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

Percentage Accurate: 100.0% → 100.0%

Time: 9.9s

Alternatives: 10

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 100.0%

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

Alternative 2: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+41}:\\ \;\;\;\;1 - \frac{x + -2}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+64}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.8e+41)
   (- 1.0 (/ (+ x -2.0) y))
   (if (<= y 6.5e+64) (/ (- x y) (- 2.0 x)) (/ (- x y) (- 2.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.8e+41) {
		tmp = 1.0 - ((x + -2.0) / y);
	} else if (y <= 6.5e+64) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = (x - y) / (2.0 - 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 <= (-5.8d+41)) then
        tmp = 1.0d0 - ((x + (-2.0d0)) / y)
    else if (y <= 6.5d+64) then
        tmp = (x - y) / (2.0d0 - x)
    else
        tmp = (x - y) / (2.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.8e+41) {
		tmp = 1.0 - ((x + -2.0) / y);
	} else if (y <= 6.5e+64) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.8e+41:
		tmp = 1.0 - ((x + -2.0) / y)
	elif y <= 6.5e+64:
		tmp = (x - y) / (2.0 - x)
	else:
		tmp = (x - y) / (2.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.8e+41)
		tmp = Float64(1.0 - Float64(Float64(x + -2.0) / y));
	elseif (y <= 6.5e+64)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	else
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.8e+41)
		tmp = 1.0 - ((x + -2.0) / y);
	elseif (y <= 6.5e+64)
		tmp = (x - y) / (2.0 - x);
	else
		tmp = (x - y) / (2.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.8e+41], N[(1.0 - N[(N[(x + -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+64], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999977e41

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. div-sub N/A

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

      7. remove-double-neg N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

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

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

      11. associate-*r/ N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. mul-1-neg N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. mul-1-neg N/A

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

      18. remove-double-neg N/A

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

      19. sub-neg N/A

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

      20. /-lowering-/.f64 N/A

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

      21. sub-neg N/A

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

      22. metadata-eval N/A

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

      23. +-lowering-+.f64 80.2%

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

   8. Simplified 80.2%

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

   if -5.79999999999999977e41 < y < 6.50000000000000007e64

   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 96.0%

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

   5. Simplified 96.0%

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

   if 6.50000000000000007e64 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 83.9%

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

   5. Simplified 83.9%

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

Alternative 3: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x + -2}{y}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+41}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+64}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ (+ x -2.0) y))))
   (if (<= y -2.1e+41) t_0 (if (<= y 7.5e+64) (/ (- x y) (- 2.0 x)) t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 - ((x + -2.0) / y);
	double tmp;
	if (y <= -2.1e+41) {
		tmp = t_0;
	} else if (y <= 7.5e+64) {
		tmp = (x - y) / (2.0 - x);
	} 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 = 1.0d0 - ((x + (-2.0d0)) / y)
    if (y <= (-2.1d+41)) then
        tmp = t_0
    else if (y <= 7.5d+64) then
        tmp = (x - y) / (2.0d0 - x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - ((x + -2.0) / y);
	double tmp;
	if (y <= -2.1e+41) {
		tmp = t_0;
	} else if (y <= 7.5e+64) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - ((x + -2.0) / y)
	tmp = 0
	if y <= -2.1e+41:
		tmp = t_0
	elif y <= 7.5e+64:
		tmp = (x - y) / (2.0 - x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(Float64(x + -2.0) / y))
	tmp = 0.0
	if (y <= -2.1e+41)
		tmp = t_0;
	elseif (y <= 7.5e+64)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - ((x + -2.0) / y);
	tmp = 0.0;
	if (y <= -2.1e+41)
		tmp = t_0;
	elseif (y <= 7.5e+64)
		tmp = (x - y) / (2.0 - x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(N[(x + -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+41], t$95$0, If[LessEqual[y, 7.5e+64], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1e41 or 7.5000000000000005e64 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. div-sub N/A

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

      7. remove-double-neg N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

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

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

      11. associate-*r/ N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. mul-1-neg N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. mul-1-neg N/A

