Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.6% → 99.1%

Time: 6.8s

Alternatives: 5

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: 77.6% 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: 99.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ t_1 := y \cdot \frac{x \cdot 2}{x - y}\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq -4 \cdot 10^{-302}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-20}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (* x 2.0) y) (- x y))) (t_1 (* y (/ (* x 2.0) (- x y)))))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 -4e-302)
       t_0
       (if (<= t_0 0.0) t_1 (if (<= t_0 5e-20) t_0 t_1))))))

C

double code(double x, double y) {
	double t_0 = ((x * 2.0) * y) / (x - y);
	double t_1 = y * ((x * 2.0) / (x - y));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= -4e-302) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 5e-20) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double t_0 = ((x * 2.0) * y) / (x - y);
	double t_1 = y * ((x * 2.0) / (x - y));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= -4e-302) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 5e-20) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((x * 2.0) * y) / (x - y)
	t_1 = y * ((x * 2.0) / (x - y))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= -4e-302:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 5e-20:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
	t_1 = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= -4e-302)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 5e-20)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((x * 2.0) * y) / (x - y);
	t_1 = y * ((x * 2.0) / (x - y));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= -4e-302)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 5e-20)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, -4e-302], t$95$0, If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 5e-20], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -inf.0 or -3.9999999999999999e-302 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -0.0 or 4.9999999999999999e-20 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y))

   1. Initial program 30.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 98.7

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

   4. Applied rewrites 98.7%

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

   if -inf.0 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -3.9999999999999999e-302 or -0.0 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < 4.9999999999999999e-20

   1. Initial program 99.0%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq -4 \cdot 10^{-302}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq 0:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq 5 \cdot 10^{-20}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x \cdot 2}{x - y}\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{-139}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (/ (* x 2.0) (- x y)))))
   (if (<= x -3.8e-139) t_0 (if (<= x 4.2e-219) (* x -2.0) t_0))))

C

double code(double x, double y) {
	double t_0 = y * ((x * 2.0) / (x - y));
	double tmp;
	if (x <= -3.8e-139) {
		tmp = t_0;
	} else if (x <= 4.2e-219) {
		tmp = x * -2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * ((x * 2.0d0) / (x - y))
    if (x <= (-3.8d-139)) then
        tmp = t_0
    else if (x <= 4.2d-219) then
        tmp = x * (-2.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * ((x * 2.0) / (x - y));
	double tmp;
	if (x <= -3.8e-139) {
		tmp = t_0;
	} else if (x <= 4.2e-219) {
		tmp = x * -2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * ((x * 2.0) / (x - y))
	tmp = 0
	if x <= -3.8e-139:
		tmp = t_0
	elif x <= 4.2e-219:
		tmp = x * -2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y)))
	tmp = 0.0
	if (x <= -3.8e-139)
		tmp = t_0;
	elseif (x <= 4.2e-219)
		tmp = Float64(x * -2.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * ((x * 2.0) / (x - y));
	tmp = 0.0;
	if (x <= -3.8e-139)
		tmp = t_0;
	elseif (x <= 4.2e-219)
		tmp = x * -2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e-139], t$95$0, If[LessEqual[x, 4.2e-219], N[(x * -2.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000008e-139 or 4.20000000000000001e-219 < x

   1. Initial program 77.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 95.8

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

   4. Applied rewrites 95.8%

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

   if -3.80000000000000008e-139 < x < 4.20000000000000001e-219

   1. Initial program 69.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 95.4

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

   5. Applied rewrites 95.4%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-64}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 2.7:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, \frac{2}{x}, 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.5e-64)
   (* 2.0 y)
   (if (<= x 2.7) (* x -2.0) (* y (fma y (/ 2.0 x) 2.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.5e-64) {
		tmp = 2.0 * y;
	} else if (x <= 2.7) {
		tmp = x * -2.0;
	} else {
		tmp = y * fma(y, (2.0 / x), 2.0);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.5e-64)
		tmp = Float64(2.0 * y);
	elseif (x <= 2.7)
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(y * fma(y, Float64(2.0 / x), 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.5e-64], N[(2.0 * y), $MachinePrecision], If[LessEqual[x, 2.7], N[(x * -2.0), $MachinePrecision], N[(y * N[(y * N[(2.0 / x), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.5000000000000003e-64

   1. Initial program 74.9%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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. lower-*.f64 77.9

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

   5. Applied rewrites 77.9%

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

   if -3.5000000000000003e-64 < x < 2.7000000000000002

   1. Initial program 77.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 82.9

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

   5. Applied rewrites 82.9%

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

   if 2.7000000000000002 < x

   1. Initial program 72.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot y + 2 \cdot \frac{{y}^{2}}{x}} \]
   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. lower-*.f64 N/A

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

      12. lower-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. lower-/.f64 76.5

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

   5. Applied rewrites 76.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-64}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 2.7:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(y, \frac{2}{x}, 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-64}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 2.4:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.5e-64) (* 2.0 y) (if (<= x 2.4) (* x -2.0) (* 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.5e-64) {
		tmp = 2.0 * y;
	} else if (x <= 2.4) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.5d-64)) then
        tmp = 2.0d0 * y
    else if (x <= 2.4d0) then
        tmp = x * (-2.0d0)
    else
        tmp = 2.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.5e-64) {
		tmp = 2.0 * y;
	} else if (x <= 2.4) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.5e-64:
		tmp = 2.0 * y
	elif x <= 2.4:
		tmp = x * -2.0
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.5e-64)
		tmp = Float64(2.0 * y);
	elseif (x <= 2.4)
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.5e-64)
		tmp = 2.0 * y;
	elseif (x <= 2.4)
		tmp = x * -2.0;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.5e-64], N[(2.0 * y), $MachinePrecision], If[LessEqual[x, 2.4], N[(x * -2.0), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5000000000000003e-64 or 2.39999999999999991 < x

   1. Initial program 74.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 77.2

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

   5. Applied rewrites 77.2%

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

   if -3.5000000000000003e-64 < x < 2.39999999999999991

   1. Initial program 77.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 82.9

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

   5. Applied rewrites 82.9%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-64}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 2.4:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.5% 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 75.8%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 53.7

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

5. Applied rewrites 53.7%

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

6. Final simplification 53.7%

   \[\leadsto x \cdot -2 \]
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 2024214 
(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)))