Data.Colour.RGB:hslsv from colour-2.3.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 8.7s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{x - y}{2 - \left(x + y\right)} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 87.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot 2 + -2}{x} + -1\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+25}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 14500000000000:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ (+ (* y 2.0) -2.0) x) -1.0)))
   (if (<= x -3.3e+25)
     t_0
     (if (<= x 14500000000000.0) (/ (- x y) (- 2.0 y)) t_0))))

C

double code(double x, double y) {
	double t_0 = (((y * 2.0) + -2.0) / x) + -1.0;
	double tmp;
	if (x <= -3.3e+25) {
		tmp = t_0;
	} else if (x <= 14500000000000.0) {
		tmp = (x - y) / (2.0 - 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 * 2.0d0) + (-2.0d0)) / x) + (-1.0d0)
    if (x <= (-3.3d+25)) then
        tmp = t_0
    else if (x <= 14500000000000.0d0) then
        tmp = (x - y) / (2.0d0 - y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (((y * 2.0) + -2.0) / x) + -1.0;
	double tmp;
	if (x <= -3.3e+25) {
		tmp = t_0;
	} else if (x <= 14500000000000.0) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (((y * 2.0) + -2.0) / x) + -1.0
	tmp = 0
	if x <= -3.3e+25:
		tmp = t_0
	elif x <= 14500000000000.0:
		tmp = (x - y) / (2.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(Float64(y * 2.0) + -2.0) / x) + -1.0)
	tmp = 0.0
	if (x <= -3.3e+25)
		tmp = t_0;
	elseif (x <= 14500000000000.0)
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (((y * 2.0) + -2.0) / x) + -1.0;
	tmp = 0.0;
	if (x <= -3.3e+25)
		tmp = t_0;
	elseif (x <= 14500000000000.0)
		tmp = (x - y) / (2.0 - y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(N[(y * 2.0), $MachinePrecision] + -2.0), $MachinePrecision] / x), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[x, -3.3e+25], t$95$0, If[LessEqual[x, 14500000000000.0], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3000000000000001e25 or 1.45e13 < x

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \frac{y}{x} - \left(1 + 2 \cdot \frac{1}{x}\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 2 \cdot \frac{y}{x} - \left(2 \cdot \frac{1}{x} + \color{blue}{1}\right) \]

      2. associate--r+ N/A

         \[\leadsto \left(2 \cdot \frac{y}{x} - 2 \cdot \frac{1}{x}\right) - \color{blue}{1} \]

      3. associate-*r/ N/A

         \[\leadsto \left(\frac{2 \cdot y}{x} - 2 \cdot \frac{1}{x}\right) - 1 \]

      4. associate-*r/ N/A

         \[\leadsto \left(\frac{2 \cdot y}{x} - \frac{2 \cdot 1}{x}\right) - 1 \]

      5. metadata-eval N/A

         \[\leadsto \left(\frac{2 \cdot y}{x} - \frac{2}{x}\right) - 1 \]

      6. div-sub N/A

         \[\leadsto \frac{2 \cdot y - 2}{x} - 1 \]

      7. sub-neg N/A

         \[\leadsto \frac{2 \cdot y - 2}{x} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)} \]

      8. metadata-eval N/A

         \[\leadsto \frac{2 \cdot y - 2}{x} + -1 \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2 \cdot y - 2}{x}\right), \color{blue}{-1}\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(2 \cdot y - 2\right), x\right), -1\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(2 \cdot y + \left(\mathsf{neg}\left(2\right)\right)\right), x\right), -1\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\mathsf{neg}\left(2\right)\right)\right), x\right), -1\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\mathsf{neg}\left(2\right)\right)\right), x\right), -1\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\mathsf{neg}\left(2\right)\right)\right), x\right), -1\right) \]

      15. metadata-eval 79.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), -2\right), x\right), -1\right) \]

   5. Simplified 79.5%

      \[\leadsto \color{blue}{\frac{y \cdot 2 + -2}{x} + -1} \]

   if -3.3000000000000001e25 < x < 1.45e13

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - y\right)}\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 98.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{y}\right)\right) \]

