Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 76.8% → 99.8%

Time: 7.7s

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: 76.8% 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: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y \cdot 2}{x - y}\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-28}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 10^{-29}:\\ \;\;\;\;y \cdot \frac{2 \cdot x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ (* y 2.0) (- x y)))))
   (if (<= y -8.2e-28) t_0 (if (<= y 1e-29) (* y (/ (* 2.0 x) (- x y))) t_0))))

C

double code(double x, double y) {
	double t_0 = x * ((y * 2.0) / (x - y));
	double tmp;
	if (y <= -8.2e-28) {
		tmp = t_0;
	} else if (y <= 1e-29) {
		tmp = y * ((2.0 * x) / (x - y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * ((y * 2.0d0) / (x - y))
    if (y <= (-8.2d-28)) then
        tmp = t_0
    else if (y <= 1d-29) then
        tmp = y * ((2.0d0 * x) / (x - y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * ((y * 2.0) / (x - y));
	double tmp;
	if (y <= -8.2e-28) {
		tmp = t_0;
	} else if (y <= 1e-29) {
		tmp = y * ((2.0 * x) / (x - y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * ((y * 2.0) / (x - y))
	tmp = 0
	if y <= -8.2e-28:
		tmp = t_0
	elif y <= 1e-29:
		tmp = y * ((2.0 * x) / (x - y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(Float64(y * 2.0) / Float64(x - y)))
	tmp = 0.0
	if (y <= -8.2e-28)
		tmp = t_0;
	elseif (y <= 1e-29)
		tmp = Float64(y * Float64(Float64(2.0 * x) / Float64(x - y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * ((y * 2.0) / (x - y));
	tmp = 0.0;
	if (y <= -8.2e-28)
		tmp = t_0;
	elseif (y <= 1e-29)
		tmp = y * ((2.0 * x) / (x - y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(N[(y * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e-28], t$95$0, If[LessEqual[y, 1e-29], N[(y * N[(N[(2.0 * x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000005e-28 or 9.99999999999999943e-30 < y

   1. Initial program 79.2%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   if -8.2000000000000005e-28 < y < 9.99999999999999943e-30

   1. Initial program 80.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.1

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

   4. Applied egg-rr 99.1%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{y \cdot 2}{x - y}\\ \mathbf{elif}\;y \leq 10^{-29}:\\ \;\;\;\;y \cdot \frac{2 \cdot x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 2}{x - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot x\right) \cdot \frac{2}{x - y}\\ t_1 := \frac{y \cdot \left(2 \cdot x\right)}{x - y}\\ t_2 := y \cdot \mathsf{fma}\left(y, \frac{2}{x}, 2\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-264}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+104}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* y x) (/ 2.0 (- x y))))
        (t_1 (/ (* y (* 2.0 x)) (- x y)))
        (t_2 (* y (fma y (/ 2.0 x) 2.0))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -5e-264)
       t_0
       (if (<= t_1 2e-296) (* y 2.0) (if (<= t_1 2e+104) t_0 t_2))))))

C

double code(double x, double y) {
	double t_0 = (y * x) * (2.0 / (x - y));
	double t_1 = (y * (2.0 * x)) / (x - y);
	double t_2 = y * fma(y, (2.0 / x), 2.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -5e-264) {
		tmp = t_0;
	} else if (t_1 <= 2e-296) {
		tmp = y * 2.0;
	} else if (t_1 <= 2e+104) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(y * x) * Float64(2.0 / Float64(x - y)))
	t_1 = Float64(Float64(y * Float64(2.0 * x)) / Float64(x - y))
	t_2 = Float64(y * fma(y, Float64(2.0 / x), 2.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -5e-264)
		tmp = t_0;
	elseif (t_1 <= 2e-296)
		tmp = Float64(y * 2.0);
	elseif (t_1 <= 2e+104)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * x), $MachinePrecision] * N[(2.0 / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y * N[(2.0 * x), $MachinePrecision]), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y * N[(2.0 / x), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -5e-264], t$95$0, If[LessEqual[t$95$1, 2e-296], N[(y * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+104], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -inf.0 or 2e104 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y))

