      3. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   if -1 < y < 5.2e-84 or 2.4999999999999998e-72 < y < 5.99999999999999981e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.0%

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

   if 5.2e-84 < y < 2.4999999999999998e-72 or 5.99999999999999981e-50 < y < 6.4999999999999997e120 or 4.8000000000000004e146 < y < 1.49999999999999992e243

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 50.1%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-72}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+120} \lor \neg \left(y \leq 4.8 \cdot 10^{+146}\right) \land y \leq 1.5 \cdot 10^{+243}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{-42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-66}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-155}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 y))))
   (if (<= x -1.35e-42)
     t_0
     (if (<= x -1.8e-66)
       y
       (if (<= x -3.9e-155) t_0 (if (<= x 1.0) y (* x (- y))))))))

C

double code(double x, double y) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (x <= -1.35e-42) {
		tmp = t_0;
	} else if (x <= -1.8e-66) {
		tmp = y;
	} else if (x <= -3.9e-155) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 - y)
    if (x <= (-1.35d-42)) then
        tmp = t_0
    else if (x <= (-1.8d-66)) then
        tmp = y
    else if (x <= (-3.9d-155)) then
        tmp = t_0
    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 t_0 = x * (1.0 - y);
	double tmp;
	if (x <= -1.35e-42) {
		tmp = t_0;
	} else if (x <= -1.8e-66) {
		tmp = y;
	} else if (x <= -3.9e-155) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (1.0 - y)
	tmp = 0
	if x <= -1.35e-42:
		tmp = t_0
	elif x <= -1.8e-66:
		tmp = y
	elif x <= -3.9e-155:
		tmp = t_0
	elif x <= 1.0:
		tmp = y
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (x <= -1.35e-42)
		tmp = t_0;
	elseif (x <= -1.8e-66)
		tmp = y;
	elseif (x <= -3.9e-155)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (1.0 - y);
	tmp = 0.0;
	if (x <= -1.35e-42)
		tmp = t_0;
	elseif (x <= -1.8e-66)
		tmp = y;
	elseif (x <= -3.9e-155)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35e-42], t$95$0, If[LessEqual[x, -1.8e-66], y, If[LessEqual[x, -3.9e-155], t$95$0, If[LessEqual[x, 1.0], y, N[(x * (-y)), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e-42 or -1.80000000000000006e-66 < x < -3.9000000000000003e-155

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.3%

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

   if -1.35e-42 < x < -1.80000000000000006e-66 or -3.9000000000000003e-155 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.4%

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

   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 98.6%

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

   4. Taylor expanded in y around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. distribute-lft-neg-out 51.8%

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

      3. *-commutative 51.8%

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

   6. Simplified 51.8%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-66}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{-43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-66}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-155}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 y))))
   (if (<= x -5.2e-43)
     t_0
     (if (<= x -1.3e-66) y (if (<= x -3.9e-155) t_0 (* y (- 1.0 x)))))))

C

double code(double x, double y) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (x <= -5.2e-43) {
		tmp = t_0;
	} else if (x <= -1.3e-66) {
		tmp = y;
	} else if (x <= -3.9e-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 * (1.0d0 - y)
    if (x <= (-5.2d-43)) then
        tmp = t_0
    else if (x <= (-1.3d-66)) then
        tmp = y
    else if (x <= (-3.9d-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 * (1.0 - y);
	double tmp;
	if (x <= -5.2e-43) {
		tmp = t_0;
	} else if (x <= -1.3e-66) {
		tmp = y;
	} else if (x <= -3.9e-155) {
		tmp = t_0;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (1.0 - y)
	tmp = 0
	if x <= -5.2e-43:
		tmp = t_0
	elif x <= -1.3e-66:
		tmp = y
	elif x <= -3.9e-155:
		tmp = t_0
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (x <= -5.2e-43)
		tmp = t_0;
	elseif (x <= -1.3e-66)
		tmp = y;
	elseif (x <= -3.9e-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 * (1.0 - y);
	tmp = 0.0;
	if (x <= -5.2e-43)
		tmp = t_0;
	elseif (x <= -1.3e-66)
		tmp = y;
	elseif (x <= -3.9e-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[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e-43], t$95$0, If[LessEqual[x, -1.3e-66], y, If[LessEqual[x, -3.9e-155], t$95$0, N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.2e-43 or -1.2999999999999999e-66 < x < -3.9000000000000003e-155

