_divideComplex, real part

Percentage Accurate: 60.9% → 84.3%

Time: 11.7s

Alternatives: 12

Speedup: 1.1×

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: 60.9% 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: 84.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{if}\;y.re \leq -3.9 \cdot 10^{+102}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.re \leq -8.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{y.im}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{y.re \cdot \left(\frac{x.re}{y.im} + \frac{x.im}{y.re}\right)}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{elif}\;y.re \leq 1.55 \cdot 10^{-110}:\\ \;\;\;\;\frac{x.im + \frac{x.re \cdot y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ (+ x.re (* x.im (/ y.im y.re))) y.re)))
   (if (<= y.re -3.9e+102)
     t_0
     (if (<= y.re -8.5e-87)
       (*
        (/ y.im (hypot y.re y.im))
        (/ (* y.re (+ (/ x.re y.im) (/ x.im y.re))) (hypot y.re y.im)))
       (if (<= y.re 1.55e-110)
         (/ (+ x.im (/ (* x.re y.re) y.im)) y.im)
         (if (<= y.re 3.5e+82)
           (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.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 + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	double tmp;
	if (y_46_re <= -3.9e+102) {
		tmp = t_0;
	} else if (y_46_re <= -8.5e-87) {
		tmp = (y_46_im / hypot(y_46_re, y_46_im)) * ((y_46_re * ((x_46_re / y_46_im) + (x_46_im / y_46_re))) / hypot(y_46_re, y_46_im));
	} else if (y_46_re <= 1.55e-110) {
		tmp = (x_46_im + ((x_46_re * y_46_re) / y_46_im)) / y_46_im;
	} else if (y_46_re <= 3.5e+82) {
		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));
	} else {
		tmp = t_0;
	}
	return tmp;
}

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 + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	double tmp;
	if (y_46_re <= -3.9e+102) {
		tmp = t_0;
	} else if (y_46_re <= -8.5e-87) {
		tmp = (y_46_im / Math.hypot(y_46_re, y_46_im)) * ((y_46_re * ((x_46_re / y_46_im) + (x_46_im / y_46_re))) / Math.hypot(y_46_re, y_46_im));
	} else if (y_46_re <= 1.55e-110) {
		tmp = (x_46_im + ((x_46_re * y_46_re) / y_46_im)) / y_46_im;
	} else if (y_46_re <= 3.5e+82) {
		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));
	} 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 + (x_46_im * (y_46_im / y_46_re))) / y_46_re
	tmp = 0
	if y_46_re <= -3.9e+102:
		tmp = t_0
	elif y_46_re <= -8.5e-87:
		tmp = (y_46_im / math.hypot(y_46_re, y_46_im)) * ((y_46_re * ((x_46_re / y_46_im) + (x_46_im / y_46_re))) / math.hypot(y_46_re, y_46_im))
	elif y_46_re <= 1.55e-110:
		tmp = (x_46_im + ((x_46_re * y_46_re) / y_46_im)) / y_46_im
	elif y_46_re <= 3.5e+82:
		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))
	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(x_46_im * Float64(y_46_im / y_46_re))) / y_46_re)
	tmp = 0.0
	if (y_46_re <= -3.9e+102)
		tmp = t_0;
	elseif (y_46_re <= -8.5e-87)
		tmp = Float64(Float64(y_46_im / hypot(y_46_re, y_46_im)) * Float64(Float64(y_46_re * Float64(Float64(x_46_re / y_46_im) + Float64(x_46_im / y_46_re))) / hypot(y_46_re, y_46_im)));
	elseif (y_46_re <= 1.55e-110)
		tmp = Float64(Float64(x_46_im + Float64(Float64(x_46_re * y_46_re) / y_46_im)) / y_46_im);
	elseif (y_46_re <= 3.5e+82)
		tmp = 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)));
	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 + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	tmp = 0.0;
	if (y_46_re <= -3.9e+102)
		tmp = t_0;
	elseif (y_46_re <= -8.5e-87)
		tmp = (y_46_im / hypot(y_46_re, y_46_im)) * ((y_46_re * ((x_46_re / y_46_im) + (x_46_im / y_46_re))) / hypot(y_46_re, y_46_im));
	elseif (y_46_re <= 1.55e-110)
		tmp = (x_46_im + ((x_46_re * y_46_re) / y_46_im)) / y_46_im;
	elseif (y_46_re <= 3.5e+82)
		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));
	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[(x$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]}, If[LessEqual[y$46$re, -3.9e+102], t$95$0, If[LessEqual[y$46$re, -8.5e-87], N[(N[(y$46$im / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(N[(y$46$re * N[(N[(x$46$re / y$46$im), $MachinePrecision] + N[(x$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.55e-110], N[(N[(x$46$im + N[(N[(x$46$re * y$46$re), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, 3.5e+82], 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], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y.re < -3.8999999999999998e102 or 3.5e82 < y.re

   1. Initial program 34.9%

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

   3. Taylor expanded in y.re around inf 79.1%

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

      1. associate-/l* 84.2%

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

   5. Simplified 84.2%

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

   if -3.8999999999999998e102 < y.re < -8.5000000000000001e-87

   1. Initial program 76.2%

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

   3. Taylor expanded in y.im around inf 63.8%

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

      1. associate-/l* 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in x.im around inf 51.3%

      \[\leadsto \frac{y.im \cdot \color{blue}{\left(x.im \cdot \left(1 + \frac{x.re \cdot y.re}{x.im \cdot y.im}\right)\right)}}{y.re \cdot y.re + y.im \cdot y.im} \]
   7. Step-by-step derivation

      1. associate-/l* 51.3%

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

   8. Simplified 51.3%

      \[\leadsto \frac{y.im \cdot \color{blue}{\left(x.im \cdot \left(1 + x.re \cdot \frac{y.re}{x.im \cdot y.im}\right)\right)}}{y.re \cdot y.re + y.im \cdot y.im} \]
   9. Step-by-step derivation

