_divideComplex, imaginary part

Percentage Accurate: 62.2% → 85.9%

Time: 11.3s

Alternatives: 12

Speedup: 1.1×

Specification

Math

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

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (/ (- (* x.im y.re) (* x.re 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_im * y_46_re) - (x_46_re * 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_46im * y_46re) - (x_46re * 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_im * y_46_re) - (x_46_re * 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_im * y_46_re) - (x_46_re * 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_im * y_46_re) - Float64(x_46_re * 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_im * y_46_re) - (x_46_re * 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$46$im * y$46$re), $MachinePrecision] - N[(x$46$re * 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

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

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (/ (- (* x.im y.re) (* x.re 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_im * y_46_re) - (x_46_re * 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_46im * y_46re) - (x_46re * 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_im * y_46_re) - (x_46_re * 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_im * y_46_re) - (x_46_re * 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_im * y_46_re) - Float64(x_46_re * 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_im * y_46_re) - (x_46_re * 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$46$im * y$46$re), $MachinePrecision] - N[(x$46$re * 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: 85.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -8.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq 1.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{\frac{y.re \cdot x.im}{x.re} - y.im}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{x.re}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{y.re \cdot \frac{1}{y.im}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -8.5e+70)
   (/ (- x.im (/ x.re (/ y.re y.im))) y.re)
   (if (<= y.re 1.2e+68)
     (*
      (/ (- (/ (* y.re x.im) x.re) y.im) (hypot y.re y.im))
      (/ x.re (hypot y.re y.im)))
     (/ (- x.im (/ x.re (* y.re (/ 1.0 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 <= -8.5e+70) {
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	} else if (y_46_re <= 1.2e+68) {
		tmp = ((((y_46_re * x_46_im) / x_46_re) - y_46_im) / hypot(y_46_re, y_46_im)) * (x_46_re / hypot(y_46_re, y_46_im));
	} else {
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / y_46_im)))) / y_46_re;
	}
	return tmp;
}

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 <= -8.5e+70) {
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	} else if (y_46_re <= 1.2e+68) {
		tmp = ((((y_46_re * x_46_im) / x_46_re) - y_46_im) / Math.hypot(y_46_re, y_46_im)) * (x_46_re / Math.hypot(y_46_re, y_46_im));
	} else {
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / 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 <= -8.5e+70:
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re
	elif y_46_re <= 1.2e+68:
		tmp = ((((y_46_re * x_46_im) / x_46_re) - y_46_im) / math.hypot(y_46_re, y_46_im)) * (x_46_re / math.hypot(y_46_re, y_46_im))
	else:
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / 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 <= -8.5e+70)
		tmp = Float64(Float64(x_46_im - Float64(x_46_re / Float64(y_46_re / y_46_im))) / y_46_re);
	elseif (y_46_re <= 1.2e+68)
		tmp = Float64(Float64(Float64(Float64(Float64(y_46_re * x_46_im) / x_46_re) - y_46_im) / hypot(y_46_re, y_46_im)) * Float64(x_46_re / hypot(y_46_re, y_46_im)));
	else
		tmp = Float64(Float64(x_46_im - Float64(x_46_re / Float64(y_46_re * Float64(1.0 / 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 <= -8.5e+70)
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	elseif (y_46_re <= 1.2e+68)
		tmp = ((((y_46_re * x_46_im) / x_46_re) - y_46_im) / hypot(y_46_re, y_46_im)) * (x_46_re / hypot(y_46_re, y_46_im));
	else
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / 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, -8.5e+70], N[(N[(x$46$im - N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 1.2e+68], N[(N[(N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] / x$46$re), $MachinePrecision] - y$46$im), $MachinePrecision] / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision] * N[(x$46$re / N[Sqrt[y$46$re ^ 2 + y$46$im ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im - N[(x$46$re / N[(y$46$re * N[(1.0 / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y.re < -8.4999999999999996e70

