Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.5% → 94.0%

Time: 6.6s

Alternatives: 7

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x}, y, y\right) \cdot 2\\ \mathbf{elif}\;x \leq 1.56 \cdot 10^{+162}:\\ \;\;\;\;\frac{2 \cdot x}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.1e+115)
   (* (fma (/ y x) y y) 2.0)
   (if (<= x 1.56e+162) (/ (* 2.0 x) (/ (- x y) y)) (* 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.1e+115) {
		tmp = fma((y / x), y, y) * 2.0;
	} else if (x <= 1.56e+162) {
		tmp = (2.0 * x) / ((x - y) / y);
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.1e+115)
		tmp = Float64(fma(Float64(y / x), y, y) * 2.0);
	elseif (x <= 1.56e+162)
		tmp = Float64(Float64(2.0 * x) / Float64(Float64(x - y) / y));
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.1e+115], N[(N[(N[(y / x), $MachinePrecision] * y + y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[x, 1.56e+162], N[(N[(2.0 * x), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.10000000000000003e115

   1. Initial program 73.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 65.8

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 65.8

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

   4. Applied rewrites 65.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l* N/A

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

      7. clear-num N/A

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

      8. associate-/r/ N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. frac-2neg N/A

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

      14. metadata-eval N/A

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

      15. associate-*l/ N/A

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

      16. metadata-eval N/A

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

      17. lower-/.f64 N/A

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

      18. neg-sub0 N/A

          \[\leadsto \frac{-2}{\color{blue}{0 - \left(x - y\right)}} \cdot \left(x \cdot y\right) \]

      19. lift--.f64 N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(x - y\right)}} \cdot \left(x \cdot y\right) \]

      20. sub-neg N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}} \cdot \left(x \cdot y\right) \]

      21. +-commutative N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}} \cdot \left(x \cdot y\right) \]

      22. associate--r+ N/A

          \[\leadsto \frac{-2}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}} \cdot \left(x \cdot y\right) \]

      23. neg-sub0 N/A

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

      24. remove-double-neg N/A

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

      25. lower--.f64 N/A

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

      26. lower-*.f64 72.7

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

   6. Applied rewrites 72.7%

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

   7. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot y + 2 \cdot \frac{{y}^{2}}{x}} \]
   8. Step-by-step derivation

      1. distribute-lft-out N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. unpow2 N/A

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

      6. associate-*l/ N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x}, y, y\right)} \cdot 2 \]

      8. lower-/.f64 93.3

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{x}}, y, y\right) \cdot 2 \]

   9. Applied rewrites 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x}, y, y\right) \cdot 2} \]

   if -2.10000000000000003e115 < x < 1.5600000000000001e162

   1. Initial program 81.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 98.0

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

   4. Applied rewrites 98.0%

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

   if 1.5600000000000001e162 < x

   1. Initial program 70.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 92.9

         \[\leadsto \color{blue}{2 \cdot y} \]

   5. Applied rewrites 92.9%

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

Alternative 2: 87.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot x\right) \cdot \frac{-2}{y - x}\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x}, y, y\right) \cdot 2\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-139}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{-155}:\\ \;\;\;\;-2 \cdot x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+139}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* y x) (/ -2.0 (- y x)))))
   (if (<= x -4.1e+110)
     (* (fma (/ y x) y y) 2.0)
     (if (<= x -1.9e-139)
       t_0
       (if (<= x 1.46e-155) (* -2.0 x) (if (<= x 1.2e+139) t_0 (* 2.0 y)))))))

C

double code(double x, double y) {
	double t_0 = (y * x) * (-2.0 / (y - x));
	double tmp;
	if (x <= -4.1e+110) {
		tmp = fma((y / x), y, y) * 2.0;
	} else if (x <= -1.9e-139) {
		tmp = t_0;
	} else if (x <= 1.46e-155) {
		tmp = -2.0 * x;
	} else if (x <= 1.2e+139) {
		tmp = t_0;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(y * x) * Float64(-2.0 / Float64(y - x)))
	tmp = 0.0
	if (x <= -4.1e+110)
		tmp = Float64(fma(Float64(y / x), y, y) * 2.0);
	elseif (x <= -1.9e-139)
		tmp = t_0;
	elseif (x <= 1.46e-155)
		tmp = Float64(-2.0 * x);
	elseif (x <= 1.2e+139)
		tmp = t_0;
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * x), $MachinePrecision] * N[(-2.0 / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.1e+110], N[(N[(N[(y / x), $MachinePrecision] * y + y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[x, -1.9e-139], t$95$0, If[LessEqual[x, 1.46e-155], N[(-2.0 * x), $MachinePrecision], If[LessEqual[x, 1.2e+139], t$95$0, N[(2.0 * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.0999999999999999e110