      1. *-commutative 51.3%

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

      2. add-sqr-sqrt 51.3%

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

      3. hypot-undefine 51.3%

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

      4. hypot-undefine 51.3%

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

      5. times-frac 74.8%

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

      6. +-commutative 74.8%

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

      7. fma-define 74.8%

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

      8. *-commutative 74.8%

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

      9. associate-/r* 74.8%

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

   10. Applied egg-rr 74.8%

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

   11. Taylor expanded in y.re around inf 87.2%

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

       1. +-commutative 87.2%

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

   13. Simplified 87.2%

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

   if -8.5000000000000001e-87 < y.re < 1.55000000000000004e-110

   1. Initial program 64.4%

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

   3. Taylor expanded in y.im around inf 93.1%

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

   if 1.55000000000000004e-110 < y.re < 3.5e82

   1. Initial program 88.1%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -3.9 \cdot 10^{+102}:\\ \;\;\;\;\frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq -8.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{y.im}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{y.re \cdot \left(\frac{x.re}{y.im} + \frac{x.im}{y.re}\right)}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{elif}\;y.re \leq 1.55 \cdot 10^{-110}:\\ \;\;\;\;\frac{x.im + \frac{x.re \cdot y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leq 10^{+260}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im \cdot \mathsf{fma}\left(x.re, \frac{\frac{y.re}{y.im}}{x.im}, 1\right)}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{y.im}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<=
      (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
      1e+260)
   (/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
   (*
    (/ (* x.im (fma x.re (/ (/ y.re y.im) x.im) 1.0)) (hypot y.re y.im))
    (/ y.im (hypot y.re y.im)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double tmp;
	if ((((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= 1e+260) {
		tmp = (fma(x_46_re, y_46_re, (x_46_im * y_46_im)) / hypot(y_46_re, y_46_im)) / hypot(y_46_re, y_46_im);
	} else {
		tmp = ((x_46_im * fma(x_46_re, ((y_46_re / y_46_im) / x_46_im), 1.0)) / hypot(y_46_re, y_46_im)) * (y_46_im / hypot(y_46_re, y_46_im));
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (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))) <= 1e+260)
		tmp = Float64(Float64(fma(x_46_re, y_46_re, Float64(x_46_im * y_46_im)) / hypot(y_46_re, y_46_im)) / hypot(y_46_re, y_46_im));
	else
		tmp = Float64(Float64(Float64(x_46_im * fma(x_46_re, Float64(Float64(y_46_re / y_46_im) / x_46_im), 1.0)) / hypot(y_46_re, y_46_im)) * Float64(y_46_im / hypot(y_46_re, y_46_im)));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[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], 1e+260], N[(N[(N[(x$46$re * y$46$re + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision], N[(N[(N[(x$46$im * N[(x$46$re * N[(N[(y$46$re / y$46$im), $MachinePrecision] / x$46$im), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(y$46$im / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))) < 1.00000000000000007e260

   1. Initial program 80.8%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-un-lft-identity 80.8%

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

      2. add-sqr-sqrt 80.8%

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

      3. times-frac 80.9%

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

      4. hypot-define 80.9%

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

      5. fma-define 80.9%

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

      6. hypot-define 96.8%

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

   4. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}} \]
   5. Step-by-step derivation

      1. associate-*l/ 97.0%

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

      2. *-un-lft-identity 97.0%

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

   6. Applied egg-rr 97.0%

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

   if 1.00000000000000007e260 < (/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

   1. Initial program 10.3%

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

   3. Taylor expanded in y.im around inf 10.3%

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

      1. associate-/l* 10.3%

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

   5. Simplified 10.3%

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

   6. Taylor expanded in x.im around inf 10.3%

      \[\leadsto \frac{y.im \cdot \color{blue}{\left(x.im \cdot \left(1 + \frac{x.re \cdot y.re}{x.im \cdot y.im}\right)\right)}}{y.re \cdot y.re + y.im \cdot y.im} \]
   7. Step-by-step derivation

      1. associate-/l* 10.4%

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

   8. Simplified 10.4%

      \[\leadsto \frac{y.im \cdot \color{blue}{\left(x.im \cdot \left(1 + x.re \cdot \frac{y.re}{x.im \cdot y.im}\right)\right)}}{y.re \cdot y.re + y.im \cdot y.im} \]
   9. Step-by-step derivation

      1. *-commutative 10.4%

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

      2. add-sqr-sqrt 10.4%

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

      3. hypot-undefine 10.4%

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

      4. hypot-undefine 10.4%

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

      5. times-frac 58.7%

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

      6. +-commutative 58.7%

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

      7. fma-define 58.7%

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

      8. *-commutative 58.7%

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

      9. associate-/r* 64.0%

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

   10. Applied egg-rr 64.0%

       \[\leadsto \color{blue}{\frac{x.im \cdot \mathsf{fma}\left(x.re, \frac{\frac{y.re}{y.im}}{x.im}, 1\right)}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{y.im}{\mathsf{hypot}\left(y.re, y.im\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leq 10^{+260}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im \cdot \mathsf{fma}\left(x.re, \frac{\frac{y.re}{y.im}}{x.im}, 1\right)}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{y.im}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leq 10^{+260}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<=
      (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
      1e+260)
   (/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
   (/ (+ x.im (* x.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) {
	double tmp;
	if ((((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))) <= 1e+260) {
		tmp = (fma(x_46_re, y_46_re, (x_46_im * y_46_im)) / hypot(y_46_re, y_46_im)) / hypot(y_46_re, y_46_im);
	} else {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (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))) <= 1e+260)
		tmp = Float64(Float64(fma(x_46_re, y_46_re, Float64(x_46_im * y_46_im)) / hypot(y_46_re, y_46_im)) / hypot(y_46_re, y_46_im));
	else
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[LessEqual[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], 1e+260], N[(N[(N[(x$46$re * y$46$re + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))) < 1.00000000000000007e260

   1. Initial program 80.8%

      \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-un-lft-identity 80.8%

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

      2. add-sqr-sqrt 80.8%

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

      3. times-frac 80.9%

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

      4. hypot-define 80.9%

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

      5. fma-define 80.9%

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

      6. hypot-define 96.8%

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

   4. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}} \]
   5. Step-by-step derivation