   1. Initial program 7.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. *-commutative N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. distribute-rgt-in N/A

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

      10. +-commutative N/A

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

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

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. associate-*r/ N/A

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

      14. metadata-eval N/A

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

      15. /-lowering-/.f64 65.1

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

   5. Simplified 65.1%

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

   if -inf.0 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -5.0000000000000001e-264 or 2e-296 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < 2e104

   1. Initial program 99.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

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

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 98.9

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

   4. Applied egg-rr 98.9%

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

   if -5.0000000000000001e-264 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < 2e-296

   1. Initial program 28.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 70.0

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

   5. Simplified 70.0%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(2 \cdot x\right)}{x - y} \leq -\infty:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, \frac{2}{x}, 2\right)\\ \mathbf{elif}\;\frac{y \cdot \left(2 \cdot x\right)}{x - y} \leq -5 \cdot 10^{-264}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{2}{x - y}\\ \mathbf{elif}\;\frac{y \cdot \left(2 \cdot x\right)}{x - y} \leq 2 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;\frac{y \cdot \left(2 \cdot x\right)}{x - y} \leq 2 \cdot 10^{+104}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{2}{x - y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, \frac{2}{x}, 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \mathsf{fma}\left(y, \frac{2}{x}, 2\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+167}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \frac{y \cdot 2}{x - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (fma y (/ 2.0 x) 2.0))))
   (if (<= x -9.5e+167)
     t_0
     (if (<= x 2.8e+128) (* x (/ (* y 2.0) (- x y))) t_0))))

C

double code(double x, double y) {
	double t_0 = y * fma(y, (2.0 / x), 2.0);
	double tmp;
	if (x <= -9.5e+167) {
		tmp = t_0;
	} else if (x <= 2.8e+128) {
		tmp = x * ((y * 2.0) / (x - y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(y * fma(y, Float64(2.0 / x), 2.0))
	tmp = 0.0
	if (x <= -9.5e+167)
		tmp = t_0;
	elseif (x <= 2.8e+128)
		tmp = Float64(x * Float64(Float64(y * 2.0) / Float64(x - y)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(y * N[(2.0 / x), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e+167], t$95$0, If[LessEqual[x, 2.8e+128], N[(x * N[(N[(y * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000006e167 or 2.79999999999999983e128 < x

   1. Initial program 69.1%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. *-commutative N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. distribute-rgt-in N/A

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

      10. +-commutative N/A

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

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

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. associate-*r/ N/A

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

      14. metadata-eval N/A

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

      15. /-lowering-/.f64 95.2

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

   5. Simplified 95.2%

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

   if -9.5000000000000006e167 < x < 2.79999999999999983e128

   1. Initial program 83.9%

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

      1. associate-*l* N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 97.4

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

   4. Applied egg-rr 97.4%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+167}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, \frac{2}{x}, 2\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \frac{y \cdot 2}{x - y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, \frac{2}{x}, 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, \frac{2}{x}, 2\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-15}:\\ \;\;\;\;-2 \cdot \mathsf{fma}\left(x, \frac{x}{y}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.15e+75)
   (* y (fma y (/ 2.0 x) 2.0))
   (if (<= x 1.05e-15) (* -2.0 (fma x (/ x y) x)) (* y 2.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.15e+75) {
		tmp = y * fma(y, (2.0 / x), 2.0);
	} else if (x <= 1.05e-15) {
		tmp = -2.0 * fma(x, (x / y), x);
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.15e+75)
		tmp = Float64(y * fma(y, Float64(2.0 / x), 2.0));
	elseif (x <= 1.05e-15)
		tmp = Float64(-2.0 * fma(x, Float64(x / y), x));
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.15e+75], N[(y * N[(y * N[(2.0 / x), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-15], N[(-2.0 * N[(x * N[(x / y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1500000000000001e75