   1. Initial program 73.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 66.6

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 66.6

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

   4. Applied rewrites 66.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l* N/A

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

      7. clear-num N/A

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

      8. associate-/r/ N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. frac-2neg N/A

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

      14. metadata-eval N/A

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

      15. associate-*l/ N/A

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

      16. metadata-eval N/A

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

      17. lower-/.f64 N/A

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

      18. neg-sub0 N/A

          \[\leadsto \frac{-2}{\color{blue}{0 - \left(x - y\right)}} \cdot \left(x \cdot y\right) \]

      19. lift--.f64 N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(x - y\right)}} \cdot \left(x \cdot y\right) \]

      20. sub-neg N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}} \cdot \left(x \cdot y\right) \]

      21. +-commutative N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}} \cdot \left(x \cdot y\right) \]

      22. associate--r+ N/A

          \[\leadsto \frac{-2}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}} \cdot \left(x \cdot y\right) \]

      23. neg-sub0 N/A

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

      24. remove-double-neg N/A

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

      25. lower--.f64 N/A

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

      26. lower-*.f64 73.4

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

   6. Applied rewrites 73.4%

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

   7. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot y + 2 \cdot \frac{{y}^{2}}{x}} \]
   8. Step-by-step derivation

      1. distribute-lft-out N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. unpow2 N/A

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

      6. associate-*l/ N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x}, y, y\right)} \cdot 2 \]

      8. lower-/.f64 93.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{x}}, y, y\right) \cdot 2 \]

   9. Applied rewrites 93.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x}, y, y\right) \cdot 2} \]

   if -4.0999999999999999e110 < x < -1.90000000000000004e-139 or 1.46e-155 < x < 1.20000000000000004e139

   1. Initial program 86.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. metadata-eval N/A

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

      16. neg-sub0 N/A

          \[\leadsto \left(y \cdot x\right) \cdot \frac{-2}{\color{blue}{0 - \left(x - y\right)}} \]

      17. lift--.f64 N/A

          \[\leadsto \left(y \cdot x\right) \cdot \frac{-2}{0 - \color{blue}{\left(x - y\right)}} \]

      18. sub-neg N/A

          \[\leadsto \left(y \cdot x\right) \cdot \frac{-2}{0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}} \]

      19. +-commutative N/A

          \[\leadsto \left(y \cdot x\right) \cdot \frac{-2}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}} \]

      20. associate--r+ N/A

          \[\leadsto \left(y \cdot x\right) \cdot \frac{-2}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}} \]

      21. neg-sub0 N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 85.9

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

   4. Applied rewrites 85.9%

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

   if -1.90000000000000004e-139 < x < 1.46e-155

   1. Initial program 73.3%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 94.8

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

   5. Applied rewrites 94.8%

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

   if 1.20000000000000004e139 < x

   1. Initial program 70.4%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 90.4

         \[\leadsto \color{blue}{2 \cdot y} \]

   5. Applied rewrites 90.4%

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

Alternative 3: 94.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x}, y, y\right) \cdot 2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+166}:\\ \;\;\;\;\frac{y}{x - y} \cdot \left(2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.1e+115)
   (* (fma (/ y x) y y) 2.0)
   (if (<= x 1.1e+166) (* (/ y (- x y)) (* 2.0 x)) (* 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.1e+115) {
		tmp = fma((y / x), y, y) * 2.0;
	} else if (x <= 1.1e+166) {
		tmp = (y / (x - y)) * (2.0 * x);
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.1e+115)
		tmp = Float64(fma(Float64(y / x), y, y) * 2.0);
	elseif (x <= 1.1e+166)
		tmp = Float64(Float64(y / Float64(x - y)) * Float64(2.0 * x));
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.1e+115], N[(N[(N[(y / x), $MachinePrecision] * y + y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[x, 1.1e+166], N[(N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision] * N[(2.0 * x), $MachinePrecision]), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.10000000000000003e115

   1. Initial program 73.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 65.8

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 65.8

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

   4. Applied rewrites 65.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l* N/A

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

      7. clear-num N/A

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

      8. associate-/r/ N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. frac-2neg N/A

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

      14. metadata-eval N/A

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

      15. associate-*l/ N/A

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

      16. metadata-eval N/A

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

      17. lower-/.f64 N/A

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

      18. neg-sub0 N/A

          \[\leadsto \frac{-2}{\color{blue}{0 - \left(x - y\right)}} \cdot \left(x \cdot y\right) \]

      19. lift--.f64 N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(x - y\right)}} \cdot \left(x \cdot y\right) \]

      20. sub-neg N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}} \cdot \left(x \cdot y\right) \]

      21. +-commutative N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}} \cdot \left(x \cdot y\right) \]

      22. associate--r+ N/A

          \[\leadsto \frac{-2}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}} \cdot \left(x \cdot y\right) \]

