_divideComplex, real part

Percentage Accurate: 62.2% → 83.1%

Time: 8.8s

Alternatives: 8

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    code = ((x_46re * y_46re) + (x_46im * y_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	return ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    code = ((x_46re * y_46re) + (x_46im * y_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	return ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 83.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x.im + \frac{x.re}{\frac{y.im}{y.re}}\\ t_1 := y.re \cdot y.re + y.im \cdot y.im\\ \mathbf{if}\;y.im \leq -4 \cdot 10^{+80}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.im \leq -8.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{x.re \cdot y.re + y.im \cdot x.im}{t\_1}\\ \mathbf{elif}\;y.im \leq 4.9 \cdot 10^{-85}:\\ \;\;\;\;\frac{x.re + \frac{y.im \cdot x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 1.6 \cdot 10^{+81}:\\ \;\;\;\;\frac{y.im}{\frac{t\_1}{t\_0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_0}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (+ x.im (/ x.re (/ y.im y.re))))
        (t_1 (+ (* y.re y.re) (* y.im y.im))))
   (if (<= y.im -4e+80)
     (/ (+ x.im (* x.re (/ y.re y.im))) y.im)
     (if (<= y.im -8.8e-112)
       (/ (+ (* x.re y.re) (* y.im x.im)) t_1)
       (if (<= y.im 4.9e-85)
         (/ (+ x.re (/ (* y.im x.im) y.re)) y.re)
         (if (<= y.im 1.6e+81) (/ y.im (/ t_1 t_0)) (/ t_0 y.im)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = x_46_im + (x_46_re / (y_46_im / y_46_re));
	double t_1 = (y_46_re * y_46_re) + (y_46_im * y_46_im);
	double tmp;
	if (y_46_im <= -4e+80) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if (y_46_im <= -8.8e-112) {
		tmp = ((x_46_re * y_46_re) + (y_46_im * x_46_im)) / t_1;
	} else if (y_46_im <= 4.9e-85) {
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_im <= 1.6e+81) {
		tmp = y_46_im / (t_1 / t_0);
	} else {
		tmp = t_0 / y_46_im;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x_46im + (x_46re / (y_46im / y_46re))
    t_1 = (y_46re * y_46re) + (y_46im * y_46im)
    if (y_46im <= (-4d+80)) then
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    else if (y_46im <= (-8.8d-112)) then
        tmp = ((x_46re * y_46re) + (y_46im * x_46im)) / t_1
    else if (y_46im <= 4.9d-85) then
        tmp = (x_46re + ((y_46im * x_46im) / y_46re)) / y_46re
    else if (y_46im <= 1.6d+81) then
        tmp = y_46im / (t_1 / t_0)
    else
        tmp = t_0 / y_46im
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = x_46_im + (x_46_re / (y_46_im / y_46_re));
	double t_1 = (y_46_re * y_46_re) + (y_46_im * y_46_im);
	double tmp;
	if (y_46_im <= -4e+80) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if (y_46_im <= -8.8e-112) {
		tmp = ((x_46_re * y_46_re) + (y_46_im * x_46_im)) / t_1;
	} else if (y_46_im <= 4.9e-85) {
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_im <= 1.6e+81) {
		tmp = y_46_im / (t_1 / t_0);
	} else {
		tmp = t_0 / y_46_im;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = x_46_im + (x_46_re / (y_46_im / y_46_re))
	t_1 = (y_46_re * y_46_re) + (y_46_im * y_46_im)
	tmp = 0
	if y_46_im <= -4e+80:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	elif y_46_im <= -8.8e-112:
		tmp = ((x_46_re * y_46_re) + (y_46_im * x_46_im)) / t_1
	elif y_46_im <= 4.9e-85:
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re
	elif y_46_im <= 1.6e+81:
		tmp = y_46_im / (t_1 / t_0)
	else:
		tmp = t_0 / y_46_im
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(x_46_im + Float64(x_46_re / Float64(y_46_im / y_46_re)))
	t_1 = Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im))
	tmp = 0.0
	if (y_46_im <= -4e+80)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	elseif (y_46_im <= -8.8e-112)
		tmp = Float64(Float64(Float64(x_46_re * y_46_re) + Float64(y_46_im * x_46_im)) / t_1);
	elseif (y_46_im <= 4.9e-85)
		tmp = Float64(Float64(x_46_re + Float64(Float64(y_46_im * x_46_im) / y_46_re)) / y_46_re);
	elseif (y_46_im <= 1.6e+81)
		tmp = Float64(y_46_im / Float64(t_1 / t_0));
	else
		tmp = Float64(t_0 / y_46_im);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = x_46_im + (x_46_re / (y_46_im / y_46_re));
	t_1 = (y_46_re * y_46_re) + (y_46_im * y_46_im);
	tmp = 0.0;
	if (y_46_im <= -4e+80)
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	elseif (y_46_im <= -8.8e-112)
		tmp = ((x_46_re * y_46_re) + (y_46_im * x_46_im)) / t_1;
	elseif (y_46_im <= 4.9e-85)
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	elseif (y_46_im <= 1.6e+81)
		tmp = y_46_im / (t_1 / t_0);
	else
		tmp = t_0 / y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(x$46$im + N[(x$46$re / N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -4e+80], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$im, -8.8e-112], N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * x$46$im), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y$46$im, 4.9e-85], N[(N[(x$46$re + N[(N[(y$46$im * x$46$im), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$im, 1.6e+81], N[(y$46$im / N[(t$95$1 / t$95$0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 / y$46$im), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y.im < -4e80