      1. associate-*l/ 97.0%

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

      2. *-un-lft-identity 97.0%

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

   6. Applied egg-rr 97.0%

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

   if 1.00000000000000007e260 < (/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

   1. Initial program 10.3%

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

   3. Taylor expanded in y.im around inf 47.6%

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

      1. associate-/l* 59.7%

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

   5. Simplified 59.7%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leq 10^{+260}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x.re, y.re, x.im \cdot y.im\right)}{\mathsf{hypot}\left(y.re, y.im\right)}}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot y.re + y.im \cdot y.im\\ t_1 := x.im + x.re \cdot \frac{y.re}{y.im}\\ \mathbf{if}\;y.im \leq -1 \cdot 10^{+89}:\\ \;\;\;\;\frac{y.im}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{t\_1}{-y.im}\\ \mathbf{elif}\;y.im \leq -2.7 \cdot 10^{-136}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{t\_0}\\ \mathbf{elif}\;y.im \leq 3.9 \cdot 10^{-135}:\\ \;\;\;\;\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 1.35 \cdot 10^{+66}:\\ \;\;\;\;\frac{y.im \cdot t\_1}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (+ (* y.re y.re) (* y.im y.im)))
        (t_1 (+ x.im (* x.re (/ y.re y.im)))))
   (if (<= y.im -1e+89)
     (* (/ y.im (hypot y.re y.im)) (/ t_1 (- y.im)))
     (if (<= y.im -2.7e-136)
       (/ (+ (* x.re y.re) (* x.im y.im)) t_0)
       (if (<= y.im 3.9e-135)
         (/ (+ x.re (/ (* x.im y.im) y.re)) y.re)
         (if (<= y.im 1.35e+66) (/ (* y.im t_1) t_0) (/ t_1 y.im)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (y_46_re * y_46_re) + (y_46_im * y_46_im);
	double t_1 = x_46_im + (x_46_re * (y_46_re / y_46_im));
	double tmp;
	if (y_46_im <= -1e+89) {
		tmp = (y_46_im / hypot(y_46_re, y_46_im)) * (t_1 / -y_46_im);
	} else if (y_46_im <= -2.7e-136) {
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / t_0;
	} else if (y_46_im <= 3.9e-135) {
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_im <= 1.35e+66) {
		tmp = (y_46_im * t_1) / t_0;
	} else {
		tmp = t_1 / y_46_im;
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (y_46_re * y_46_re) + (y_46_im * y_46_im);
	double t_1 = x_46_im + (x_46_re * (y_46_re / y_46_im));
	double tmp;
	if (y_46_im <= -1e+89) {
		tmp = (y_46_im / Math.hypot(y_46_re, y_46_im)) * (t_1 / -y_46_im);
	} else if (y_46_im <= -2.7e-136) {
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / t_0;
	} else if (y_46_im <= 3.9e-135) {
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_im <= 1.35e+66) {
		tmp = (y_46_im * t_1) / t_0;
	} else {
		tmp = t_1 / y_46_im;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (y_46_re * y_46_re) + (y_46_im * y_46_im)
	t_1 = x_46_im + (x_46_re * (y_46_re / y_46_im))
	tmp = 0
	if y_46_im <= -1e+89:
		tmp = (y_46_im / math.hypot(y_46_re, y_46_im)) * (t_1 / -y_46_im)
	elif y_46_im <= -2.7e-136:
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / t_0
	elif y_46_im <= 3.9e-135:
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re
	elif y_46_im <= 1.35e+66:
		tmp = (y_46_im * t_1) / t_0
	else:
		tmp = t_1 / y_46_im
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im))
	t_1 = Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im)))
	tmp = 0.0
	if (y_46_im <= -1e+89)
		tmp = Float64(Float64(y_46_im / hypot(y_46_re, y_46_im)) * Float64(t_1 / Float64(-y_46_im)));
	elseif (y_46_im <= -2.7e-136)
		tmp = Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / t_0);
	elseif (y_46_im <= 3.9e-135)
		tmp = Float64(Float64(x_46_re + Float64(Float64(x_46_im * y_46_im) / y_46_re)) / y_46_re);
	elseif (y_46_im <= 1.35e+66)
		tmp = Float64(Float64(y_46_im * t_1) / t_0);
	else
		tmp = Float64(t_1 / 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 = (y_46_re * y_46_re) + (y_46_im * y_46_im);
	t_1 = x_46_im + (x_46_re * (y_46_re / y_46_im));
	tmp = 0.0;
	if (y_46_im <= -1e+89)
		tmp = (y_46_im / hypot(y_46_re, y_46_im)) * (t_1 / -y_46_im);
	elseif (y_46_im <= -2.7e-136)
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / t_0;
	elseif (y_46_im <= 3.9e-135)
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re;
	elseif (y_46_im <= 1.35e+66)
		tmp = (y_46_im * t_1) / t_0;
	else
		tmp = t_1 / 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[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, -1e+89], N[(N[(y$46$im / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(t$95$1 / (-y$46$im)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$im, -2.7e-136], N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], If[LessEqual[y$46$im, 3.9e-135], N[(N[(x$46$re + N[(N[(x$46$im * y$46$im), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$im, 1.35e+66], N[(N[(y$46$im * t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision], N[(t$95$1 / y$46$im), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y.im < -9.99999999999999995e88

   1. Initial program 34.6%

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

   3. Taylor expanded in y.im around inf 34.6%

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

      1. associate-/l* 34.6%

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

   5. Simplified 34.6%

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

   6. Taylor expanded in x.im around inf 34.6%

      \[\leadsto \frac{y.im \cdot \color{blue}{\left(x.im \cdot \left(1 + \frac{x.re \cdot y.re}{x.im \cdot y.im}\right)\right)}}{y.re \cdot y.re + y.im \cdot y.im} \]
   7. Step-by-step derivation

      1. associate-/l* 34.6%

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

   8. Simplified 34.6%

      \[\leadsto \frac{y.im \cdot \color{blue}{\left(x.im \cdot \left(1 + x.re \cdot \frac{y.re}{x.im \cdot y.im}\right)\right)}}{y.re \cdot y.re + y.im \cdot y.im} \]
   9. Step-by-step derivation