   5. Simplified 98.0%

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

Alternative 3: 87.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.3 \cdot 10^{+17}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+20}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - \left(x + y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.3e+17)
   (/ (- x y) (- 2.0 x))
   (if (<= x 1.85e+20) (/ (- x y) (- 2.0 y)) (/ x (- 2.0 (+ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.3e+17) {
		tmp = (x - y) / (2.0 - x);
	} else if (x <= 1.85e+20) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = x / (2.0 - (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 <= (-9.3d+17)) then
        tmp = (x - y) / (2.0d0 - x)
    else if (x <= 1.85d+20) then
        tmp = (x - y) / (2.0d0 - y)
    else
        tmp = x / (2.0d0 - (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9.3e+17) {
		tmp = (x - y) / (2.0 - x);
	} else if (x <= 1.85e+20) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = x / (2.0 - (x + y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.3e+17:
		tmp = (x - y) / (2.0 - x)
	elif x <= 1.85e+20:
		tmp = (x - y) / (2.0 - y)
	else:
		tmp = x / (2.0 - (x + y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.3e+17)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	elseif (x <= 1.85e+20)
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	else
		tmp = Float64(x / Float64(2.0 - Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.3e+17)
		tmp = (x - y) / (2.0 - x);
	elseif (x <= 1.85e+20)
		tmp = (x - y) / (2.0 - y);
	else
		tmp = x / (2.0 - (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.3e+17], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e+20], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.3e17

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - x\right)}\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 77.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 77.3%

      \[\leadsto \frac{x - y}{\color{blue}{2 - x}} \]

   if -9.3e17 < x < 1.85e20

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - y\right)}\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 98.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{y}\right)\right) \]

   5. Simplified 98.6%

      \[\leadsto \frac{x - y}{\color{blue}{2 - y}} \]

   if 1.85e20 < x

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{\_.f64}\left(2, \mathsf{+.f64}\left(x, y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 78.8%

      \[\leadsto \frac{\color{blue}{x}}{2 - \left(x + y\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 87.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+23}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{elif}\;y \leq 0.38:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.32e+23)
   (+ 1.0 (/ (* x -2.0) y))
   (if (<= y 0.38) (/ (- x y) (- 2.0 x)) (/ y (+ y -2.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.32e+23) {
		tmp = 1.0 + ((x * -2.0) / y);
	} else if (y <= 0.38) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.32d+23)) then
        tmp = 1.0d0 + ((x * (-2.0d0)) / y)
    else if (y <= 0.38d0) then
        tmp = (x - y) / (2.0d0 - x)
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.32e+23) {
		tmp = 1.0 + ((x * -2.0) / y);
	} else if (y <= 0.38) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.32e+23:
		tmp = 1.0 + ((x * -2.0) / y)
	elif y <= 0.38:
		tmp = (x - y) / (2.0 - x)
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.32e+23)
		tmp = Float64(1.0 + Float64(Float64(x * -2.0) / y));
	elseif (y <= 0.38)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.32e+23)
		tmp = 1.0 + ((x * -2.0) / y);
	elseif (y <= 0.38)
		tmp = (x - y) / (2.0 - x);
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.32e+23], N[(1.0 + N[(N[(x * -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.38], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3199999999999999e23

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{2 - \left(x + y\right)}{x - y}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{2 - \left(x + y\right)}{x - y}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(2 - \left(x + y\right)\right), \color{blue}{\left(x - y\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(2, \left(x + y\right)\right), \left(\color{blue}{x} - y\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(2, \mathsf{+.f64}\left(x, y\right)\right), \left(x - y\right)\right)\right) \]

      6. --lowering--.f64 99.9%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(2, \mathsf{+.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{2 - \left(x + y\right)}{x - y}}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{2 - x}{y}} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto 1 + \color{blue}{\left(-1 \cdot \frac{x}{y} - -1 \cdot \frac{2 - x}{y}\right)} \]

      2. associate-*r/ N/A

         \[\leadsto 1 + \left(\frac{-1 \cdot x}{y} - \color{blue}{-1} \cdot \frac{2 - x}{y}\right) \]

      3. associate-*r/ N/A

         \[\leadsto 1 + \left(\frac{-1 \cdot x}{y} - \frac{-1 \cdot \left(2 - x\right)}{\color{blue}{y}}\right) \]

      4. div-sub N/A

         \[\leadsto 1 + \frac{-1 \cdot x - -1 \cdot \left(2 - x\right)}{\color{blue}{y}} \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1 \cdot x - -1 \cdot \left(2 - x\right)}{y}\right)}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot x - -1 \cdot \left(2 - x\right)\right), \color{blue}{y}\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot x + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(2 - x\right)\right), y\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot x + 1 \cdot \left(2 - x\right)\right), y\right)\right) \]

      9. *-lft-identity N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot x + \left(2 - x\right)\right), y\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(2 - x\right) + -1 \cdot x\right), y\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(2 - x\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(2 - x\right) - x\right), y\right)\right) \]