   1. Initial program 42.3%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.im + \frac{x.re \cdot y.re}{y.im}\right), \color{blue}{y.im}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(\frac{x.re \cdot y.re}{y.im}\right)\right), y.im\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(x.re \cdot \frac{y.re}{y.im}\right)\right), y.im\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{y.re}{y.im}\right)\right)\right), y.im\right) \]

      5. /-lowering-/.f64 86.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{/.f64}\left(y.re, y.im\right)\right)\right), y.im\right) \]

   5. Simplified 86.4%

      \[\leadsto \color{blue}{\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}} \]

   if -4e80 < y.im < -8.80000000000000085e-112

   1. Initial program 94.3%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   if -8.80000000000000085e-112 < y.im < 4.90000000000000015e-85

   1. Initial program 62.7%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.re + \frac{x.im \cdot y.im}{y.re}\right), \color{blue}{y.re}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(\frac{x.im \cdot y.im}{y.re}\right)\right), y.re\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\left(x.im \cdot y.im\right), y.re\right)\right), y.re\right) \]

      4. *-lowering-*.f64 87.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x.im, y.im\right), y.re\right)\right), y.re\right) \]

   5. Simplified 87.7%

      \[\leadsto \color{blue}{\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}} \]

   if 4.90000000000000015e-85 < y.im < 1.6e81

   1. Initial program 71.3%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(y.im \cdot \left(x.im + \frac{x.re \cdot y.re}{y.im}\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y.im, \left(x.im + \frac{x.re \cdot y.re}{y.im}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(y.re, y.re\right)}, \mathsf{*.f64}\left(y.im, y.im\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y.im, \mathsf{+.f64}\left(x.im, \left(\frac{x.re \cdot y.re}{y.im}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, \color{blue}{y.re}\right), \mathsf{*.f64}\left(y.im, y.im\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y.im, \mathsf{+.f64}\left(x.im, \left(x.re \cdot \frac{y.re}{y.im}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y.im, \mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{y.re}{y.im}\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right)\right) \]

      5. /-lowering-/.f64 68.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y.im, \mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{/.f64}\left(y.re, y.im\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right)\right) \]

   5. Simplified 68.7%

      \[\leadsto \frac{\color{blue}{y.im \cdot \left(x.im + x.re \cdot \frac{y.re}{y.im}\right)}}{y.re \cdot y.re + y.im \cdot y.im} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto y.im \cdot \color{blue}{\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.re \cdot y.re + y.im \cdot y.im}} \]

      2. clear-num N/A

         \[\leadsto y.im \cdot \frac{1}{\color{blue}{\frac{y.re \cdot y.re + y.im \cdot y.im}{x.im + x.re \cdot \frac{y.re}{y.im}}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{y.im}{\color{blue}{\frac{y.re \cdot y.re + y.im \cdot y.im}{x.im + x.re \cdot \frac{y.re}{y.im}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(y.im, \color{blue}{\left(\frac{y.re \cdot y.re + y.im \cdot y.im}{x.im + x.re \cdot \frac{y.re}{y.im}}\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(y.im, \mathsf{/.f64}\left(\left(y.re \cdot y.re + y.im \cdot y.im\right), \color{blue}{\left(x.im + x.re \cdot \frac{y.re}{y.im}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(y.im, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y.re \cdot y.re\right), \left(y.im \cdot y.im\right)\right), \left(\color{blue}{x.im} + x.re \cdot \frac{y.re}{y.im}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(y.im, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \left(y.im \cdot y.im\right)\right), \left(x.im + x.re \cdot \frac{y.re}{y.im}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(y.im, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right), \left(x.im + x.re \cdot \frac{y.re}{y.im}\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y.im, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right), \mathsf{+.f64}\left(x.im, \color{blue}{\left(x.re \cdot \frac{y.re}{y.im}\right)}\right)\right)\right) \]

      10. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(y.im, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right), \mathsf{+.f64}\left(x.im, \left(x.re \cdot \frac{1}{\color{blue}{\frac{y.im}{y.re}}}\right)\right)\right)\right) \]

      11. un-div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(y.im, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right), \mathsf{+.f64}\left(x.im, \left(\frac{x.re}{\color{blue}{\frac{y.im}{y.re}}}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(y.im, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right), \mathsf{+.f64}\left(x.im, \mathsf{/.f64}\left(x.re, \color{blue}{\left(\frac{y.im}{y.re}\right)}\right)\right)\right)\right) \]

      13. /-lowering-/.f64 73.4%

          \[\leadsto \mathsf{/.f64}\left(y.im, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right), \mathsf{+.f64}\left(x.im, \mathsf{/.f64}\left(x.re, \mathsf{/.f64}\left(y.im, \color{blue}{y.re}\right)\right)\right)\right)\right) \]