   1. Initial program 45.1%

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

   3. Taylor expanded in y.re around inf 95.6%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. mul-1-neg 95.6%

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

      2. unsub-neg 95.6%

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

      3. associate-/l* 97.7%

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

   5. Simplified 97.7%

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

      1. clear-num 97.7%

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

      2. *-un-lft-identity 97.7%

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

      3. associate-*l/ 97.7%

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

      4. div-inv 97.8%

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

      5. associate-*l/ 97.8%

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

      6. *-un-lft-identity 97.8%

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

   7. Applied egg-rr 97.8%

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

   if -8.4999999999999996e70 < y.re < 1.20000000000000004e68

   1. Initial program 77.0%

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

   3. Taylor expanded in x.re around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. add-sqr-sqrt 73.9%

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

      3. times-frac 71.5%

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

      4. *-commutative 71.5%

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

      5. hypot-define 71.5%

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

      6. hypot-define 89.3%

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

   5. Applied egg-rr 89.3%

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

   if 1.20000000000000004e68 < y.re

   1. Initial program 38.2%

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

   3. Taylor expanded in y.re around inf 81.3%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. *-commutative 81.3%

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

      2. *-un-lft-identity 81.3%

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

      3. times-frac 87.6%

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

   5. Applied egg-rr 87.6%

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

      1. clear-num 87.6%

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

      2. frac-times 87.7%

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

      3. *-un-lft-identity 87.7%

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

   7. Applied egg-rr 87.7%

      \[\leadsto \frac{x.im + -1 \cdot \color{blue}{\frac{x.re}{\frac{1}{y.im} \cdot y.re}}}{y.re} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -8.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq 1.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{\frac{y.re \cdot x.im}{x.re} - y.im}{\mathsf{hypot}\left(y.re, y.im\right)} \cdot \frac{x.re}{\mathsf{hypot}\left(y.re, y.im\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{y.re \cdot \frac{1}{y.im}}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot y.re + y.im \cdot y.im\\ \mathbf{if}\;y.re \leq -3.8 \cdot 10^{+77}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -5 \cdot 10^{-40}:\\ \;\;\;\;x.im \cdot \left(\frac{y.re}{t\_0} - x.re \cdot \frac{y.im}{x.im \cdot t\_0}\right)\\ \mathbf{elif}\;y.re \leq 3.3 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{y.re \cdot x.im}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 1.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{y.re \cdot x.im - x.re \cdot y.im}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{y.re \cdot \frac{1}{y.im}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (+ (* y.re y.re) (* y.im y.im))))
   (if (<= y.re -3.8e+77)
     (/ (- x.im (/ x.re (/ y.re y.im))) y.re)
     (if (<= y.re -5e-40)
       (* x.im (- (/ y.re t_0) (* x.re (/ y.im (* x.im t_0)))))
       (if (<= y.re 3.3e-120)
         (/ (- (/ (* y.re x.im) y.im) x.re) y.im)
         (if (<= y.re 1.4e+60)
           (/ (- (* y.re x.im) (* x.re y.im)) t_0)
           (/ (- x.im (/ x.re (* y.re (/ 1.0 y.im)))) y.re)))))))