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

      18. remove-double-neg N/A

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

      19. sub-neg N/A

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

      20. /-lowering-/.f64 N/A

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

      21. sub-neg N/A

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

      22. metadata-eval N/A

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

      23. +-lowering-+.f64 82.0%

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

   8. Simplified 82.0%

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

   if -2.1e41 < y < 7.5000000000000005e64

   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 96.0%

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

   5. Simplified 96.0%

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

Alternative 4: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{2 - \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x + -2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7e-67)
   (/ y (+ y -2.0))
   (if (<= y 6e+64) (/ x (- 2.0 (+ x y))) (- 1.0 (/ (+ x -2.0) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7e-67) {
		tmp = y / (y + -2.0);
	} else if (y <= 6e+64) {
		tmp = x / (2.0 - (x + y));
	} else {
		tmp = 1.0 - ((x + -2.0) / 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 <= (-7d-67)) then
        tmp = y / (y + (-2.0d0))
    else if (y <= 6d+64) then
        tmp = x / (2.0d0 - (x + y))
    else
        tmp = 1.0d0 - ((x + (-2.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -7e-67) {
		tmp = y / (y + -2.0);
	} else if (y <= 6e+64) {
		tmp = x / (2.0 - (x + y));
	} else {
		tmp = 1.0 - ((x + -2.0) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7e-67:
		tmp = y / (y + -2.0)
	elif y <= 6e+64:
		tmp = x / (2.0 - (x + y))
	else:
		tmp = 1.0 - ((x + -2.0) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7e-67)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (y <= 6e+64)
		tmp = Float64(x / Float64(2.0 - Float64(x + y)));
	else
		tmp = Float64(1.0 - Float64(Float64(x + -2.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7e-67)
		tmp = y / (y + -2.0);
	elseif (y <= 6e+64)
		tmp = x / (2.0 - (x + y));
	else
		tmp = 1.0 - ((x + -2.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7e-67], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+64], N[(x / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x + -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.0000000000000001e-67

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 71.5%

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

   5. Simplified 71.5%

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

   if -7.0000000000000001e-67 < y < 6.0000000000000004e64

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 79.9%

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

   if 6.0000000000000004e64 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. div-sub N/A

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

      7. remove-double-neg N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

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

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

      11. associate-*r/ N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. mul-1-neg N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. mul-1-neg N/A

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

      18. remove-double-neg N/A

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

      19. sub-neg N/A

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

      20. /-lowering-/.f64 N/A

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

      21. sub-neg N/A

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

      22. metadata-eval N/A

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

      23. +-lowering-+.f64 83.9%

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

   8. Simplified 83.9%

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

Alternative 5: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x + -2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.8e-67)
   (/ y (+ y -2.0))
   (if (<= y 1.2e+65) (/ x (- 2.0 x)) (- 1.0 (/ (+ x -2.0) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.8e-67) {
		tmp = y / (y + -2.0);
	} else if (y <= 1.2e+65) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0 - ((x + -2.0) / 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 <= (-7.8d-67)) then
        tmp = y / (y + (-2.0d0))
    else if (y <= 1.2d+65) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0 - ((x + (-2.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -7.8e-67) {
		tmp = y / (y + -2.0);
	} else if (y <= 1.2e+65) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0 - ((x + -2.0) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.8e-67:
		tmp = y / (y + -2.0)
	elif y <= 1.2e+65:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0 - ((x + -2.0) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.8e-67)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (y <= 1.2e+65)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(1.0 - Float64(Float64(x + -2.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7.8e-67)
		tmp = y / (y + -2.0);
	elseif (y <= 1.2e+65)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0 - ((x + -2.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.8e-67], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+65], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x + -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.7999999999999997e-67

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 71.5%

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

   5. Simplified 71.5%

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

   if -7.7999999999999997e-67 < y < 1.2000000000000001e65

   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 79.8%

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

   5. Simplified 79.8%

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

   if 1.2000000000000001e65 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. div-sub N/A

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

      7. remove-double-neg N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

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

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

      11. associate-*r/ N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. mul-1-neg N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. mul-1-neg N/A