   7. Applied egg-rr 73.4%

      \[\leadsto \color{blue}{\frac{y.im}{\frac{y.re \cdot y.re + y.im \cdot y.im}{x.im + \frac{x.re}{\frac{y.im}{y.re}}}}} \]

   if 1.6e81 < y.im

   1. Initial program 38.6%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(y.im \cdot \left(x.im + \frac{x.re \cdot y.re}{y.im}\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y.im, \left(x.im + \frac{x.re \cdot y.re}{y.im}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(y.re, y.re\right)}, \mathsf{*.f64}\left(y.im, y.im\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y.im, \mathsf{+.f64}\left(x.im, \left(\frac{x.re \cdot y.re}{y.im}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, \color{blue}{y.re}\right), \mathsf{*.f64}\left(y.im, y.im\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y.im, \mathsf{+.f64}\left(x.im, \left(x.re \cdot \frac{y.re}{y.im}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y.im, \mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{y.re}{y.im}\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right)\right) \]

      5. /-lowering-/.f64 38.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y.im, \mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{/.f64}\left(y.re, y.im\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y.re, y.re\right), \mathsf{*.f64}\left(y.im, y.im\right)\right)\right) \]

   5. Simplified 38.6%

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

   6. Taylor expanded in y.re around 0

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

      1. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y.im, \mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{/.f64}\left(y.re, y.im\right)\right)\right)\right), \left(y.im \cdot \color{blue}{y.im}\right)\right) \]

      2. *-lowering-*.f64 38.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y.im, \mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{/.f64}\left(y.re, y.im\right)\right)\right)\right), \mathsf{*.f64}\left(y.im, \color{blue}{y.im}\right)\right) \]

   8. Simplified 38.7%

      \[\leadsto \frac{y.im \cdot \left(x.im + x.re \cdot \frac{y.re}{y.im}\right)}{\color{blue}{y.im \cdot y.im}} \]
   9. Step-by-step derivation

      1. times-frac N/A

         \[\leadsto \frac{y.im}{y.im} \cdot \color{blue}{\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}} \]

      2. *-inverses N/A

         \[\leadsto 1 \cdot \frac{\color{blue}{x.im + x.re \cdot \frac{y.re}{y.im}}}{y.im} \]

      3. clear-num N/A

         \[\leadsto 1 \cdot \frac{1}{\color{blue}{\frac{y.im}{x.im + x.re \cdot \frac{y.re}{y.im}}}} \]

      4. div-inv N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y.im}{x.im + x.re \cdot \frac{y.re}{y.im}}}} \]

      5. clear-num N/A

         \[\leadsto \frac{x.im + x.re \cdot \frac{y.re}{y.im}}{\color{blue}{y.im}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(x.im + x.re \cdot \frac{y.re}{y.im}\right), \color{blue}{y.im}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(x.re \cdot \frac{y.re}{y.im}\right)\right), y.im\right) \]

      8. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(x.re \cdot \frac{1}{\frac{y.im}{y.re}}\right)\right), y.im\right) \]

      9. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(\frac{x.re}{\frac{y.im}{y.re}}\right)\right), y.im\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{/.f64}\left(x.re, \left(\frac{y.im}{y.re}\right)\right)\right), y.im\right) \]

      11. /-lowering-/.f64 85.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{/.f64}\left(x.re, \mathsf{/.f64}\left(y.im, y.re\right)\right)\right), y.im\right) \]