      1. *-commutative 34.6%

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

      2. add-sqr-sqrt 34.6%

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

      3. hypot-undefine 34.6%

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

      4. hypot-undefine 34.6%

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

      5. times-frac 89.4%

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

      6. +-commutative 89.4%

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

      7. fma-define 89.4%

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

      8. *-commutative 89.4%

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

      9. associate-/r* 90.0%

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

   10. Applied egg-rr 90.0%

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

   11. Taylor expanded in y.im around -inf 77.3%

       \[\leadsto \color{blue}{\left(-1 \cdot \frac{x.im + \frac{x.re \cdot y.re}{y.im}}{y.im}\right)} \cdot \frac{y.im}{\mathsf{hypot}\left(y.re, y.im\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 77.3%

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

       2. associate-/l* 81.9%

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

   13. Simplified 81.9%

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

   if -9.99999999999999995e88 < y.im < -2.6999999999999998e-136

   1. Initial program 84.8%

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

   if -2.6999999999999998e-136 < y.im < 3.90000000000000022e-135

   1. Initial program 65.4%

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

   3. Taylor expanded in y.re around inf 93.1%

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

   if 3.90000000000000022e-135 < y.im < 1.35e66

   1. Initial program 86.8%

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

   3. Taylor expanded in y.im around inf 86.8%

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

      1. associate-/l* 86.9%

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

   5. Simplified 86.9%

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

   if 1.35e66 < y.im

   1. Initial program 40.2%

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

   3. Taylor expanded in y.im around inf 77.9%

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

      1. associate-/l* 88.4%

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

   5. Simplified 88.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -1 \cdot 10^{+89}:\\ \;\;\;\;\frac{y.im}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{x.im + x.re \cdot \frac{y.re}{y.im}}{-y.im}\\ \mathbf{elif}\;y.im \leq -2.7 \cdot 10^{-136}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq 3.9 \cdot 10^{-135}:\\ \;\;\;\;\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 1.35 \cdot 10^{+66}:\\ \;\;\;\;\frac{y.im \cdot \left(x.im + x.re \cdot \frac{y.re}{y.im}\right)}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot y.re + y.im \cdot y.im\\ t_1 := x.im + x.re \cdot \frac{y.re}{y.im}\\ t_2 := \frac{t\_1}{y.im}\\ \mathbf{if}\;y.im \leq -3.5 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y.im \leq -1.45 \cdot 10^{-144}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{t\_0}\\ \mathbf{elif}\;y.im \leq 8.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 3.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{y.im \cdot t\_1}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (+ (* y.re y.re) (* y.im y.im)))
        (t_1 (+ x.im (* x.re (/ y.re y.im))))
        (t_2 (/ t_1 y.im)))
   (if (<= y.im -3.5e+98)
     t_2
     (if (<= y.im -1.45e-144)
       (/ (+ (* x.re y.re) (* x.im y.im)) t_0)
       (if (<= y.im 8.5e-134)
         (/ (+ x.re (/ (* x.im y.im) y.re)) y.re)
         (if (<= y.im 3.8e+65) (/ (* y.im t_1) t_0) t_2))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (y_46_re * y_46_re) + (y_46_im * y_46_im);
	double t_1 = x_46_im + (x_46_re * (y_46_re / y_46_im));
	double t_2 = t_1 / y_46_im;
	double tmp;
	if (y_46_im <= -3.5e+98) {
		tmp = t_2;
	} else if (y_46_im <= -1.45e-144) {
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / t_0;
	} else if (y_46_im <= 8.5e-134) {
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_im <= 3.8e+65) {
		tmp = (y_46_im * t_1) / t_0;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_0 = (y_46re * y_46re) + (y_46im * y_46im)
    t_1 = x_46im + (x_46re * (y_46re / y_46im))
    t_2 = t_1 / y_46im
    if (y_46im <= (-3.5d+98)) then
        tmp = t_2
    else if (y_46im <= (-1.45d-144)) then
        tmp = ((x_46re * y_46re) + (x_46im * y_46im)) / t_0
    else if (y_46im <= 8.5d-134) then
        tmp = (x_46re + ((x_46im * y_46im) / y_46re)) / y_46re
    else if (y_46im <= 3.8d+65) then
        tmp = (y_46im * t_1) / t_0
    else
        tmp = t_2
    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 = (y_46_re * y_46_re) + (y_46_im * y_46_im);
	double t_1 = x_46_im + (x_46_re * (y_46_re / y_46_im));
	double t_2 = t_1 / y_46_im;
	double tmp;
	if (y_46_im <= -3.5e+98) {
		tmp = t_2;
	} else if (y_46_im <= -1.45e-144) {
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / t_0;
	} else if (y_46_im <= 8.5e-134) {
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_im <= 3.8e+65) {
		tmp = (y_46_im * t_1) / t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = (y_46_re * y_46_re) + (y_46_im * y_46_im)
	t_1 = x_46_im + (x_46_re * (y_46_re / y_46_im))
	t_2 = t_1 / y_46_im
	tmp = 0
	if y_46_im <= -3.5e+98:
		tmp = t_2
	elif y_46_im <= -1.45e-144:
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / t_0
	elif y_46_im <= 8.5e-134:
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re
	elif y_46_im <= 3.8e+65:
		tmp = (y_46_im * t_1) / t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im))
	t_1 = Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im)))
	t_2 = Float64(t_1 / y_46_im)
	tmp = 0.0
	if (y_46_im <= -3.5e+98)
		tmp = t_2;
	elseif (y_46_im <= -1.45e-144)
		tmp = Float64(Float64(Float64(x_46_re * y_46_re) + Float64(x_46_im * y_46_im)) / t_0);
	elseif (y_46_im <= 8.5e-134)
		tmp = Float64(Float64(x_46_re + Float64(Float64(x_46_im * y_46_im) / y_46_re)) / y_46_re);
	elseif (y_46_im <= 3.8e+65)
		tmp = Float64(Float64(y_46_im * t_1) / t_0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = (y_46_re * y_46_re) + (y_46_im * y_46_im);
	t_1 = x_46_im + (x_46_re * (y_46_re / y_46_im));
	t_2 = t_1 / y_46_im;
	tmp = 0.0;
	if (y_46_im <= -3.5e+98)
		tmp = t_2;
	elseif (y_46_im <= -1.45e-144)
		tmp = ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / t_0;
	elseif (y_46_im <= 8.5e-134)
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re;
	elseif (y_46_im <= 3.8e+65)
		tmp = (y_46_im * t_1) / t_0;
	else
		tmp = t_2;
	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[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / y$46$im), $MachinePrecision]}, If[LessEqual[y$46$im, -3.5e+98], t$95$2, If[LessEqual[y$46$im, -1.45e-144], N[(N[(N[(x$46$re * y$46$re), $MachinePrecision] + N[(x$46$im * y$46$im), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], If[LessEqual[y$46$im, 8.5e-134], N[(N[(x$46$re + N[(N[(x$46$im * y$46$im), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$im, 3.8e+65], N[(N[(y$46$im * t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y.im < -3.5e98 or 3.80000000000000011e65 < y.im

