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

Percentage Accurate: 100.0% → 100.0%

Time: 3.9s

Alternatives: 8

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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, 1 - x, x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma y (- 1.0 x) x))

C

double code(double x, double y) {
	return fma(y, (1.0 - x), x);
}

Julia

function code(x, y)
	return fma(y, Float64(1.0 - x), x)
end

Wolfram

code[x_, y_] := N[(y * N[(1.0 - x), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 100.0%

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

   1. sub-neg 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-rgt-identity 100.0%

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

   4. +-commutative 100.0%

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

   5. associate-+l+ 100.0%

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

   6. +-commutative 100.0%

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

   7. distribute-rgt-neg-out 100.0%

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

   8. distribute-lft-neg-in 100.0%

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

   9. distribute-lft1-in 100.0%

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

   10. +-commutative 100.0%

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

   11. neg-mul-1 100.0%

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

   12. *-commutative 100.0%

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

   13. neg-mul-1 100.0%

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

   14. sub-neg 100.0%

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

   15. fma-define 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, 1 - x, x\right) \]
7. Add Preprocessing

Alternative 2: 60.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+213}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+156}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+65}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= x -3.8e+213)
     x
     (if (<= x -9e+156)
       t_0
       (if (<= x -3e+120)
         x
         (if (<= x -6e+65)
           t_0
           (if (<= x -2.8e-130) x (if (<= x 1.0) y t_0))))))))

C

double code(double x, double y) {
	double t_0 = y * -x;
	double tmp;
	if (x <= -3.8e+213) {
		tmp = x;
	} else if (x <= -9e+156) {
		tmp = t_0;
	} else if (x <= -3e+120) {
		tmp = x;
	} else if (x <= -6e+65) {
		tmp = t_0;
	} else if (x <= -2.8e-130) {
		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 = y * -x
    if (x <= (-3.8d+213)) then
        tmp = x
    else if (x <= (-9d+156)) then
        tmp = t_0
    else if (x <= (-3d+120)) then
        tmp = x
    else if (x <= (-6d+65)) then
        tmp = t_0
    else if (x <= (-2.8d-130)) 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 = y * -x;
	double tmp;
	if (x <= -3.8e+213) {
		tmp = x;
	} else if (x <= -9e+156) {
		tmp = t_0;
	} else if (x <= -3e+120) {
		tmp = x;
	} else if (x <= -6e+65) {
		tmp = t_0;
	} else if (x <= -2.8e-130) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * -x
	tmp = 0
	if x <= -3.8e+213:
		tmp = x
	elif x <= -9e+156:
		tmp = t_0
	elif x <= -3e+120:
		tmp = x
	elif x <= -6e+65:
		tmp = t_0
	elif x <= -2.8e-130:
		tmp = x
	elif x <= 1.0:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (x <= -3.8e+213)
		tmp = x;
	elseif (x <= -9e+156)
		tmp = t_0;
	elseif (x <= -3e+120)
		tmp = x;
	elseif (x <= -6e+65)
		tmp = t_0;
	elseif (x <= -2.8e-130)
		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 = y * -x;
	tmp = 0.0;
	if (x <= -3.8e+213)
		tmp = x;
	elseif (x <= -9e+156)
		tmp = t_0;
	elseif (x <= -3e+120)
		tmp = x;
	elseif (x <= -6e+65)
		tmp = t_0;
	elseif (x <= -2.8e-130)
		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[(y * (-x)), $MachinePrecision]}, If[LessEqual[x, -3.8e+213], x, If[LessEqual[x, -9e+156], t$95$0, If[LessEqual[x, -3e+120], x, If[LessEqual[x, -6e+65], t$95$0, If[LessEqual[x, -2.8e-130], x, If[LessEqual[x, 1.0], y, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999997e213 or -9.00000000000000061e156 < x < -3e120 or -6.0000000000000004e65 < x < -2.80000000000000016e-130

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 63.1%

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

   if -3.7999999999999997e213 < x < -9.00000000000000061e156 or -3e120 < x < -6.0000000000000004e65 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 100.0%

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

   4. Taylor expanded in y around inf 63.6%

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

      1. mul-1-neg 63.6%

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

      2. *-commutative 63.6%

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

      3. distribute-rgt-neg-in 63.6%

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

   6. Simplified 63.6%

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

   if -2.80000000000000016e-130 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.9%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+213}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+156}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.8e-139) (* x (- 1.0 y)) (if (<= x 1.0) y (* y (- x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.8e-139) {
		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 <= (-4.8d-139)) 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 <= -4.8e-139) {
		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 <= -4.8e-139:
		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 <= -4.8e-139)
		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 <= -4.8e-139)
		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, -4.8e-139], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], y, N[(y * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.80000000000000029e-139

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.1%

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

   if -4.80000000000000029e-139 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.5%

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

   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 100.0%

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

   4. Taylor expanded in y around inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. *-commutative 60.1%

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

      3. distribute-rgt-neg-in 60.1%

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

   6. Simplified 60.1%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.35e-127) (* x (- 1.0 y)) (* y (- 1.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.35e-127) {
		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 (y <= 1.35d-127) 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 (y <= 1.35e-127) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.35e-127:
		tmp = x * (1.0 - y)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.35e-127)
		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 (y <= 1.35e-127)
		tmp = x * (1.0 - y);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.35e-127], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.35e-127

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.5%

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

   if 1.35e-127 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 87.2%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{-127}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.75e-127) (- x (* y x)) (* y (- 1.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.75e-127) {
		tmp = x - (y * 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 <= 1.75d-127) then
        tmp = x - (y * 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 <= 1.75e-127) {
		tmp = x - (y * x);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.75e-127:
		tmp = x - (y * x)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.75e-127)
		tmp = Float64(x - Float64(y * 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 <= 1.75e-127)
		tmp = x - (y * x);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.75e-127], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.74999999999999995e-127

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.5%

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

      1. sub-neg 73.5%

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

      2. distribute-rgt-in 73.5%

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

      3. *-un-lft-identity 73.5%

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

   5. Applied egg-rr 73.5%

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

      1. distribute-lft-neg-out 73.5%

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

      2. unsub-neg 73.5%

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

      3. *-commutative 73.5%

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

   7. Applied egg-rr 73.5%

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

   if 1.74999999999999995e-127 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 87.2%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{-127}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 7: 48.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 1.4e-127) x y))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.4e-127) {
		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 <= 1.4d-127) 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 <= 1.4e-127) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.4e-127:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.4e-127)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.4e-127)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.4e-127], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.4e-127

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 52.5%

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

   if 1.4e-127 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 57.0%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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. Add Preprocessing

3. Taylor expanded in y around 0 38.1%

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

4. Final simplification 38.1%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))