   10. Applied egg-rr 85.7%

       \[\leadsto \color{blue}{\frac{x.im + \frac{x.re}{\frac{y.im}{y.re}}}{y.im}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -4 \cdot 10^{+80}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.im \leq -8.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{x.re \cdot y.re + y.im \cdot x.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq 4.9 \cdot 10^{-85}:\\ \;\;\;\;\frac{x.re + \frac{y.im \cdot x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 1.6 \cdot 10^{+81}:\\ \;\;\;\;\frac{y.im}{\frac{y.re \cdot y.re + y.im \cdot y.im}{x.im + \frac{x.re}{\frac{y.im}{y.re}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + \frac{x.re}{\frac{y.im}{y.re}}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re \cdot y.re + y.im \cdot x.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.im \leq -3.9 \cdot 10^{+80}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.im \leq -4.4 \cdot 10^{-112}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.im \leq 3.5 \cdot 10^{-164}:\\ \;\;\;\;\frac{x.re + \frac{y.im \cdot x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 2.8 \cdot 10^{+25}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \left(y.re \cdot \frac{1}{y.im}\right)}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (/ (+ (* x.re y.re) (* y.im x.im)) (+ (* y.re y.re) (* y.im y.im)))))
   (if (<= y.im -3.9e+80)
     (/ (+ x.im (* x.re (/ y.re y.im))) y.im)
     (if (<= y.im -4.4e-112)
       t_0
       (if (<= y.im 3.5e-164)
         (/ (+ x.re (/ (* y.im x.im) y.re)) y.re)
         (if (<= y.im 2.8e+25)
           t_0
           (/ (+ x.im (* x.re (* y.re (/ 1.0 y.im)))) y.im)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = ((x_46_re * y_46_re) + (y_46_im * x_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_im <= -3.9e+80) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if (y_46_im <= -4.4e-112) {
		tmp = t_0;
	} else if (y_46_im <= 3.5e-164) {
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_im <= 2.8e+25) {
		tmp = t_0;
	} else {
		tmp = (x_46_im + (x_46_re * (y_46_re * (1.0 / y_46_im)))) / y_46_im;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x_46re * y_46re) + (y_46im * x_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
    if (y_46im <= (-3.9d+80)) then
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    else if (y_46im <= (-4.4d-112)) then
        tmp = t_0
    else if (y_46im <= 3.5d-164) then
        tmp = (x_46re + ((y_46im * x_46im) / y_46re)) / y_46re
    else if (y_46im <= 2.8d+25) then
        tmp = t_0
    else
        tmp = (x_46im + (x_46re * (y_46re * (1.0d0 / y_46im)))) / y_46im
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = ((x_46_re * y_46_re) + (y_46_im * x_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_im <= -3.9e+80) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if (y_46_im <= -4.4e-112) {
		tmp = t_0;
	} else if (y_46_im <= 3.5e-164) {
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_im <= 2.8e+25) {
		tmp = t_0;
	} else {
		tmp = (x_46_im + (x_46_re * (y_46_re * (1.0 / y_46_im)))) / y_46_im;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = ((x_46_re * y_46_re) + (y_46_im * x_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	tmp = 0
	if y_46_im <= -3.9e+80:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	elif y_46_im <= -4.4e-112:
		tmp = t_0
	elif y_46_im <= 3.5e-164:
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re
	elif y_46_im <= 2.8e+25:
		tmp = t_0
	else:
		tmp = (x_46_im + (x_46_re * (y_46_re * (1.0 / y_46_im)))) / y_46_im
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(Float64(x_46_re * y_46_re) + Float64(y_46_im * x_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
	tmp = 0.0
	if (y_46_im <= -3.9e+80)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	elseif (y_46_im <= -4.4e-112)
		tmp = t_0;
	elseif (y_46_im <= 3.5e-164)
		tmp = Float64(Float64(x_46_re + Float64(Float64(y_46_im * x_46_im) / y_46_re)) / y_46_re);
	elseif (y_46_im <= 2.8e+25)
		tmp = t_0;
	else
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re * Float64(1.0 / y_46_im)))) / y_46_im);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = ((x_46_re * y_46_re) + (y_46_im * x_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	tmp = 0.0;
	if (y_46_im <= -3.9e+80)
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	elseif (y_46_im <= -4.4e-112)
		tmp = t_0;
	elseif (y_46_im <= 3.5e-164)
		tmp = (x_46_re + ((y_46_im * x_46_im) / y_46_re)) / y_46_re;
	elseif (y_46_im <= 2.8e+25)
		tmp = t_0;
	else
		tmp = (x_46_im + (x_46_re * (y_46_re * (1.0 / y_46_im)))) / y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * x$46$im), $MachinePrecision]), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -3.9e+80], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$im, -4.4e-112], t$95$0, If[LessEqual[y$46$im, 3.5e-164], N[(N[(x$46$re + N[(N[(y$46$im * x$46$im), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$im, 2.8e+25], t$95$0, N[(N[(x$46$im + N[(x$46$re * N[(y$46$re * N[(1.0 / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y.im < -3.89999999999999999e80

   1. Initial program 42.3%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.im + \frac{x.re \cdot y.re}{y.im}\right), \color{blue}{y.im}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(\frac{x.re \cdot y.re}{y.im}\right)\right), y.im\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(x.re \cdot \frac{y.re}{y.im}\right)\right), y.im\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{y.re}{y.im}\right)\right)\right), y.im\right) \]

      5. /-lowering-/.f64 86.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{/.f64}\left(y.re, y.im\right)\right)\right), y.im\right) \]

   5. Simplified 86.4%

      \[\leadsto \color{blue}{\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}} \]

   if -3.89999999999999999e80 < y.im < -4.40000000000000042e-112 or 3.5e-164 < y.im < 2.8000000000000002e25

   1. Initial program 84.1%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   if -4.40000000000000042e-112 < y.im < 3.5e-164

   1. Initial program 59.4%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.re + \frac{x.im \cdot y.im}{y.re}\right), \color{blue}{y.re}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(\frac{x.im \cdot y.im}{y.re}\right)\right), y.re\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\left(x.im \cdot y.im\right), y.re\right)\right), y.re\right) \]

      4. *-lowering-*.f64 92.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x.im, y.im\right), y.re\right)\right), y.re\right) \]

   5. Simplified 92.7%

      \[\leadsto \color{blue}{\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}} \]

   if 2.8000000000000002e25 < y.im

   1. Initial program 39.8%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.im + \frac{x.re \cdot y.re}{y.im}\right), \color{blue}{y.im}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(\frac{x.re \cdot y.re}{y.im}\right)\right), y.im\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(x.re \cdot \frac{y.re}{y.im}\right)\right), y.im\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{y.re}{y.im}\right)\right)\right), y.im\right) \]

      5. /-lowering-/.f64 78.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{/.f64}\left(y.re, y.im\right)\right)\right), y.im\right) \]

   5. Simplified 78.5%

      \[\leadsto \color{blue}{\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}} \]
   6. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{1}{\frac{y.im}{y.re}}\right)\right)\right), y.im\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{1}{y.im} \cdot y.re\right)\right)\right), y.im\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{*.f64}\left(\left(\frac{1}{y.im}\right), y.re\right)\right)\right), y.im\right) \]

      4. /-lowering-/.f64 78.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, y.im\right), y.re\right)\right)\right), y.im\right) \]