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 tmp;
	if (y_46_re <= -3.8e+77) {
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	} else if (y_46_re <= -5e-40) {
		tmp = x_46_im * ((y_46_re / t_0) - (x_46_re * (y_46_im / (x_46_im * t_0))));
	} else if (y_46_re <= 3.3e-120) {
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im;
	} else if (y_46_re <= 1.4e+60) {
		tmp = ((y_46_re * x_46_im) - (x_46_re * y_46_im)) / t_0;
	} else {
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / 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) :: t_0
    real(8) :: tmp
    t_0 = (y_46re * y_46re) + (y_46im * y_46im)
    if (y_46re <= (-3.8d+77)) then
        tmp = (x_46im - (x_46re / (y_46re / y_46im))) / y_46re
    else if (y_46re <= (-5d-40)) then
        tmp = x_46im * ((y_46re / t_0) - (x_46re * (y_46im / (x_46im * t_0))))
    else if (y_46re <= 3.3d-120) then
        tmp = (((y_46re * x_46im) / y_46im) - x_46re) / y_46im
    else if (y_46re <= 1.4d+60) then
        tmp = ((y_46re * x_46im) - (x_46re * y_46im)) / t_0
    else
        tmp = (x_46im - (x_46re / (y_46re * (1.0d0 / 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 t_0 = (y_46_re * y_46_re) + (y_46_im * y_46_im);
	double tmp;
	if (y_46_re <= -3.8e+77) {
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	} else if (y_46_re <= -5e-40) {
		tmp = x_46_im * ((y_46_re / t_0) - (x_46_re * (y_46_im / (x_46_im * t_0))));
	} else if (y_46_re <= 3.3e-120) {
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im;
	} else if (y_46_re <= 1.4e+60) {
		tmp = ((y_46_re * x_46_im) - (x_46_re * y_46_im)) / t_0;
	} else {
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / y_46_im)))) / y_46_re;
	}
	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)
	tmp = 0
	if y_46_re <= -3.8e+77:
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re
	elif y_46_re <= -5e-40:
		tmp = x_46_im * ((y_46_re / t_0) - (x_46_re * (y_46_im / (x_46_im * t_0))))
	elif y_46_re <= 3.3e-120:
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im
	elif y_46_re <= 1.4e+60:
		tmp = ((y_46_re * x_46_im) - (x_46_re * y_46_im)) / t_0
	else:
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / y_46_im)))) / y_46_re
	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))
	tmp = 0.0
	if (y_46_re <= -3.8e+77)
		tmp = Float64(Float64(x_46_im - Float64(x_46_re / Float64(y_46_re / y_46_im))) / y_46_re);
	elseif (y_46_re <= -5e-40)
		tmp = Float64(x_46_im * Float64(Float64(y_46_re / t_0) - Float64(x_46_re * Float64(y_46_im / Float64(x_46_im * t_0)))));
	elseif (y_46_re <= 3.3e-120)
		tmp = Float64(Float64(Float64(Float64(y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im);
	elseif (y_46_re <= 1.4e+60)
		tmp = Float64(Float64(Float64(y_46_re * x_46_im) - Float64(x_46_re * y_46_im)) / 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_re);
	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);
	tmp = 0.0;
	if (y_46_re <= -3.8e+77)
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	elseif (y_46_re <= -5e-40)
		tmp = x_46_im * ((y_46_re / t_0) - (x_46_re * (y_46_im / (x_46_im * t_0))));
	elseif (y_46_re <= 3.3e-120)
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im;
	elseif (y_46_re <= 1.4e+60)
		tmp = ((y_46_re * x_46_im) - (x_46_re * y_46_im)) / t_0;
	else
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / 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_] := Block[{t$95$0 = N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -3.8e+77], N[(N[(x$46$im - N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, -5e-40], N[(x$46$im * N[(N[(y$46$re / t$95$0), $MachinePrecision] - N[(x$46$re * N[(y$46$im / N[(x$46$im * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 3.3e-120], N[(N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] / y$46$im), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, 1.4e+60], N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] - N[(x$46$re * y$46$im), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], N[(N[(x$46$im - N[(x$46$re / N[(y$46$re * N[(1.0 / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y.re < -3.8000000000000001e77