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

      18. remove-double-neg N/A

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

      19. sub-neg N/A

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

      20. /-lowering-/.f64 N/A

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

      21. sub-neg N/A

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

      22. metadata-eval N/A

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

      23. +-lowering-+.f64 83.9%

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

   8. Simplified 83.9%

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

Alternative 6: 62.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{-2}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+65}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.0)
   1.0
   (if (<= y -7.4e-67) (/ y -2.0) (if (<= y 2e+65) -1.0 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.0) {
		tmp = 1.0;
	} else if (y <= -7.4e-67) {
		tmp = y / -2.0;
	} else if (y <= 2e+65) {
		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 (y <= (-2.0d0)) then
        tmp = 1.0d0
    else if (y <= (-7.4d-67)) then
        tmp = y / (-2.0d0)
    else if (y <= 2d+65) 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 (y <= -2.0) {
		tmp = 1.0;
	} else if (y <= -7.4e-67) {
		tmp = y / -2.0;
	} else if (y <= 2e+65) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.0:
		tmp = 1.0
	elif y <= -7.4e-67:
		tmp = y / -2.0
	elif y <= 2e+65:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.0)
		tmp = 1.0;
	elseif (y <= -7.4e-67)
		tmp = Float64(y / -2.0);
	elseif (y <= 2e+65)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.0)
		tmp = 1.0;
	elseif (y <= -7.4e-67)
		tmp = y / -2.0;
	elseif (y <= 2e+65)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.0], 1.0, If[LessEqual[y, -7.4e-67], N[(y / -2.0), $MachinePrecision], If[LessEqual[y, 2e+65], -1.0, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -2 or 2e65 < 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 79.1%

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

   if -2 < y < -7.3999999999999999e-67

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 59.1%

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

   if -7.3999999999999999e-67 < y < 2e65

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 58.6%

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

Alternative 7: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.2e-67) (/ y (+ y -2.0)) (if (<= y 1.7e+65) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.2e-67) {
		tmp = y / (y + -2.0);
	} else if (y <= 1.7e+65) {
		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 <= (-6.2d-67)) then
        tmp = y / (y + (-2.0d0))
    else if (y <= 1.7d+65) 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 <= -6.2e-67) {
		tmp = y / (y + -2.0);
	} else if (y <= 1.7e+65) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.2e-67:
		tmp = y / (y + -2.0)
	elif y <= 1.7e+65:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.2e-67)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (y <= 1.7e+65)
		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 <= -6.2e-67)
		tmp = y / (y + -2.0);
	elseif (y <= 1.7e+65)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.2e-67], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+65], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2000000000000005e-67

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 71.5%

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

   5. Simplified 71.5%

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

   if -6.2000000000000005e-67 < y < 1.7e65

   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 79.8%

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

   5. Simplified 79.8%

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

   if 1.7e65 < 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 83.2%

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

Alternative 8: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+41}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.9e+41) 1.0 (if (<= y 1.35e+65) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.9e+41) {
		tmp = 1.0;
	} else if (y <= 1.35e+65) {
		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 <= (-5.9d+41)) then
        tmp = 1.0d0
    else if (y <= 1.35d+65) 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 <= -5.9e+41) {
		tmp = 1.0;
	} else if (y <= 1.35e+65) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.9e+41:
		tmp = 1.0
	elif y <= 1.35e+65:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.9e+41)
		tmp = 1.0;
	elseif (y <= 1.35e+65)
		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 <= -5.9e+41)
		tmp = 1.0;
	elseif (y <= 1.35e+65)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.9e+41], 1.0, If[LessEqual[y, 1.35e+65], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.9000000000000001e41 or 1.35000000000000009e65 < 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 81.4%

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

   if -5.9000000000000001e41 < y < 1.35000000000000009e65

   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 71.8%

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

   5. Simplified 71.8%

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

Alternative 9: 62.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+41}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+65}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.2e+41) 1.0 (if (<= y 1.42e+65) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.2e+41) {
		tmp = 1.0;
	} else if (y <= 1.42e+65) {
		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 (y <= (-3.2d+41)) then
        tmp = 1.0d0
    else if (y <= 1.42d+65) 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 (y <= -3.2e+41) {
		tmp = 1.0;
	} else if (y <= 1.42e+65) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.2e+41:
		tmp = 1.0
	elif y <= 1.42e+65:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.2e+41)
		tmp = 1.0;
	elseif (y <= 1.42e+65)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.2e+41)
		tmp = 1.0;
	elseif (y <= 1.42e+65)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.2e+41], 1.0, If[LessEqual[y, 1.42e+65], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2000000000000001e41 or 1.42000000000000012e65 < 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 81.4%

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

   if -3.2000000000000001e41 < y < 1.42000000000000012e65

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 53.9%

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

Alternative 10: 38.1% 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 100.0%

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

3. Taylor expanded in x around inf

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

5. Simplified 37.5%

   \[\leadsto \color{blue}{-1} \]
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 2024191 
(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))))