Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.6% → 99.2%

Time: 6.3s

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: 99.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ t_1 := x \cdot \frac{2 \cdot y}{x - y}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq -1 \cdot 10^{-306}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-32}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (* x 2.0) y) (- x y))) (t_1 (* x (/ (* 2.0 y) (- x y)))))
   (if (<= t_0 -5e+144)
     t_1
     (if (<= t_0 -1e-306)
       t_0
       (if (<= t_0 0.0) t_1 (if (<= t_0 2e-32) t_0 t_1))))))

C

double code(double x, double y) {
	double t_0 = ((x * 2.0) * y) / (x - y);
	double t_1 = x * ((2.0 * y) / (x - y));
	double tmp;
	if (t_0 <= -5e+144) {
		tmp = t_1;
	} else if (t_0 <= -1e-306) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e-32) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = ((x * 2.0d0) * y) / (x - y)
    t_1 = x * ((2.0d0 * y) / (x - y))
    if (t_0 <= (-5d+144)) then
        tmp = t_1
    else if (t_0 <= (-1d-306)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = t_1
    else if (t_0 <= 2d-32) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((x * 2.0) * y) / (x - y);
	double t_1 = x * ((2.0 * y) / (x - y));
	double tmp;
	if (t_0 <= -5e+144) {
		tmp = t_1;
	} else if (t_0 <= -1e-306) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e-32) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((x * 2.0) * y) / (x - y)
	t_1 = x * ((2.0 * y) / (x - y))
	tmp = 0
	if t_0 <= -5e+144:
		tmp = t_1
	elif t_0 <= -1e-306:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 2e-32:
		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(x * Float64(Float64(2.0 * y) / Float64(x - y)))
	tmp = 0.0
	if (t_0 <= -5e+144)
		tmp = t_1;
	elseif (t_0 <= -1e-306)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e-32)
		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 = x * ((2.0 * y) / (x - y));
	tmp = 0.0;
	if (t_0 <= -5e+144)
		tmp = t_1;
	elseif (t_0 <= -1e-306)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e-32)
		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[(x * N[(N[(2.0 * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+144], t$95$1, If[LessEqual[t$95$0, -1e-306], t$95$0, If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 2e-32], 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)) < -4.9999999999999999e144 or -1.00000000000000003e-306 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -0.0 or 2.00000000000000011e-32 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y))

   1. Initial program 29.8%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   if -4.9999999999999999e144 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -1.00000000000000003e-306 or -0.0 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < 2.00000000000000011e-32

   1. Initial program 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq -5 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \frac{2 \cdot y}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq -1 \cdot 10^{-306}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq 0:\\ \;\;\;\;x \cdot \frac{2 \cdot y}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq 2 \cdot 10^{-32}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2 \cdot y}{x - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{2 \cdot y}{x - y}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-194}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-158}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ (* 2.0 y) (- x y)))))
   (if (<= y -1.7e-194) t_0 (if (<= y 4.7e-158) (* 2.0 y) t_0))))

C

double code(double x, double y) {
	double t_0 = x * ((2.0 * y) / (x - y));
	double tmp;
	if (y <= -1.7e-194) {
		tmp = t_0;
	} else if (y <= 4.7e-158) {
		tmp = 2.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * ((2.0d0 * y) / (x - y))
    if (y <= (-1.7d-194)) then
        tmp = t_0
    else if (y <= 4.7d-158) then
        tmp = 2.0d0 * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * ((2.0 * y) / (x - y));
	double tmp;
	if (y <= -1.7e-194) {
		tmp = t_0;
	} else if (y <= 4.7e-158) {
		tmp = 2.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * ((2.0 * y) / (x - y))
	tmp = 0
	if y <= -1.7e-194:
		tmp = t_0
	elif y <= 4.7e-158:
		tmp = 2.0 * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(Float64(2.0 * y) / Float64(x - y)))
	tmp = 0.0
	if (y <= -1.7e-194)
		tmp = t_0;
	elseif (y <= 4.7e-158)
		tmp = Float64(2.0 * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * ((2.0 * y) / (x - y));
	tmp = 0.0;
	if (y <= -1.7e-194)
		tmp = t_0;
	elseif (y <= 4.7e-158)
		tmp = 2.0 * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(N[(2.0 * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e-194], t$95$0, If[LessEqual[y, 4.7e-158], N[(2.0 * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.70000000000000005e-194 or 4.70000000000000036e-158 < y