   1. Initial program 36.8%

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

   3. Taylor expanded in y.im around inf 77.1%

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

      1. associate-/l* 84.4%

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

   5. Simplified 84.4%

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

   if -3.5e98 < y.im < -1.4500000000000001e-144

   1. Initial program 83.5%

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

   if -1.4500000000000001e-144 < y.im < 8.50000000000000015e-134

   1. Initial program 65.4%

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

   3. Taylor expanded in y.re around inf 93.1%

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

   if 8.50000000000000015e-134 < y.im < 3.80000000000000011e65

   1. Initial program 86.8%

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

   3. Taylor expanded in y.im around inf 86.8%

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

      1. associate-/l* 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -3.5 \cdot 10^{+98}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.im \leq -1.45 \cdot 10^{-144}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq 8.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 3.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{y.im \cdot \left(x.im + x.re \cdot \frac{y.re}{y.im}\right)}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ t_1 := \frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{if}\;y.im \leq -5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y.im \leq -2.6 \cdot 10^{-137}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.im \leq 4.2 \cdot 10^{-134}:\\ \;\;\;\;\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 4 \cdot 10^{+64}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))
        (t_1 (/ (+ x.im (* x.re (/ y.re y.im))) y.im)))
   (if (<= y.im -5e+98)
     t_1
     (if (<= y.im -2.6e-137)
       t_0
       (if (<= y.im 4.2e-134)
         (/ (+ x.re (/ (* x.im y.im) y.re)) y.re)
         (if (<= y.im 4e+64) t_0 t_1))))))

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) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double t_1 = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	double tmp;
	if (y_46_im <= -5e+98) {
		tmp = t_1;
	} else if (y_46_im <= -2.6e-137) {
		tmp = t_0;
	} else if (y_46_im <= 4.2e-134) {
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_im <= 4e+64) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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_46re * y_46re) + (x_46im * y_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
    t_1 = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    if (y_46im <= (-5d+98)) then
        tmp = t_1
    else if (y_46im <= (-2.6d-137)) then
        tmp = t_0
    else if (y_46im <= 4.2d-134) then
        tmp = (x_46re + ((x_46im * y_46im) / y_46re)) / y_46re
    else if (y_46im <= 4d+64) then
        tmp = t_0
    else
        tmp = t_1
    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) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double t_1 = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	double tmp;
	if (y_46_im <= -5e+98) {
		tmp = t_1;
	} else if (y_46_im <= -2.6e-137) {
		tmp = t_0;
	} else if (y_46_im <= 4.2e-134) {
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_im <= 4e+64) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	t_1 = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	tmp = 0
	if y_46_im <= -5e+98:
		tmp = t_1
	elif y_46_im <= -2.6e-137:
		tmp = t_0
	elif y_46_im <= 4.2e-134:
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re
	elif y_46_im <= 4e+64:
		tmp = t_0
	else:
		tmp = t_1
	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(x_46_im * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
	t_1 = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im)
	tmp = 0.0
	if (y_46_im <= -5e+98)
		tmp = t_1;
	elseif (y_46_im <= -2.6e-137)
		tmp = t_0;
	elseif (y_46_im <= 4.2e-134)
		tmp = Float64(Float64(x_46_re + Float64(Float64(x_46_im * y_46_im) / y_46_re)) / y_46_re);
	elseif (y_46_im <= 4e+64)
		tmp = t_0;
	else
		tmp = t_1;
	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) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	t_1 = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	tmp = 0.0;
	if (y_46_im <= -5e+98)
		tmp = t_1;
	elseif (y_46_im <= -2.6e-137)
		tmp = t_0;
	elseif (y_46_im <= 4.2e-134)
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re;
	elseif (y_46_im <= 4e+64)
		tmp = t_0;
	else
		tmp = t_1;
	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[(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]}, Block[{t$95$1 = 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, -5e+98], t$95$1, If[LessEqual[y$46$im, -2.6e-137], t$95$0, If[LessEqual[y$46$im, 4.2e-134], N[(N[(x$46$re + N[(N[(x$46$im * y$46$im), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$im, 4e+64], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y.im < -4.9999999999999998e98 or 4.00000000000000009e64 < y.im

   1. Initial program 36.8%

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

   3. Taylor expanded in y.im around inf 77.1%

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

      1. associate-/l* 84.4%

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

   5. Simplified 84.4%

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

   if -4.9999999999999998e98 < y.im < -2.6e-137 or 4.1999999999999998e-134 < y.im < 4.00000000000000009e64