   1. Initial program 46.0%

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

   3. Taylor expanded in y.re around inf 95.5%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. mul-1-neg 95.5%

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

      2. unsub-neg 95.5%

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

      3. associate-/l* 97.7%

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

   5. Simplified 97.7%

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

      1. clear-num 97.6%

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

      2. *-un-lft-identity 97.6%

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

      3. associate-*l/ 97.6%

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

      4. div-inv 97.7%

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

      5. associate-*l/ 97.7%

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

      6. *-un-lft-identity 97.7%

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

   7. Applied egg-rr 97.7%

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

   if -3.8000000000000001e77 < y.re < -4.99999999999999965e-40

   1. Initial program 77.6%

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

   3. Taylor expanded in x.im around inf 84.6%

      \[\leadsto \color{blue}{x.im \cdot \left(-1 \cdot \frac{x.re \cdot y.im}{x.im \cdot \left({y.im}^{2} + {y.re}^{2}\right)} + \frac{y.re}{{y.im}^{2} + {y.re}^{2}}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 84.6%

         \[\leadsto x.im \cdot \color{blue}{\left(\frac{y.re}{{y.im}^{2} + {y.re}^{2}} + -1 \cdot \frac{x.re \cdot y.im}{x.im \cdot \left({y.im}^{2} + {y.re}^{2}\right)}\right)} \]

      2. mul-1-neg 84.6%

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

      3. unsub-neg 84.6%

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

      4. unpow2 84.6%

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

      5. unpow2 84.6%

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

      6. +-commutative 84.6%

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

      7. associate-/l* 85.2%

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

      8. unpow2 85.2%

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

      9. unpow2 85.2%

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

      10. +-commutative 85.2%

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

   5. Simplified 85.2%

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

   if -4.99999999999999965e-40 < y.re < 3.29999999999999967e-120

   1. Initial program 73.0%

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

   3. Taylor expanded in y.re around 0 81.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{x.im \cdot y.re}{{y.im}^{2}}} \]
   4. Step-by-step derivation

      1. +-commutative 81.9%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} + -1 \cdot \frac{x.re}{y.im}} \]

      2. mul-1-neg 81.9%

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

      3. unsub-neg 81.9%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} - \frac{x.re}{y.im}} \]

      4. unpow2 81.9%

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

      5. associate-/r* 86.4%

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

      6. div-sub 87.5%

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

      7. associate-/l* 86.1%

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

   5. Simplified 86.1%

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

      1. associate-*r/ 87.5%

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

      2. *-commutative 87.5%

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

   7. Applied egg-rr 87.5%

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

   if 3.29999999999999967e-120 < y.re < 1.4e60

   1. Initial program 85.5%

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

   if 1.4e60 < y.re

   1. Initial program 38.2%

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

   3. Taylor expanded in y.re around inf 81.3%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. *-commutative 81.3%

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

      2. *-un-lft-identity 81.3%

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

      3. times-frac 87.6%

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

   5. Applied egg-rr 87.6%

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

      1. clear-num 87.6%

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

      2. frac-times 87.7%

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

      3. *-un-lft-identity 87.7%

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

   7. Applied egg-rr 87.7%

      \[\leadsto \frac{x.im + -1 \cdot \color{blue}{\frac{x.re}{\frac{1}{y.im} \cdot y.re}}}{y.re} \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -3.8 \cdot 10^{+77}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -5 \cdot 10^{-40}:\\ \;\;\;\;x.im \cdot \left(\frac{y.re}{y.re \cdot y.re + y.im \cdot y.im} - x.re \cdot \frac{y.im}{x.im \cdot \left(y.re \cdot y.re + y.im \cdot y.im\right)}\right)\\ \mathbf{elif}\;y.re \leq 3.3 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{y.re \cdot x.im}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 1.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{y.re \cdot x.im - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{y.re \cdot \frac{1}{y.im}}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y.re \cdot x.im - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{if}\;y.re \leq -9 \cdot 10^{+70}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -2.6 \cdot 10^{-44}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.re \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{y.re \cdot x.im}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 3.1 \cdot 10^{+59}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{y.re \cdot \frac{1}{y.im}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (/ (- (* y.re x.im) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))))
   (if (<= y.re -9e+70)
     (/ (- x.im (/ x.re (/ y.re y.im))) y.re)
     (if (<= y.re -2.6e-44)
       t_0
       (if (<= y.re 3.8e-120)
         (/ (- (/ (* y.re x.im) y.im) x.re) y.im)
         (if (<= y.re 3.1e+59)
           t_0
           (/ (- x.im (/ x.re (* y.re (/ 1.0 y.im)))) y.re)))))))