      13. associate--l- N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(2 - \left(x + x\right)\right), y\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(2, \left(x + x\right)\right), y\right)\right) \]

      15. +-lowering-+.f64 71.5%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(2, \mathsf{+.f64}\left(x, x\right)\right), y\right)\right) \]

   7. Simplified 71.5%

      \[\leadsto \color{blue}{1 + \frac{2 - \left(x + x\right)}{y}} \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(-2 \cdot \frac{x}{y}\right)}\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{-2 \cdot x}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(-2 \cdot x\right), \color{blue}{y}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(x \cdot -2\right), y\right)\right) \]

      4. *-lowering-*.f64 71.5%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, -2\right), y\right)\right) \]

   10. Simplified 71.5%

       \[\leadsto 1 + \color{blue}{\frac{x \cdot -2}{y}} \]

   if -1.3199999999999999e23 < y < 0.38

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - x\right)}\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 97.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 97.1%

      \[\leadsto \frac{x - y}{\color{blue}{2 - x}} \]

   if 0.38 < y

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{y}{2 - y}\right) \]

      2. distribute-neg-frac2 N/A

         \[\leadsto \frac{y}{\color{blue}{\mathsf{neg}\left(\left(2 - y\right)\right)}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(2 - y\right)}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(-1 \cdot \left(2 - y\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(2 - y\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(2 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + 2\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(-1 \cdot \left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(-1 \cdot \left(-1 \cdot y\right) + \left(\mathsf{neg}\left(2\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(\left(-1 \cdot -1\right) \cdot y + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(1 \cdot y + \left(\mathsf{neg}\left(2\right)\right)\right)\right) \]

      13. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(y + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      15. metadata-eval 79.1%

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(y, -2\right)\right) \]

   5. Simplified 79.1%

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

Alternative 5: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - \left(x + y\right)}\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 10^{-22}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 (+ x y)))))
   (if (<= x -4.5e+19) t_0 (if (<= x 1e-22) (/ y (+ y -2.0)) t_0))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - (x + y));
	double tmp;
	if (x <= -4.5e+19) {
		tmp = t_0;
	} else if (x <= 1e-22) {
		tmp = y / (y + -2.0);
	} 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 / (2.0d0 - (x + y))
    if (x <= (-4.5d+19)) then
        tmp = t_0
    else if (x <= 1d-22) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - (x + y));
	double tmp;
	if (x <= -4.5e+19) {
		tmp = t_0;
	} else if (x <= 1e-22) {
		tmp = y / (y + -2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - (x + y))
	tmp = 0
	if x <= -4.5e+19:
		tmp = t_0
	elif x <= 1e-22:
		tmp = y / (y + -2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - Float64(x + y)))
	tmp = 0.0
	if (x <= -4.5e+19)
		tmp = t_0;
	elseif (x <= 1e-22)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - (x + y));
	tmp = 0.0;
	if (x <= -4.5e+19)
		tmp = t_0;
	elseif (x <= 1e-22)
		tmp = y / (y + -2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+19], t$95$0, If[LessEqual[x, 1e-22], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5e19 or 1e-22 < x

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{\_.f64}\left(2, \mathsf{+.f64}\left(x, y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 77.2%

      \[\leadsto \frac{\color{blue}{x}}{2 - \left(x + y\right)} \]

   if -4.5e19 < x < 1e-22

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{y}{2 - y}\right) \]

      2. distribute-neg-frac2 N/A

         \[\leadsto \frac{y}{\color{blue}{\mathsf{neg}\left(\left(2 - y\right)\right)}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(2 - y\right)}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(-1 \cdot \left(2 - y\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(2 - y\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(2 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + 2\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(-1 \cdot \left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(-1 \cdot \left(-1 \cdot y\right) + \left(\mathsf{neg}\left(2\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(\left(-1 \cdot -1\right) \cdot y + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(1 \cdot y + \left(\mathsf{neg}\left(2\right)\right)\right)\right) \]

      13. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(y + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      15. metadata-eval 80.6%

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(y, -2\right)\right) \]