   1. Initial program 85.0%

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

   if -2.6e-137 < y.im < 4.1999999999999998e-134

   1. Initial program 65.4%

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

   3. Taylor expanded in y.re around inf 93.1%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -5 \cdot 10^{+98}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.im \leq -2.6 \cdot 10^{-137}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.im \leq 4.2 \cdot 10^{-134}:\\ \;\;\;\;\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.im \leq 4 \cdot 10^{+64}:\\ \;\;\;\;\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -4 \cdot 10^{+86} \lor \neg \left(y.re \leq -14000000\right) \land \left(y.re \leq -7.4 \cdot 10^{-29} \lor \neg \left(y.re \leq 1.76 \cdot 10^{+19}\right)\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -4e+86)
         (and (not (<= y.re -14000000.0))
              (or (<= y.re -7.4e-29) (not (<= y.re 1.76e+19)))))
   (/ x.re y.re)
   (/ (+ x.im (* x.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) {
	double tmp;
	if ((y_46_re <= -4e+86) || (!(y_46_re <= -14000000.0) && ((y_46_re <= -7.4e-29) || !(y_46_re <= 1.76e+19)))) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = (x_46_im + (x_46_re * (y_46_re / 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) :: tmp
    if ((y_46re <= (-4d+86)) .or. (.not. (y_46re <= (-14000000.0d0))) .and. (y_46re <= (-7.4d-29)) .or. (.not. (y_46re <= 1.76d+19))) then
        tmp = x_46re / y_46re
    else
        tmp = (x_46im + (x_46re * (y_46re / 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 tmp;
	if ((y_46_re <= -4e+86) || (!(y_46_re <= -14000000.0) && ((y_46_re <= -7.4e-29) || !(y_46_re <= 1.76e+19)))) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_re <= -4e+86) or (not (y_46_re <= -14000000.0) and ((y_46_re <= -7.4e-29) or not (y_46_re <= 1.76e+19))):
		tmp = x_46_re / y_46_re
	else:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_re <= -4e+86) || (!(y_46_re <= -14000000.0) && ((y_46_re <= -7.4e-29) || !(y_46_re <= 1.76e+19))))
		tmp = Float64(x_46_re / y_46_re);
	else
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / 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)
	tmp = 0.0;
	if ((y_46_re <= -4e+86) || (~((y_46_re <= -14000000.0)) && ((y_46_re <= -7.4e-29) || ~((y_46_re <= 1.76e+19)))))
		tmp = x_46_re / y_46_re;
	else
		tmp = (x_46_im + (x_46_re * (y_46_re / 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_] := If[Or[LessEqual[y$46$re, -4e+86], And[N[Not[LessEqual[y$46$re, -14000000.0]], $MachinePrecision], Or[LessEqual[y$46$re, -7.4e-29], N[Not[LessEqual[y$46$re, 1.76e+19]], $MachinePrecision]]]], N[(x$46$re / y$46$re), $MachinePrecision], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.re < -4.0000000000000001e86 or -1.4e7 < y.re < -7.3999999999999995e-29 or 1.76e19 < y.re

   1. Initial program 50.6%

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

   3. Taylor expanded in y.re around inf 71.9%

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

   if -4.0000000000000001e86 < y.re < -1.4e7 or -7.3999999999999995e-29 < y.re < 1.76e19

   1. Initial program 69.6%

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

   3. Taylor expanded in y.im around inf 83.1%

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

      1. associate-/l* 84.9%

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

   5. Simplified 84.9%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -4 \cdot 10^{+86} \lor \neg \left(y.re \leq -14000000\right) \land \left(y.re \leq -7.4 \cdot 10^{-29} \lor \neg \left(y.re \leq 1.76 \cdot 10^{+19}\right)\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -1.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq -155000000:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq -6.5 \cdot 10^{-29} \lor \neg \left(y.re \leq 5.4 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + \frac{x.re \cdot y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -1.9e+91)
   (/ x.re y.re)
   (if (<= y.re -155000000.0)
     (/ (+ x.im (* x.re (/ y.re y.im))) y.im)
     (if (or (<= y.re -6.5e-29) (not (<= y.re 5.4e+18)))
       (/ x.re y.re)
       (/ (+ x.im (/ (* x.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) {
	double tmp;
	if (y_46_re <= -1.9e+91) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= -155000000.0) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if ((y_46_re <= -6.5e-29) || !(y_46_re <= 5.4e+18)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = (x_46_im + ((x_46_re * y_46_re) / 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) :: tmp
    if (y_46re <= (-1.9d+91)) then
        tmp = x_46re / y_46re
    else if (y_46re <= (-155000000.0d0)) then
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    else if ((y_46re <= (-6.5d-29)) .or. (.not. (y_46re <= 5.4d+18))) then
        tmp = x_46re / y_46re
    else
        tmp = (x_46im + ((x_46re * y_46re) / 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 tmp;
	if (y_46_re <= -1.9e+91) {
		tmp = x_46_re / y_46_re;
	} else if (y_46_re <= -155000000.0) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if ((y_46_re <= -6.5e-29) || !(y_46_re <= 5.4e+18)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = (x_46_im + ((x_46_re * y_46_re) / y_46_im)) / y_46_im;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if y_46_re <= -1.9e+91:
		tmp = x_46_re / y_46_re
	elif y_46_re <= -155000000.0:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	elif (y_46_re <= -6.5e-29) or not (y_46_re <= 5.4e+18):
		tmp = x_46_re / y_46_re
	else:
		tmp = (x_46_im + ((x_46_re * y_46_re) / y_46_im)) / y_46_im
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if (y_46_re <= -1.9e+91)
		tmp = Float64(x_46_re / y_46_re);
	elseif (y_46_re <= -155000000.0)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	elseif ((y_46_re <= -6.5e-29) || !(y_46_re <= 5.4e+18))
		tmp = Float64(x_46_re / y_46_re);
	else
		tmp = Float64(Float64(x_46_im + Float64(Float64(x_46_re * y_46_re) / 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)
	tmp = 0.0;
	if (y_46_re <= -1.9e+91)
		tmp = x_46_re / y_46_re;
	elseif (y_46_re <= -155000000.0)
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	elseif ((y_46_re <= -6.5e-29) || ~((y_46_re <= 5.4e+18)))
		tmp = x_46_re / y_46_re;
	else
		tmp = (x_46_im + ((x_46_re * y_46_re) / 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_] := If[LessEqual[y$46$re, -1.9e+91], N[(x$46$re / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, -155000000.0], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], If[Or[LessEqual[y$46$re, -6.5e-29], N[Not[LessEqual[y$46$re, 5.4e+18]], $MachinePrecision]], N[(x$46$re / y$46$re), $MachinePrecision], N[(N[(x$46$im + N[(N[(x$46$re * y$46$re), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y.re < -1.8999999999999999e91 or -1.55e8 < y.re < -6.5e-29 or 5.4e18 < y.re