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 * x_46_im) - (x_46_re * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_re <= -9e+70) {
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	} else if (y_46_re <= -2.6e-44) {
		tmp = t_0;
	} else if (y_46_re <= 3.8e-120) {
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im;
	} else if (y_46_re <= 3.1e+59) {
		tmp = t_0;
	} else {
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / 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) :: t_0
    real(8) :: tmp
    t_0 = ((y_46re * x_46im) - (x_46re * y_46im)) / ((y_46re * y_46re) + (y_46im * y_46im))
    if (y_46re <= (-9d+70)) then
        tmp = (x_46im - (x_46re / (y_46re / y_46im))) / y_46re
    else if (y_46re <= (-2.6d-44)) then
        tmp = t_0
    else if (y_46re <= 3.8d-120) then
        tmp = (((y_46re * x_46im) / y_46im) - x_46re) / y_46im
    else if (y_46re <= 3.1d+59) then
        tmp = t_0
    else
        tmp = (x_46im - (x_46re / (y_46re * (1.0d0 / 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 t_0 = ((y_46_re * x_46_im) - (x_46_re * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	double tmp;
	if (y_46_re <= -9e+70) {
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	} else if (y_46_re <= -2.6e-44) {
		tmp = t_0;
	} else if (y_46_re <= 3.8e-120) {
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im;
	} else if (y_46_re <= 3.1e+59) {
		tmp = t_0;
	} else {
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / y_46_im)))) / y_46_re;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = ((y_46_re * x_46_im) - (x_46_re * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	tmp = 0
	if y_46_re <= -9e+70:
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re
	elif y_46_re <= -2.6e-44:
		tmp = t_0
	elif y_46_re <= 3.8e-120:
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im
	elif y_46_re <= 3.1e+59:
		tmp = t_0
	else:
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / y_46_im)))) / y_46_re
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64(Float64(y_46_re * x_46_im) - Float64(x_46_re * y_46_im)) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)))
	tmp = 0.0
	if (y_46_re <= -9e+70)
		tmp = Float64(Float64(x_46_im - Float64(x_46_re / Float64(y_46_re / y_46_im))) / y_46_re);
	elseif (y_46_re <= -2.6e-44)
		tmp = t_0;
	elseif (y_46_re <= 3.8e-120)
		tmp = Float64(Float64(Float64(Float64(y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im);
	elseif (y_46_re <= 3.1e+59)
		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_re);
	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 * x_46_im) - (x_46_re * y_46_im)) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	tmp = 0.0;
	if (y_46_re <= -9e+70)
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	elseif (y_46_re <= -2.6e-44)
		tmp = t_0;
	elseif (y_46_re <= 3.8e-120)
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im;
	elseif (y_46_re <= 3.1e+59)
		tmp = t_0;
	else
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / 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_] := Block[{t$95$0 = N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] - N[(x$46$re * y$46$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$46$re, -9e+70], N[(N[(x$46$im - N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, -2.6e-44], t$95$0, If[LessEqual[y$46$re, 3.8e-120], N[(N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] / y$46$im), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, 3.1e+59], 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$46$re), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y.re < -8.9999999999999999e70

   1. Initial program 45.1%

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

   3. Taylor expanded in y.re around inf 95.6%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. mul-1-neg 95.6%

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

      2. unsub-neg 95.6%

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

      3. associate-/l* 97.7%

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

   5. Simplified 97.7%

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

      1. clear-num 97.7%

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

      2. *-un-lft-identity 97.7%

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

      3. associate-*l/ 97.7%

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

      4. div-inv 97.8%

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

      5. associate-*l/ 97.8%

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

      6. *-un-lft-identity 97.8%

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

   7. Applied egg-rr 97.8%

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

   if -8.9999999999999999e70 < y.re < -2.5999999999999998e-44 or 3.7999999999999997e-120 < y.re < 3.10000000000000015e59