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.3%

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

   if -5.2e-43 < x < -1.2999999999999999e-66

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.9%

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

   if -3.9000000000000003e-155 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 67.3%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-66}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-48}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-66}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.4e-48)
   (- x (* x y))
   (if (<= x -2.25e-66)
     y
     (if (<= x -3.9e-155) (* x (- 1.0 y)) (* y (- 1.0 x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.4e-48) {
		tmp = x - (x * y);
	} else if (x <= -2.25e-66) {
		tmp = y;
	} else if (x <= -3.9e-155) {
		tmp = x * (1.0 - y);
	} 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 (x <= (-2.4d-48)) then
        tmp = x - (x * y)
    else if (x <= (-2.25d-66)) then
        tmp = y
    else if (x <= (-3.9d-155)) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.4e-48) {
		tmp = x - (x * y);
	} else if (x <= -2.25e-66) {
		tmp = y;
	} else if (x <= -3.9e-155) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.4e-48:
		tmp = x - (x * y)
	elif x <= -2.25e-66:
		tmp = y
	elif x <= -3.9e-155:
		tmp = x * (1.0 - y)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.4e-48)
		tmp = Float64(x - Float64(x * y));
	elseif (x <= -2.25e-66)
		tmp = y;
	elseif (x <= -3.9e-155)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.4e-48)
		tmp = x - (x * y);
	elseif (x <= -2.25e-66)
		tmp = y;
	elseif (x <= -3.9e-155)
		tmp = x * (1.0 - y);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.4e-48], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.25e-66], y, If[LessEqual[x, -3.9e-155], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.4e-48

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 94.3%

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

      1. sub-neg 94.3%

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

      2. distribute-rgt-in 94.4%

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

      3. *-un-lft-identity 94.4%

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

   5. Applied egg-rr 94.4%

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

      1. distribute-lft-neg-out 94.4%

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

      2. unsub-neg 94.4%

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

      3. *-commutative 94.4%

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

   7. Applied egg-rr 94.4%

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

   if -2.4e-48 < x < -2.2499999999999999e-66

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.9%

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

   if -2.2499999999999999e-66 < x < -3.9000000000000003e-155

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 33.6%

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

   if -3.9000000000000003e-155 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 67.3%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-48}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-66}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.75 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-72}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 2.75e-85) x (if (<= y 2.5e-72) y (if (<= y 4.3e-50) x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.75e-85) {
		tmp = x;
	} else if (y <= 2.5e-72) {
		tmp = y;
	} else if (y <= 4.3e-50) {
		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 <= 2.75d-85) then
        tmp = x
    else if (y <= 2.5d-72) then
        tmp = y
    else if (y <= 4.3d-50) 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 <= 2.75e-85) {
		tmp = x;
	} else if (y <= 2.5e-72) {
		tmp = y;
	} else if (y <= 4.3e-50) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.75e-85:
		tmp = x
	elif y <= 2.5e-72:
		tmp = y
	elif y <= 4.3e-50:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.75e-85)
		tmp = x;
	elseif (y <= 2.5e-72)
		tmp = y;
	elseif (y <= 4.3e-50)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.75e-85)
		tmp = x;
	elseif (y <= 2.5e-72)
		tmp = y;
	elseif (y <= 4.3e-50)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.75e-85], x, If[LessEqual[y, 2.5e-72], y, If[LessEqual[y, 4.3e-50], x, y]]]

Derivation

1. Split input into 2 regimes

2. if y < 2.7499999999999999e-85 or 2.4999999999999998e-72 < y < 4.29999999999999997e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 47.5%

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

   if 2.7499999999999999e-85 < y < 2.4999999999999998e-72 or 4.29999999999999997e-50 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 41.6%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.75 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-72}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.2% 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 y around 0 35.5%

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

4. Final simplification 35.5%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024089 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))