   1. Initial program 80.4%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 95.7

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

   4. Applied rewrites 95.7%

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

   if -1.70000000000000005e-194 < y < 4.70000000000000036e-158

   1. Initial program 72.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 92.3

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

   5. Applied rewrites 92.3%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \frac{2 \cdot y}{x - y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-158}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2 \cdot y}{x - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-29}:\\ \;\;\;\;-2 \cdot \mathsf{fma}\left(x, \frac{x}{y}, x\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.2e-29)
   (* -2.0 (fma x (/ x y) x))
   (if (<= y 1.25e-34) (* 2.0 y) (* x -2.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.2e-29) {
		tmp = -2.0 * fma(x, (x / y), x);
	} else if (y <= 1.25e-34) {
		tmp = 2.0 * y;
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.2e-29)
		tmp = Float64(-2.0 * fma(x, Float64(x / y), x));
	elseif (y <= 1.25e-34)
		tmp = Float64(2.0 * y);
	else
		tmp = Float64(x * -2.0);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.2e-29], N[(-2.0 * N[(x * N[(x / y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-34], N[(2.0 * y), $MachinePrecision], N[(x * -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2000000000000004e-29

   1. Initial program 86.2%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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. lower-*.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. lower-fma.f64 N/A

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

      15. lower-/.f64 81.0

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

   5. Applied rewrites 81.0%

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

   if -5.2000000000000004e-29 < y < 1.2500000000000001e-34

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 80.3

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

   5. Applied rewrites 80.3%

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

   if 1.2500000000000001e-34 < y

   1. Initial program 75.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 83.1

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

   5. Applied rewrites 83.1%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-29}:\\ \;\;\;\;-2 \cdot \mathsf{fma}\left(x, \frac{x}{y}, x\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;x \cdot -2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.25e-29) (* x -2.0) (if (<= y 1.25e-34) (* 2.0 y) (* x -2.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.25e-29) {
		tmp = x * -2.0;
	} else if (y <= 1.25e-34) {
		tmp = 2.0 * y;
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.25d-29)) then
        tmp = x * (-2.0d0)
    else if (y <= 1.25d-34) then
        tmp = 2.0d0 * y
    else
        tmp = x * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.25e-29) {
		tmp = x * -2.0;
	} else if (y <= 1.25e-34) {
		tmp = 2.0 * y;
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.25e-29:
		tmp = x * -2.0
	elif y <= 1.25e-34:
		tmp = 2.0 * y
	else:
		tmp = x * -2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.25e-29)
		tmp = Float64(x * -2.0);
	elseif (y <= 1.25e-34)
		tmp = Float64(2.0 * y);
	else
		tmp = Float64(x * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.25e-29)
		tmp = x * -2.0;
	elseif (y <= 1.25e-34)
		tmp = 2.0 * y;
	else
		tmp = x * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.25e-29], N[(x * -2.0), $MachinePrecision], If[LessEqual[y, 1.25e-34], N[(2.0 * y), $MachinePrecision], N[(x * -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2499999999999999e-29 or 1.2500000000000001e-34 < y

   1. Initial program 80.4%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 82.0

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

   5. Applied rewrites 82.0%

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

   if -2.2499999999999999e-29 < y < 1.2500000000000001e-34

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 80.3

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

   5. Applied rewrites 80.3%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;x \cdot -2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \]
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 78.6%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 54.1

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

5. Applied rewrites 54.1%

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

6. Final simplification 54.1%

   \[\leadsto x \cdot -2 \]
7. 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 2024220 
(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)))