   7. Applied egg-rr 78.5%

      \[\leadsto \frac{x.im + x.re \cdot \color{blue}{\left(\frac{1}{y.im} \cdot y.re\right)}}{y.im} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -3.9 \cdot 10^{+80}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.im \leq -4.4 \cdot 10^{-112}:\\ \;\;\;\;\frac{x.re \cdot y.re + y.im \cdot x.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq 3.5 \cdot 10^{-164}:\\ \;\;\;\;\frac{x.re + \frac{y.im \cdot x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 2.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{x.re \cdot y.re + y.im \cdot x.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \left(y.re \cdot \frac{1}{y.im}\right)}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -2.25 \cdot 10^{+73}:\\ \;\;\;\;\frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 2.6 \cdot 10^{+31}:\\ \;\;\;\;\frac{x.im + x.re \cdot \left(y.re \cdot \frac{1}{y.im}\right)}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{x.im}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -2.25e+73)
   (/ (+ x.re (* y.im (/ x.im y.re))) y.re)
   (if (<= y.re 2.6e+31)
     (/ (+ x.im (* x.re (* y.re (/ 1.0 y.im)))) y.im)
     (/ (+ x.re (/ x.im (/ y.re y.im))) y.re))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -2.25e+73) {
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	} else if (y_46_re <= 2.6e+31) {
		tmp = (x_46_im + (x_46_re * (y_46_re * (1.0 / y_46_im)))) / y_46_im;
	} else {
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if (y_46re <= (-2.25d+73)) then
        tmp = (x_46re + (y_46im * (x_46im / y_46re))) / y_46re
    else if (y_46re <= 2.6d+31) then
        tmp = (x_46im + (x_46re * (y_46re * (1.0d0 / y_46im)))) / y_46im
    else
        tmp = (x_46re + (x_46im / (y_46re / y_46im))) / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -2.25e+73) {
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	} else if (y_46_re <= 2.6e+31) {
		tmp = (x_46_im + (x_46_re * (y_46_re * (1.0 / y_46_im)))) / y_46_im;
	} else {
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if y_46_re <= -2.25e+73:
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re
	elif y_46_re <= 2.6e+31:
		tmp = (x_46_im + (x_46_re * (y_46_re * (1.0 / y_46_im)))) / y_46_im
	else:
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (y_46_re <= -2.25e+73)
		tmp = Float64(Float64(x_46_re + Float64(y_46_im * Float64(x_46_im / y_46_re))) / y_46_re);
	elseif (y_46_re <= 2.6e+31)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re * Float64(1.0 / y_46_im)))) / y_46_im);
	else
		tmp = Float64(Float64(x_46_re + Float64(x_46_im / Float64(y_46_re / y_46_im))) / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if (y_46_re <= -2.25e+73)
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	elseif (y_46_re <= 2.6e+31)
		tmp = (x_46_im + (x_46_re * (y_46_re * (1.0 / y_46_im)))) / y_46_im;
	else
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[y$46$re, -2.25e+73], N[(N[(x$46$re + N[(y$46$im * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 2.6e+31], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re * N[(1.0 / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], N[(N[(x$46$re + N[(x$46$im / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y.re < -2.24999999999999992e73

   1. Initial program 42.6%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.re + \frac{x.im \cdot y.im}{y.re}\right), \color{blue}{y.re}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(\frac{x.im \cdot y.im}{y.re}\right)\right), y.re\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\left(x.im \cdot y.im\right), y.re\right)\right), y.re\right) \]

      4. *-lowering-*.f64 76.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x.im, y.im\right), y.re\right)\right), y.re\right) \]

   5. Simplified 76.0%

      \[\leadsto \color{blue}{\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(\frac{y.im \cdot x.im}{y.re}\right)\right), y.re\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(y.im \cdot \frac{x.im}{y.re}\right)\right), y.re\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{*.f64}\left(y.im, \left(\frac{x.im}{y.re}\right)\right)\right), y.re\right) \]

      4. /-lowering-/.f64 83.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{*.f64}\left(y.im, \mathsf{/.f64}\left(x.im, y.re\right)\right)\right), y.re\right) \]

   7. Applied egg-rr 83.4%

      \[\leadsto \frac{x.re + \color{blue}{y.im \cdot \frac{x.im}{y.re}}}{y.re} \]

   if -2.24999999999999992e73 < y.re < 2.6e31

   1. Initial program 69.9%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.im + \frac{x.re \cdot y.re}{y.im}\right), \color{blue}{y.im}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(\frac{x.re \cdot y.re}{y.im}\right)\right), y.im\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(x.re \cdot \frac{y.re}{y.im}\right)\right), y.im\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{y.re}{y.im}\right)\right)\right), y.im\right) \]

      5. /-lowering-/.f64 79.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{/.f64}\left(y.re, y.im\right)\right)\right), y.im\right) \]

   5. Simplified 79.1%

      \[\leadsto \color{blue}{\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}} \]
   6. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{1}{\frac{y.im}{y.re}}\right)\right)\right), y.im\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{1}{y.im} \cdot y.re\right)\right)\right), y.im\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{*.f64}\left(\left(\frac{1}{y.im}\right), y.re\right)\right)\right), y.im\right) \]

      4. /-lowering-/.f64 79.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, y.im\right), y.re\right)\right)\right), y.im\right) \]