   1. Initial program 84.3%

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

   if -2.5999999999999998e-44 < y.re < 3.7999999999999997e-120

   1. Initial program 71.8%

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

   3. Taylor expanded in y.re around 0 82.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{x.im \cdot y.re}{{y.im}^{2}}} \]
   4. Step-by-step derivation

      1. +-commutative 82.1%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} + -1 \cdot \frac{x.re}{y.im}} \]

      2. mul-1-neg 82.1%

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

      3. unsub-neg 82.1%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} - \frac{x.re}{y.im}} \]

      4. unpow2 82.1%

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

      5. associate-/r* 86.8%

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

      6. div-sub 88.0%

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

      7. associate-/l* 86.5%

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

   5. Simplified 86.5%

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

      1. associate-*r/ 88.0%

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

      2. *-commutative 88.0%

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

   7. Applied egg-rr 88.0%

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

   if 3.10000000000000015e59 < y.re

   1. Initial program 38.2%

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

   3. Taylor expanded in y.re around inf 81.3%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. *-commutative 81.3%

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

      2. *-un-lft-identity 81.3%

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

      3. times-frac 87.6%

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

   5. Applied egg-rr 87.6%

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

      1. clear-num 87.6%

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

      2. frac-times 87.7%

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

      3. *-un-lft-identity 87.7%

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

   7. Applied egg-rr 87.7%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -9 \cdot 10^{+70}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -2.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{y.re \cdot x.im - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.re \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{y.re \cdot x.im}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq 3.1 \cdot 10^{+59}:\\ \;\;\;\;\frac{y.re \cdot x.im - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{y.re \cdot \frac{1}{y.im}}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.re \leq -3.3 \cdot 10^{+64}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq -9 \cdot 10^{-9}:\\ \;\;\;\;\frac{y.re \cdot x.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.re \leq 1.95 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{y.re \cdot x.im}{y.im} - x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{y.re \cdot \frac{1}{y.im}}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (<= y.re -3.3e+64)
   (/ (- x.im (/ x.re (/ y.re y.im))) y.re)
   (if (<= y.re -2e+41)
     (/ (- (* x.im (/ y.re y.im)) x.re) y.im)
     (if (<= y.re -9e-9)
       (/ (* y.re x.im) (+ (* y.re y.re) (* y.im y.im)))
       (if (<= y.re 1.95e+29)
         (/ (- (/ (* y.re x.im) y.im) x.re) y.im)
         (/ (- x.im (/ x.re (* y.re (/ 1.0 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 <= -3.3e+64) {
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	} else if (y_46_re <= -2e+41) {
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	} else if (y_46_re <= -9e-9) {
		tmp = (y_46_re * x_46_im) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_re <= 1.95e+29) {
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im;
	} else {
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / 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 <= (-3.3d+64)) then
        tmp = (x_46im - (x_46re / (y_46re / y_46im))) / y_46re
    else if (y_46re <= (-2d+41)) then
        tmp = ((x_46im * (y_46re / y_46im)) - x_46re) / y_46im
    else if (y_46re <= (-9d-9)) then
        tmp = (y_46re * x_46im) / ((y_46re * y_46re) + (y_46im * y_46im))
    else if (y_46re <= 1.95d+29) then
        tmp = (((y_46re * x_46im) / y_46im) - x_46re) / y_46im
    else
        tmp = (x_46im - (x_46re / (y_46re * (1.0d0 / 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 <= -3.3e+64) {
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	} else if (y_46_re <= -2e+41) {
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	} else if (y_46_re <= -9e-9) {
		tmp = (y_46_re * x_46_im) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_re <= 1.95e+29) {
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im;
	} else {
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / 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 <= -3.3e+64:
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re
	elif y_46_re <= -2e+41:
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im
	elif y_46_re <= -9e-9:
		tmp = (y_46_re * x_46_im) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	elif y_46_re <= 1.95e+29:
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im
	else:
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / 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 <= -3.3e+64)
		tmp = Float64(Float64(x_46_im - Float64(x_46_re / Float64(y_46_re / y_46_im))) / y_46_re);
	elseif (y_46_re <= -2e+41)
		tmp = Float64(Float64(Float64(x_46_im * Float64(y_46_re / y_46_im)) - x_46_re) / y_46_im);
	elseif (y_46_re <= -9e-9)
		tmp = Float64(Float64(y_46_re * x_46_im) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	elseif (y_46_re <= 1.95e+29)
		tmp = Float64(Float64(Float64(Float64(y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im);
	else
		tmp = Float64(Float64(x_46_im - Float64(x_46_re / Float64(y_46_re * Float64(1.0 / 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 <= -3.3e+64)
		tmp = (x_46_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	elseif (y_46_re <= -2e+41)
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	elseif (y_46_re <= -9e-9)
		tmp = (y_46_re * x_46_im) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	elseif (y_46_re <= 1.95e+29)
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / y_46_im;
	else
		tmp = (x_46_im - (x_46_re / (y_46_re * (1.0 / 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, -3.3e+64], N[(N[(x$46$im - N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, -2e+41], N[(N[(N[(x$46$im * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, -9e-9], N[(N[(y$46$re * x$46$im), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.95e+29], N[(N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] / y$46$im), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], N[(N[(x$46$im - N[(x$46$re / N[(y$46$re * N[(1.0 / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y.re < -3.29999999999999988e64