   1. Initial program 65.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. *-commutative N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. distribute-rgt-in N/A

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

      10. +-commutative N/A

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

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

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. associate-*r/ N/A

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

      14. metadata-eval N/A

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

      15. /-lowering-/.f64 87.7

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

   5. Simplified 87.7%

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

   if -2.1500000000000001e75 < x < 1.0499999999999999e-15

   1. Initial program 82.1%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-lft-in N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

      7. unpow2 N/A

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

      8. distribute-rgt-out N/A

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

      9. +-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unpow2 N/A

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

      13. associate-/l* N/A

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

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

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

      15. /-lowering-/.f64 73.8

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

   5. Simplified 73.8%

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

   if 1.0499999999999999e-15 < x

   1. Initial program 85.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 75.6

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

   5. Simplified 75.6%

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

Alternative 5: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+34}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-15}:\\ \;\;\;\;-2 \cdot \mathsf{fma}\left(x, \frac{x}{y}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.32e+34)
   (* y 2.0)
   (if (<= x 4.4e-15) (* -2.0 (fma x (/ x y) x)) (* y 2.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.32e+34) {
		tmp = y * 2.0;
	} else if (x <= 4.4e-15) {
		tmp = -2.0 * fma(x, (x / y), x);
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.32e+34)
		tmp = Float64(y * 2.0);
	elseif (x <= 4.4e-15)
		tmp = Float64(-2.0 * fma(x, Float64(x / y), x));
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.32e+34], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 4.4e-15], N[(-2.0 * N[(x * N[(x / y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.31999999999999991e34 or 4.39999999999999971e-15 < x

   1. Initial program 77.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 78.3

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

   5. Simplified 78.3%

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

   if -1.31999999999999991e34 < x < 4.39999999999999971e-15

   1. Initial program 82.2%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-lft-in N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

      7. unpow2 N/A

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

      8. distribute-rgt-out N/A

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

      9. +-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unpow2 N/A

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

      13. associate-/l* N/A

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

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

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

      15. /-lowering-/.f64 75.8

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

   5. Simplified 75.8%

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

Alternative 6: 75.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+52}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+31}:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.06e+52) (* y 2.0) (if (<= x 1.25e+31) (* x -2.0) (* y 2.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.06e+52) {
		tmp = y * 2.0;
	} else if (x <= 1.25e+31) {
		tmp = x * -2.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.06d+52)) then
        tmp = y * 2.0d0
    else if (x <= 1.25d+31) then
        tmp = x * (-2.0d0)
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.06e+52) {
		tmp = y * 2.0;
	} else if (x <= 1.25e+31) {
		tmp = x * -2.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.06e+52:
		tmp = y * 2.0
	elif x <= 1.25e+31:
		tmp = x * -2.0
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.06e+52)
		tmp = Float64(y * 2.0);
	elseif (x <= 1.25e+31)
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.06e+52)
		tmp = y * 2.0;
	elseif (x <= 1.25e+31)
		tmp = x * -2.0;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.06e+52], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 1.25e+31], N[(x * -2.0), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0599999999999999e52 or 1.25000000000000007e31 < x

   1. Initial program 74.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 82.6

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

   5. Simplified 82.6%

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

   if -1.0599999999999999e52 < x < 1.25000000000000007e31

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 72.3

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

   5. Simplified 72.3%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+52}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+31}:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.0% accurate, 4.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.6%

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

3. Taylor expanded in x around 0

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

   1. *-lowering-*.f64 47.1

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

5. Simplified 47.1%

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

6. Final simplification 47.1%

   \[\leadsto x \cdot -2 \]
7. Add Preprocessing

Developer Target 1: 99.5% 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 2024199 
(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)))