   7. Applied egg-rr 79.1%

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

   if 2.6e31 < y.re

   1. Initial program 55.5%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.re + \frac{x.im \cdot y.im}{y.re}\right), \color{blue}{y.re}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(\frac{x.im \cdot y.im}{y.re}\right)\right), y.re\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\left(x.im \cdot y.im\right), y.re\right)\right), y.re\right) \]

      4. *-lowering-*.f64 78.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x.im, y.im\right), y.re\right)\right), y.re\right) \]

   5. Simplified 78.7%

      \[\leadsto \color{blue}{\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x.im \cdot y.im}{y.re} + x.re\right), y.re\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{x.im \cdot y.im}{y.re}\right), x.re\right), y.re\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x.im \cdot \frac{y.im}{y.re}\right), x.re\right), y.re\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x.im \cdot \frac{1}{\frac{y.re}{y.im}}\right), x.re\right), y.re\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{x.im}{\frac{y.re}{y.im}}\right), x.re\right), y.re\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(x.im, \left(\frac{y.re}{y.im}\right)\right), x.re\right), y.re\right) \]

      7. /-lowering-/.f64 82.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(x.im, \mathsf{/.f64}\left(y.re, y.im\right)\right), x.re\right), y.re\right) \]

   7. Applied egg-rr 82.7%

      \[\leadsto \frac{\color{blue}{\frac{x.im}{\frac{y.re}{y.im}} + x.re}}{y.re} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -2.25 \cdot 10^{+73}:\\ \;\;\;\;\frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 2.6 \cdot 10^{+31}:\\ \;\;\;\;\frac{x.im + x.re \cdot \left(y.re \cdot \frac{1}{y.im}\right)}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{x.im}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -4.2 \cdot 10^{+72}:\\ \;\;\;\;\frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 1.15 \cdot 10^{+31}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{x.im}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -4.2e+72)
   (/ (+ x.re (* y.im (/ x.im y.re))) y.re)
   (if (<= y.re 1.15e+31)
     (/ (+ x.im (* x.re (/ y.re y.im))) y.im)
     (/ (+ x.re (/ x.im (/ y.re y.im))) y.re))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -4.2e+72) {
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	} else if (y_46_re <= 1.15e+31) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else {
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if (y_46re <= (-4.2d+72)) then
        tmp = (x_46re + (y_46im * (x_46im / y_46re))) / y_46re
    else if (y_46re <= 1.15d+31) then
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    else
        tmp = (x_46re + (x_46im / (y_46re / y_46im))) / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -4.2e+72) {
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	} else if (y_46_re <= 1.15e+31) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else {
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if y_46_re <= -4.2e+72:
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re
	elif y_46_re <= 1.15e+31:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	else:
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (y_46_re <= -4.2e+72)
		tmp = Float64(Float64(x_46_re + Float64(y_46_im * Float64(x_46_im / y_46_re))) / y_46_re);
	elseif (y_46_re <= 1.15e+31)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	else
		tmp = Float64(Float64(x_46_re + Float64(x_46_im / Float64(y_46_re / y_46_im))) / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if (y_46_re <= -4.2e+72)
		tmp = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	elseif (y_46_re <= 1.15e+31)
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	else
		tmp = (x_46_re + (x_46_im / (y_46_re / y_46_im))) / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[y$46$re, -4.2e+72], N[(N[(x$46$re + N[(y$46$im * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 1.15e+31], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], N[(N[(x$46$re + N[(x$46$im / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y.re < -4.2000000000000003e72

   1. Initial program 42.6%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.re + \frac{x.im \cdot y.im}{y.re}\right), \color{blue}{y.re}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(\frac{x.im \cdot y.im}{y.re}\right)\right), y.re\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\left(x.im \cdot y.im\right), y.re\right)\right), y.re\right) \]

      4. *-lowering-*.f64 76.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x.im, y.im\right), y.re\right)\right), y.re\right) \]

   5. Simplified 76.0%

      \[\leadsto \color{blue}{\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(\frac{y.im \cdot x.im}{y.re}\right)\right), y.re\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(y.im \cdot \frac{x.im}{y.re}\right)\right), y.re\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{*.f64}\left(y.im, \left(\frac{x.im}{y.re}\right)\right)\right), y.re\right) \]

      4. /-lowering-/.f64 83.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{*.f64}\left(y.im, \mathsf{/.f64}\left(x.im, y.re\right)\right)\right), y.re\right) \]

   7. Applied egg-rr 83.4%

      \[\leadsto \frac{x.re + \color{blue}{y.im \cdot \frac{x.im}{y.re}}}{y.re} \]

   if -4.2000000000000003e72 < y.re < 1.15e31

   1. Initial program 69.9%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.im + \frac{x.re \cdot y.re}{y.im}\right), \color{blue}{y.im}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(\frac{x.re \cdot y.re}{y.im}\right)\right), y.im\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(x.re \cdot \frac{y.re}{y.im}\right)\right), y.im\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{y.re}{y.im}\right)\right)\right), y.im\right) \]

      5. /-lowering-/.f64 79.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{/.f64}\left(y.re, y.im\right)\right)\right), y.im\right) \]