   1. Initial program 50.6%

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

   3. Taylor expanded in y.re around inf 71.9%

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

   if -1.8999999999999999e91 < y.re < -1.55e8

   1. Initial program 54.0%

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

   3. Taylor expanded in y.im around inf 38.4%

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

      1. associate-/l* 57.9%

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

   5. Simplified 57.9%

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

   if -6.5e-29 < y.re < 5.4e18

   1. Initial program 71.5%

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

   3. Taylor expanded in y.im around inf 88.3%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -1.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{elif}\;y.re \leq -155000000:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq -6.5 \cdot 10^{-29} \lor \neg \left(y.re \leq 5.4 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + \frac{x.re \cdot y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{if}\;y.re \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.re \leq -24000000:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq -7.4 \cdot 10^{-29} \lor \neg \left(y.re \leq 1.55 \cdot 10^{+18}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + \frac{x.re \cdot y.re}{y.im}}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ (+ x.re (* x.im (/ y.im y.re))) y.re)))
   (if (<= y.re -1.15e+64)
     t_0
     (if (<= y.re -24000000.0)
       (/ (+ x.im (* x.re (/ y.re y.im))) y.im)
       (if (or (<= y.re -7.4e-29) (not (<= y.re 1.55e+18)))
         t_0
         (/ (+ x.im (/ (* x.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) {
	double t_0 = (x_46_re + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	double tmp;
	if (y_46_re <= -1.15e+64) {
		tmp = t_0;
	} else if (y_46_re <= -24000000.0) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if ((y_46_re <= -7.4e-29) || !(y_46_re <= 1.55e+18)) {
		tmp = t_0;
	} else {
		tmp = (x_46_im + ((x_46_re * y_46_re) / 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 + (x_46im * (y_46im / y_46re))) / y_46re
    if (y_46re <= (-1.15d+64)) then
        tmp = t_0
    else if (y_46re <= (-24000000.0d0)) then
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    else if ((y_46re <= (-7.4d-29)) .or. (.not. (y_46re <= 1.55d+18))) then
        tmp = t_0
    else
        tmp = (x_46im + ((x_46re * y_46re) / 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 + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	double tmp;
	if (y_46_re <= -1.15e+64) {
		tmp = t_0;
	} else if (y_46_re <= -24000000.0) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if ((y_46_re <= -7.4e-29) || !(y_46_re <= 1.55e+18)) {
		tmp = t_0;
	} else {
		tmp = (x_46_im + ((x_46_re * y_46_re) / 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 + (x_46_im * (y_46_im / y_46_re))) / y_46_re
	tmp = 0
	if y_46_re <= -1.15e+64:
		tmp = t_0
	elif y_46_re <= -24000000.0:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	elif (y_46_re <= -7.4e-29) or not (y_46_re <= 1.55e+18):
		tmp = t_0
	else:
		tmp = (x_46_im + ((x_46_re * y_46_re) / 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(x_46_re + Float64(x_46_im * Float64(y_46_im / y_46_re))) / y_46_re)
	tmp = 0.0
	if (y_46_re <= -1.15e+64)
		tmp = t_0;
	elseif (y_46_re <= -24000000.0)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	elseif ((y_46_re <= -7.4e-29) || !(y_46_re <= 1.55e+18))
		tmp = t_0;
	else
		tmp = Float64(Float64(x_46_im + Float64(Float64(x_46_re * y_46_re) / 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 + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	tmp = 0.0;
	if (y_46_re <= -1.15e+64)
		tmp = t_0;
	elseif (y_46_re <= -24000000.0)
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	elseif ((y_46_re <= -7.4e-29) || ~((y_46_re <= 1.55e+18)))
		tmp = t_0;
	else
		tmp = (x_46_im + ((x_46_re * y_46_re) / 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[(x$46$re + N[(x$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]}, If[LessEqual[y$46$re, -1.15e+64], t$95$0, If[LessEqual[y$46$re, -24000000.0], N[(N[(x$46$im + N[(x$46$re * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], If[Or[LessEqual[y$46$re, -7.4e-29], N[Not[LessEqual[y$46$re, 1.55e+18]], $MachinePrecision]], t$95$0, N[(N[(x$46$im + N[(N[(x$46$re * y$46$re), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y.re < -1.15e64 or -2.4e7 < y.re < -7.3999999999999995e-29 or 1.55e18 < y.re