      23. neg-sub0 N/A

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

      24. remove-double-neg N/A

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

      25. lower--.f64 N/A

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

      26. lower-*.f64 72.7

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

   6. Applied rewrites 72.7%

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

   7. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot y + 2 \cdot \frac{{y}^{2}}{x}} \]
   8. Step-by-step derivation

      1. distribute-lft-out N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. unpow2 N/A

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

      6. associate-*l/ N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x}, y, y\right)} \cdot 2 \]

      8. lower-/.f64 93.3

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{x}}, y, y\right) \cdot 2 \]

   9. Applied rewrites 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x}, y, y\right) \cdot 2} \]

   if -2.10000000000000003e115 < x < 1.1e166

   1. Initial program 81.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 98.0

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 98.0

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

   4. Applied rewrites 98.0%

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

   if 1.1e166 < x

   1. Initial program 70.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 92.9

         \[\leadsto \color{blue}{2 \cdot y} \]

   5. Applied rewrites 92.9%

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

Alternative 4: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-73}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x}, y, y\right) \cdot 2\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, -2, -2\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7e-73)
   (* (fma (/ y x) y y) 2.0)
   (if (<= x 1.16e+66) (* (fma (/ x y) -2.0 -2.0) x) (* 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7e-73) {
		tmp = fma((y / x), y, y) * 2.0;
	} else if (x <= 1.16e+66) {
		tmp = fma((x / y), -2.0, -2.0) * x;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7e-73)
		tmp = Float64(fma(Float64(y / x), y, y) * 2.0);
	elseif (x <= 1.16e+66)
		tmp = Float64(fma(Float64(x / y), -2.0, -2.0) * x);
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7e-73], N[(N[(N[(y / x), $MachinePrecision] * y + y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[x, 1.16e+66], N[(N[(N[(x / y), $MachinePrecision] * -2.0 + -2.0), $MachinePrecision] * x), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.9999999999999995e-73

   1. Initial program 81.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 80.1

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 80.1

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

   4. Applied rewrites 80.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l* N/A

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

      7. clear-num N/A

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

      8. associate-/r/ N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. frac-2neg N/A

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

      14. metadata-eval N/A

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

      15. associate-*l/ N/A

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

      16. metadata-eval N/A

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

      17. lower-/.f64 N/A

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

      18. neg-sub0 N/A

          \[\leadsto \frac{-2}{\color{blue}{0 - \left(x - y\right)}} \cdot \left(x \cdot y\right) \]

      19. lift--.f64 N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(x - y\right)}} \cdot \left(x \cdot y\right) \]

      20. sub-neg N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}} \cdot \left(x \cdot y\right) \]

      21. +-commutative N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}} \cdot \left(x \cdot y\right) \]

      22. associate--r+ N/A

          \[\leadsto \frac{-2}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}} \cdot \left(x \cdot y\right) \]

      23. neg-sub0 N/A

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

      24. remove-double-neg N/A

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

      25. lower--.f64 N/A

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

      26. lower-*.f64 81.4

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

   6. Applied rewrites 81.4%

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

   7. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot y + 2 \cdot \frac{{y}^{2}}{x}} \]
   8. Step-by-step derivation

      1. distribute-lft-out N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. unpow2 N/A

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

      6. associate-*l/ N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x}, y, y\right)} \cdot 2 \]

      8. lower-/.f64 77.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{x}}, y, y\right) \cdot 2 \]

   9. Applied rewrites 77.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x}, y, y\right) \cdot 2} \]

   if -6.9999999999999995e-73 < x < 1.16e66

   1. Initial program 77.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 78.3

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

   5. Applied rewrites 78.3%

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

   if 1.16e66 < x

   1. Initial program 78.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 78.9

         \[\leadsto \color{blue}{2 \cdot y} \]

   5. Applied rewrites 78.9%

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

Alternative 5: 73.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-73}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x}, y, y\right) \cdot 2\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+66}:\\ \;\;\;\;-2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7e-73)
   (* (fma (/ y x) y y) 2.0)
   (if (<= x 1.16e+66) (* -2.0 x) (* 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7e-73) {
		tmp = fma((y / x), y, y) * 2.0;
	} else if (x <= 1.16e+66) {
		tmp = -2.0 * x;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7e-73)
		tmp = Float64(fma(Float64(y / x), y, y) * 2.0);
	elseif (x <= 1.16e+66)
		tmp = Float64(-2.0 * x);
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7e-73], N[(N[(N[(y / x), $MachinePrecision] * y + y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[x, 1.16e+66], N[(-2.0 * x), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.9999999999999995e-73

   1. Initial program 81.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 80.1

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 80.1

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

   4. Applied rewrites 80.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. associate-/l* N/A

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

      7. clear-num N/A

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

      8. associate-/r/ N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. frac-2neg N/A