   5. Simplified 79.1%

      \[\leadsto \color{blue}{\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}} \]

   if 1.15e31 < y.re

   1. Initial program 55.5%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.re + \frac{x.im \cdot y.im}{y.re}\right), \color{blue}{y.re}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(\frac{x.im \cdot y.im}{y.re}\right)\right), y.re\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\left(x.im \cdot y.im\right), y.re\right)\right), y.re\right) \]

      4. *-lowering-*.f64 78.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x.im, y.im\right), y.re\right)\right), y.re\right) \]

   5. Simplified 78.7%

      \[\leadsto \color{blue}{\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x.im \cdot y.im}{y.re} + x.re\right), y.re\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{x.im \cdot y.im}{y.re}\right), x.re\right), y.re\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x.im \cdot \frac{y.im}{y.re}\right), x.re\right), y.re\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x.im \cdot \frac{1}{\frac{y.re}{y.im}}\right), x.re\right), y.re\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{x.im}{\frac{y.re}{y.im}}\right), x.re\right), y.re\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(x.im, \left(\frac{y.re}{y.im}\right)\right), x.re\right), y.re\right) \]

      7. /-lowering-/.f64 82.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(x.im, \mathsf{/.f64}\left(y.re, y.im\right)\right), x.re\right), y.re\right) \]

   7. Applied egg-rr 82.7%

      \[\leadsto \frac{\color{blue}{\frac{x.im}{\frac{y.re}{y.im}} + x.re}}{y.re} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -4.2 \cdot 10^{+72}:\\ \;\;\;\;\frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 1.15 \cdot 10^{+31}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + \frac{x.im}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re + y.im \cdot \frac{x.im}{y.re}}{y.re}\\ \mathbf{if}\;y.re \leq -1 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.re \leq 6.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ (+ x.re (* y.im (/ x.im y.re))) y.re)))
   (if (<= y.re -1e+73)
     t_0
     (if (<= y.re 6.1e+32) (/ (+ x.im (* x.re (/ y.re y.im))) y.im) t_0))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	double tmp;
	if (y_46_re <= -1e+73) {
		tmp = t_0;
	} else if (y_46_re <= 6.1e+32) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x_46re + (y_46im * (x_46im / y_46re))) / y_46re
    if (y_46re <= (-1d+73)) then
        tmp = t_0
    else if (y_46re <= 6.1d+32) then
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	double tmp;
	if (y_46_re <= -1e+73) {
		tmp = t_0;
	} else if (y_46_re <= 6.1e+32) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re
	tmp = 0
	if y_46_re <= -1e+73:
		tmp = t_0
	elif y_46_re <= 6.1e+32:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	else:
		tmp = t_0
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(x_46_re + Float64(y_46_im * Float64(x_46_im / y_46_re))) / y_46_re)
	tmp = 0.0
	if (y_46_re <= -1e+73)
		tmp = t_0;
	elseif (y_46_re <= 6.1e+32)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (x_46_re + (y_46_im * (x_46_im / y_46_re))) / y_46_re;
	tmp = 0.0;
	if (y_46_re <= -1e+73)
		tmp = t_0;
	elseif (y_46_re <= 6.1e+32)
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(x$46$re + N[(y$46$im * N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]}, If[LessEqual[y$46$re, -1e+73], t$95$0, If[LessEqual[y$46$re, 6.1e+32], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y.re < -9.99999999999999983e72 or 6.10000000000000027e32 < y.re

   1. Initial program 49.0%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.re + \frac{x.im \cdot y.im}{y.re}\right), \color{blue}{y.re}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(\frac{x.im \cdot y.im}{y.re}\right)\right), y.re\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\left(x.im \cdot y.im\right), y.re\right)\right), y.re\right) \]

      4. *-lowering-*.f64 77.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x.im, y.im\right), y.re\right)\right), y.re\right) \]

   5. Simplified 77.4%

      \[\leadsto \color{blue}{\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(\frac{y.im \cdot x.im}{y.re}\right)\right), y.re\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \left(y.im \cdot \frac{x.im}{y.re}\right)\right), y.re\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{*.f64}\left(y.im, \left(\frac{x.im}{y.re}\right)\right)\right), y.re\right) \]

      4. /-lowering-/.f64 83.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.re, \mathsf{*.f64}\left(y.im, \mathsf{/.f64}\left(x.im, y.re\right)\right)\right), y.re\right) \]

   7. Applied egg-rr 83.0%

      \[\leadsto \frac{x.re + \color{blue}{y.im \cdot \frac{x.im}{y.re}}}{y.re} \]

   if -9.99999999999999983e72 < y.re < 6.10000000000000027e32

   1. Initial program 69.9%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.im + \frac{x.re \cdot y.re}{y.im}\right), \color{blue}{y.im}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(\frac{x.re \cdot y.re}{y.im}\right)\right), y.im\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(x.re \cdot \frac{y.re}{y.im}\right)\right), y.im\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{y.re}{y.im}\right)\right)\right), y.im\right) \]

      5. /-lowering-/.f64 79.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{/.f64}\left(y.re, y.im\right)\right)\right), y.im\right) \]