   1. Initial program 51.4%

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

   3. Taylor expanded in y.re around inf 77.0%

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

      1. associate-/l* 81.3%

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

   5. Simplified 81.3%

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

   if -1.15e64 < y.re < -2.4e7

   1. Initial program 45.0%

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

   3. Taylor expanded in y.im around inf 39.8%

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

      1. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

   if -7.3999999999999995e-29 < y.re < 1.55e18

   1. Initial program 71.5%

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

   3. Taylor expanded in y.im around inf 88.3%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;\frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq -24000000:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq -7.4 \cdot 10^{-29} \lor \neg \left(y.re \leq 1.55 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im + \frac{x.re \cdot y.re}{y.im}}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{if}\;y.re \leq -1.9 \cdot 10^{+63}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.re \leq -7200000:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq -7.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x.im + \frac{x.re \cdot y.re}{y.im}}{y.im}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ (+ x.re (* x.im (/ y.im y.re))) y.re)))
   (if (<= y.re -1.9e+63)
     t_0
     (if (<= y.re -7200000.0)
       (/ (+ x.im (* x.re (/ y.re y.im))) y.im)
       (if (<= y.re -7.4e-29)
         (/ (+ x.re (/ (* x.im y.im) y.re)) y.re)
         (if (<= y.re 6.5e+18)
           (/ (+ 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 + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	double tmp;
	if (y_46_re <= -1.9e+63) {
		tmp = t_0;
	} else if (y_46_re <= -7200000.0) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if (y_46_re <= -7.4e-29) {
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_re <= 6.5e+18) {
		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 + (x_46im * (y_46im / y_46re))) / y_46re
    if (y_46re <= (-1.9d+63)) then
        tmp = t_0
    else if (y_46re <= (-7200000.0d0)) then
        tmp = (x_46im + (x_46re * (y_46re / y_46im))) / y_46im
    else if (y_46re <= (-7.4d-29)) then
        tmp = (x_46re + ((x_46im * y_46im) / y_46re)) / y_46re
    else if (y_46re <= 6.5d+18) 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 + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	double tmp;
	if (y_46_re <= -1.9e+63) {
		tmp = t_0;
	} else if (y_46_re <= -7200000.0) {
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	} else if (y_46_re <= -7.4e-29) {
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_re <= 6.5e+18) {
		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 + (x_46_im * (y_46_im / y_46_re))) / y_46_re
	tmp = 0
	if y_46_re <= -1.9e+63:
		tmp = t_0
	elif y_46_re <= -7200000.0:
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im
	elif y_46_re <= -7.4e-29:
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re
	elif y_46_re <= 6.5e+18:
		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(x_46_im * Float64(y_46_im / y_46_re))) / y_46_re)
	tmp = 0.0
	if (y_46_re <= -1.9e+63)
		tmp = t_0;
	elseif (y_46_re <= -7200000.0)
		tmp = Float64(Float64(x_46_im + Float64(x_46_re * Float64(y_46_re / y_46_im))) / y_46_im);
	elseif (y_46_re <= -7.4e-29)
		tmp = Float64(Float64(x_46_re + Float64(Float64(x_46_im * y_46_im) / y_46_re)) / y_46_re);
	elseif (y_46_re <= 6.5e+18)
		tmp = Float64(Float64(x_46_im + Float64(Float64(x_46_re * 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 + (x_46_im * (y_46_im / y_46_re))) / y_46_re;
	tmp = 0.0;
	if (y_46_re <= -1.9e+63)
		tmp = t_0;
	elseif (y_46_re <= -7200000.0)
		tmp = (x_46_im + (x_46_re * (y_46_re / y_46_im))) / y_46_im;
	elseif (y_46_re <= -7.4e-29)
		tmp = (x_46_re + ((x_46_im * y_46_im) / y_46_re)) / y_46_re;
	elseif (y_46_re <= 6.5e+18)
		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[(x$46$im * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]}, If[LessEqual[y$46$re, -1.9e+63], t$95$0, If[LessEqual[y$46$re, -7200000.0], 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$46$re, -7.4e-29], N[(N[(x$46$re + N[(N[(x$46$im * y$46$im), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 6.5e+18], N[(N[(x$46$im + N[(N[(x$46$re * y$46$re), $MachinePrecision] / y$46$im), $MachinePrecision]), $MachinePrecision] / y$46$im), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y.re < -1.9000000000000001e63 or 6.5e18 < y.re

   1. Initial program 46.3%

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

   3. Taylor expanded in y.re around inf 77.4%

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

      1. associate-/l* 82.3%

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

   5. Simplified 82.3%

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

   if -1.9000000000000001e63 < y.re < -7.2e6

   1. Initial program 45.0%

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

   3. Taylor expanded in y.im around inf 39.8%

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

      1. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

   if -7.2e6 < y.re < -7.3999999999999995e-29

   1. Initial program 86.6%

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

   3. Taylor expanded in y.re around inf 74.6%

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

   if -7.3999999999999995e-29 < y.re < 6.5e18

   1. Initial program 71.5%

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

   3. Taylor expanded in y.im around inf 88.3%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -1.9 \cdot 10^{+63}:\\ \;\;\;\;\frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq -7200000:\\ \;\;\;\;\frac{x.im + x.re \cdot \frac{y.re}{y.im}}{y.im}\\ \mathbf{elif}\;y.re \leq -7.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{x.re + \frac{x.im \cdot y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x.im + \frac{x.re \cdot y.re}{y.im}}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.re + x.im \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -5 \cdot 10^{-35} \lor \neg \left(y.re \leq 7.5\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.re -5e-35) (not (<= y.re 7.5))) (/ x.re y.re) (/ x.im y.im)))

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 <= -5e-35) || !(y_46_re <= 7.5)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = x_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) :: tmp
    if ((y_46re <= (-5d-35)) .or. (.not. (y_46re <= 7.5d0))) then
        tmp = x_46re / y_46re
    else
        tmp = x_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 tmp;
	if ((y_46_re <= -5e-35) || !(y_46_re <= 7.5)) {
		tmp = x_46_re / y_46_re;
	} else {
		tmp = x_46_im / y_46_im;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	tmp = 0
	if (y_46_re <= -5e-35) or not (y_46_re <= 7.5):
		tmp = x_46_re / y_46_re
	else:
		tmp = x_46_im / y_46_im
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = 0.0
	if ((y_46_re <= -5e-35) || !(y_46_re <= 7.5))
		tmp = Float64(x_46_re / y_46_re);
	else
		tmp = Float64(x_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)
	tmp = 0.0;
	if ((y_46_re <= -5e-35) || ~((y_46_re <= 7.5)))
		tmp = x_46_re / y_46_re;
	else
		tmp = x_46_im / y_46_im;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := If[Or[LessEqual[y$46$re, -5e-35], N[Not[LessEqual[y$46$re, 7.5]], $MachinePrecision]], N[(x$46$re / y$46$re), $MachinePrecision], N[(x$46$im / y$46$im), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.re < -4.99999999999999964e-35 or 7.5 < y.re

   1. Initial program 53.1%

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

   3. Taylor expanded in y.re around inf 65.2%

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

   if -4.99999999999999964e-35 < y.re < 7.5

   1. Initial program 70.4%

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

   3. Taylor expanded in y.re around 0 69.5%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -5 \cdot 10^{-35} \lor \neg \left(y.re \leq 7.5\right):\\ \;\;\;\;\frac{x.re}{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.4% 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 61.3%

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

3. Taylor expanded in y.re around 0 43.1%

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

4. Final simplification 43.1%

   \[\leadsto \frac{x.im}{y.im} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024061 
(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))))