   5. Simplified 80.6%

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

Alternative 6: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.6e+27)
   -1.0
   (if (<= x 1.65e-22) (/ y (+ y -2.0)) (/ x (- 2.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.6e+27) {
		tmp = -1.0;
	} else if (x <= 1.65e-22) {
		tmp = y / (y + -2.0);
	} else {
		tmp = x / (2.0 - 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 <= (-4.6d+27)) then
        tmp = -1.0d0
    else if (x <= 1.65d-22) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.6e+27) {
		tmp = -1.0;
	} else if (x <= 1.65e-22) {
		tmp = y / (y + -2.0);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.6e+27:
		tmp = -1.0
	elif x <= 1.65e-22:
		tmp = y / (y + -2.0)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.6e+27)
		tmp = -1.0;
	elseif (x <= 1.65e-22)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.6e+27)
		tmp = -1.0;
	elseif (x <= 1.65e-22)
		tmp = y / (y + -2.0);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.6e+27], -1.0, If[LessEqual[x, 1.65e-22], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.6000000000000001e27

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Simplified 77.3%

      \[\leadsto \color{blue}{-1} \]

   if -4.6000000000000001e27 < x < 1.65e-22

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{y}{2 - y}\right) \]

      2. distribute-neg-frac2 N/A

         \[\leadsto \frac{y}{\color{blue}{\mathsf{neg}\left(\left(2 - y\right)\right)}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(2 - y\right)}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(-1 \cdot \left(2 - y\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(2 - y\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(2 + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + 2\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(-1 \cdot \left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(-1 \cdot \left(-1 \cdot y\right) + \left(\mathsf{neg}\left(2\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(\left(-1 \cdot -1\right) \cdot y + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(1 \cdot y + \left(\mathsf{neg}\left(2\right)\right)\right)\right) \]

      13. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(y + \left(\mathsf{neg}\left(\color{blue}{2}\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right) \]

      15. metadata-eval 80.6%

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(y, -2\right)\right) \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{\frac{y}{y + -2}} \]

   if 1.65e-22 < x

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(2 - x\right)}\right) \]

      2. --lowering--.f64 76.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 76.0%

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

Alternative 7: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.1e+22) 1.0 (if (<= y 2.5e+63) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.1e+22) {
		tmp = 1.0;
	} else if (y <= 2.5e+63) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.1d+22)) then
        tmp = 1.0d0
    else if (y <= 2.5d+63) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.1e+22) {
		tmp = 1.0;
	} else if (y <= 2.5e+63) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.1e+22:
		tmp = 1.0
	elif y <= 2.5e+63:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.1e+22)
		tmp = 1.0;
	elseif (y <= 2.5e+63)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.1e+22)
		tmp = 1.0;
	elseif (y <= 2.5e+63)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.1e+22], 1.0, If[LessEqual[y, 2.5e+63], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0999999999999998e22 or 2.50000000000000005e63 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 77.9%

      \[\leadsto \color{blue}{1} \]

   if -2.0999999999999998e22 < y < 2.50000000000000005e63

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(2 - x\right)}\right) \]

      2. --lowering--.f64 69.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 69.1%

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

Alternative 8: 62.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.5e+22) -1.0 (if (<= x 3.25e+16) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.5e+22) {
		tmp = -1.0;
	} else if (x <= 3.25e+16) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.5d+22)) then
        tmp = -1.0d0
    else if (x <= 3.25d+16) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.5e+22) {
		tmp = -1.0;
	} else if (x <= 3.25e+16) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.5e+22:
		tmp = -1.0
	elif x <= 3.25e+16:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.5e+22)
		tmp = -1.0;
	elseif (x <= 3.25e+16)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.5e+22)
		tmp = -1.0;
	elseif (x <= 3.25e+16)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.5e+22], -1.0, If[LessEqual[x, 3.25e+16], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4999999999999998e22 or 3.25e16 < x

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Simplified 77.7%

      \[\leadsto \color{blue}{-1} \]

   if -2.4999999999999998e22 < x < 3.25e16

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 53.6%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 38.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -1.0d0
end function

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

function tmp = code(x, y)
	tmp = -1.0;
end

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 99.9%

   \[\frac{x - y}{2 - \left(x + y\right)} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{-1} \]
4. Step-by-step derivation

5. Simplified 36.5%

   \[\leadsto \color{blue}{-1} \]
6. Add Preprocessing

Developer Target 1: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 - \left(x + y\right)\\ \frac{x}{t\_0} - \frac{y}{t\_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y)))) (- (/ x t_0) (/ y t_0))))

C

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = 2.0d0 - (x + y)
    code = (x / t_0) - (y / t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Python

def code(x, y):
	t_0 = 2.0 - (x + y)
	return (x / t_0) - (y / t_0)

Julia

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	return Float64(Float64(x / t_0) - Float64(y / t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = (x / t_0) - (y / t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(x / t$95$0), $MachinePrecision] - N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024158 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y)))))

  (/ (- x y) (- 2.0 (+ x y))))