   5. Simplified 79.1%

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

Alternative 6: 72.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -3.8 \cdot 10^{+107}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 3.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -3.8e+107)
   (/ x.re y.re)
   (if (<= y.re 3.9e+46)
     (/ (+ x.im (* x.re (/ y.re y.im))) y.im)
     (/ x.re y.re))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -3.8e+107) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 3.9e+46) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else {
		tmp = x_46_re / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if (y_46re <= (-3.8d+107)) then
        tmp = x_46re / y_46re
    else if (y_46re <= 3.9d+46) then
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    else
        tmp = x_46re / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -3.8e+107) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 3.9e+46) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else {
		tmp = x_46_re / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if y_46_re <= -3.8e+107:
		tmp = x_46_re / y_46_re
	elif y_46_re <= 3.9e+46:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	else:
		tmp = x_46_re / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (y_46_re <= -3.8e+107)
		tmp = Float64(x_46_re / y_46_re);
	elseif (y_46_re <= 3.9e+46)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	else
		tmp = Float64(x_46_re / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if (y_46_re <= -3.8e+107)
		tmp = x_46_re / y_46_re;
	elseif (y_46_re <= 3.9e+46)
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	else
		tmp = x_46_re / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[y$46$re, -3.8e+107], N[(x$46$re / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 3.9e+46], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], N[(x$46$re / y$46$re), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y.re < -3.7999999999999998e107 or 3.89999999999999995e46 < y.re

   1. Initial program 47.0%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around inf

      \[\leadsto \color{blue}{\frac{x.re}{y.re}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 72.9%

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

   5. Simplified 72.9%

      \[\leadsto \color{blue}{\frac{x.re}{y.re}} \]

   if -3.7999999999999998e107 < y.re < 3.89999999999999995e46

   1. Initial program 69.4%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x.im + \frac{x.re \cdot y.re}{y.im}\right), \color{blue}{y.im}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(\frac{x.re \cdot y.re}{y.im}\right)\right), y.im\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \left(x.re \cdot \frac{y.re}{y.im}\right)\right), y.im\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \left(\frac{y.re}{y.im}\right)\right)\right), y.im\right) \]

      5. /-lowering-/.f64 76.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x.im, \mathsf{*.f64}\left(x.re, \mathsf{/.f64}\left(y.re, y.im\right)\right)\right), y.im\right) \]

   5. Simplified 76.7%

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

Alternative 7: 63.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -4.5 \cdot 10^{+72}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq 3.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -4.5e+72)
   (/ x.re y.re)
   (if (<= y.re 3.6e+36) (/ x.im y.im) (/ x.re y.re))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -4.5e+72) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 3.6e+36) {
		tmp = x_46_im / y_46_im;
	} else {
		tmp = x_46_re / y_46_re;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: tmp
    if (y_46re <= (-4.5d+72)) then
        tmp = x_46re / y_46re
    else if (y_46re <= 3.6d+36) then
        tmp = x_46im / y_46im
    else
        tmp = x_46re / y_46re
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if (y_46_re <= -4.5e+72) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= 3.6e+36) {
		tmp = x_46_im / y_46_im;
	} else {
		tmp = x_46_re / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if y_46_re <= -4.5e+72:
		tmp = x_46_re / y_46_re
	elif y_46_re <= 3.6e+36:
		tmp = x_46_im / y_46_im
	else:
		tmp = x_46_re / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (y_46_re <= -4.5e+72)
		tmp = Float64(x_46_re / y_46_re);
	elseif (y_46_re <= 3.6e+36)
		tmp = Float64(x_46_im / y_46_im);
	else
		tmp = Float64(x_46_re / y_46_re);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0;
	if (y_46_re <= -4.5e+72)
		tmp = x_46_re / y_46_re;
	elseif (y_46_re <= 3.6e+36)
		tmp = x_46_im / y_46_im;
	else
		tmp = x_46_re / y_46_re;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[y$46$re, -4.5e+72], N[(x$46$re / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 3.6e+36], N[(x$46$im / y$46$im), $MachinePrecision], N[(x$46$re / y$46$re), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y.re < -4.4999999999999998e72 or 3.5999999999999997e36 < y.re

   1. Initial program 49.0%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around inf

      \[\leadsto \color{blue}{\frac{x.re}{y.re}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 68.0%

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

   5. Simplified 68.0%

      \[\leadsto \color{blue}{\frac{x.re}{y.re}} \]

   if -4.4999999999999998e72 < y.re < 3.5999999999999997e36

   1. Initial program 69.9%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around 0

      \[\leadsto \color{blue}{\frac{x.im}{y.im}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 65.2%

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

   5. Simplified 65.2%

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

Alternative 8: 42.2% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \frac{x.im}{y.im} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im) :precision binary64 (/ x.im y.im))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return x_46_im / y_46_im;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    code = x_46im / y_46im
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return x_46_im / y_46_im;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	return x_46_im / y_46_im

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return Float64(x_46_im / y_46_im)
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = x_46_im / y_46_im;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := N[(x$46$im / y$46$im), $MachinePrecision]

Derivation

1. Initial program 61.5%

   \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
2. Add Preprocessing

3. Taylor expanded in y.re around 0

   \[\leadsto \color{blue}{\frac{x.im}{y.im}} \]
4. Step-by-step derivation

   1. /-lowering-/.f64 45.1%

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

5. Simplified 45.1%

   \[\leadsto \color{blue}{\frac{x.im}{y.im}} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024139 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, real part"
  :precision binary64
  (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))