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

      14. metadata-eval N/A

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

      15. associate-*l/ N/A

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

      16. metadata-eval N/A

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

      17. lower-/.f64 N/A

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

      18. neg-sub0 N/A

          \[\leadsto \frac{-2}{\color{blue}{0 - \left(x - y\right)}} \cdot \left(x \cdot y\right) \]

      19. lift--.f64 N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(x - y\right)}} \cdot \left(x \cdot y\right) \]

      20. sub-neg N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}} \cdot \left(x \cdot y\right) \]

      21. +-commutative N/A

          \[\leadsto \frac{-2}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}} \cdot \left(x \cdot y\right) \]

      22. associate--r+ N/A

          \[\leadsto \frac{-2}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}} \cdot \left(x \cdot y\right) \]

      23. neg-sub0 N/A

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

      24. remove-double-neg N/A

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

      25. lower--.f64 N/A

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

      26. lower-*.f64 81.4

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

   6. Applied rewrites 81.4%

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

   7. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot y + 2 \cdot \frac{{y}^{2}}{x}} \]
   8. Step-by-step derivation

      1. distribute-lft-out N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. unpow2 N/A

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

      6. associate-*l/ N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x}, y, y\right)} \cdot 2 \]

      8. lower-/.f64 77.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{x}}, y, y\right) \cdot 2 \]

   9. Applied rewrites 77.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x}, y, y\right) \cdot 2} \]

   if -6.9999999999999995e-73 < x < 1.16e66

   1. Initial program 77.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 78.2

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

   5. Applied rewrites 78.2%

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

   if 1.16e66 < x

   1. Initial program 78.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 78.9

         \[\leadsto \color{blue}{2 \cdot y} \]

   5. Applied rewrites 78.9%

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

Alternative 6: 73.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-73} \lor \neg \left(x \leq 1.16 \cdot 10^{+66}\right):\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -7e-73) (not (<= x 1.16e+66))) (* 2.0 y) (* -2.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -7e-73) || !(x <= 1.16e+66)) {
		tmp = 2.0 * y;
	} else {
		tmp = -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 <= (-7d-73)) .or. (.not. (x <= 1.16d+66))) then
        tmp = 2.0d0 * y
    else
        tmp = (-2.0d0) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -7e-73) || !(x <= 1.16e+66)) {
		tmp = 2.0 * y;
	} else {
		tmp = -2.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -7e-73) or not (x <= 1.16e+66):
		tmp = 2.0 * y
	else:
		tmp = -2.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -7e-73) || !(x <= 1.16e+66))
		tmp = Float64(2.0 * y);
	else
		tmp = Float64(-2.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -7e-73) || ~((x <= 1.16e+66)))
		tmp = 2.0 * y;
	else
		tmp = -2.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -7e-73], N[Not[LessEqual[x, 1.16e+66]], $MachinePrecision]], N[(2.0 * y), $MachinePrecision], N[(-2.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.9999999999999995e-73 or 1.16e66 < x

   1. Initial program 80.2%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 77.9

         \[\leadsto \color{blue}{2 \cdot y} \]

   5. Applied rewrites 77.9%

      \[\leadsto \color{blue}{2 \cdot y} \]

   if -6.9999999999999995e-73 < x < 1.16e66

   1. Initial program 77.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 78.2

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

   5. Applied rewrites 78.2%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-73} \lor \neg \left(x \leq 1.16 \cdot 10^{+66}\right):\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.9% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ -2 \cdot x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* -2.0 x))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -2.0 * x

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.8%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 52.4

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

5. Applied rewrites 52.4%

   \[\leadsto \color{blue}{-2 \cdot x} \]
6. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 83645045635564430:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ (* 2.0 x) (- x y)) y)))
   (if (< x -1.7210442634149447e+81)
     t_0
     (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) t_0))))

C

double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / 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 = ((2.0d0 * x) / (x - y)) * y
    if (x < (-1.7210442634149447d+81)) then
        tmp = t_0
    else if (x < 83645045635564430.0d0) then
        tmp = (x * 2.0d0) / ((x - y) / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((2.0 * x) / (x - y)) * y
	tmp = 0
	if x < -1.7210442634149447e+81:
		tmp = t_0
	elif x < 83645045635564430.0:
		tmp = (x * 2.0) / ((x - y) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(2.0 * x) / Float64(x - y)) * y)
	tmp = 0.0
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((2.0 * x) / (x - y)) * y;
	tmp = 0.0;
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = (x * 2.0) / ((x - y) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(2.0 * x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[Less[x, -1.7210442634149447e+81], t$95$0, If[Less[x, 83645045635564430.0], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024324 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -1721044263414944700000000000000000000000000000000000000000000000000000000000000000) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564430) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y))))

  (/ (* (* x 2.0) y) (- x y)))