   1. Initial program 47.4%

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

   3. Taylor expanded in y.re around inf 93.7%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. mul-1-neg 93.7%

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

      2. unsub-neg 93.7%

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

      3. associate-/l* 95.8%

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

   5. Simplified 95.8%

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

      1. clear-num 95.7%

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

      2. *-un-lft-identity 95.7%

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

      3. associate-*l/ 95.7%

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

      4. div-inv 95.8%

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

      5. associate-*l/ 95.8%

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

      6. *-un-lft-identity 95.8%

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

   7. Applied egg-rr 95.8%

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

   if -3.29999999999999988e64 < y.re < -2.00000000000000001e41

   1. Initial program 40.4%

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

   3. Taylor expanded in y.re around 0 60.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{x.im \cdot y.re}{{y.im}^{2}}} \]
   4. Step-by-step derivation

      1. +-commutative 60.7%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} + -1 \cdot \frac{x.re}{y.im}} \]

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} - \frac{x.re}{y.im}} \]

      4. unpow2 60.7%

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

      5. associate-/r* 61.3%

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

      6. div-sub 61.3%

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

      7. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   if -2.00000000000000001e41 < y.re < -8.99999999999999953e-9

   1. Initial program 91.1%

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

   3. Taylor expanded in x.im around inf 83.7%

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

      1. *-commutative 83.7%

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

      2. unpow2 83.7%

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

      3. unpow2 83.7%

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

      4. +-commutative 83.7%

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

   5. Simplified 83.7%

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

   if -8.99999999999999953e-9 < y.re < 1.94999999999999984e29

   1. Initial program 76.8%

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

   3. Taylor expanded in y.re around 0 77.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{x.im \cdot y.re}{{y.im}^{2}}} \]
   4. Step-by-step derivation

      1. +-commutative 77.4%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} + -1 \cdot \frac{x.re}{y.im}} \]

      2. mul-1-neg 77.4%

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

      3. unsub-neg 77.4%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} - \frac{x.re}{y.im}} \]

      4. unpow2 77.4%

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

      5. associate-/r* 80.7%

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

      6. div-sub 81.7%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

      1. associate-*r/ 81.7%

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

      2. *-commutative 81.7%

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

   7. Applied egg-rr 81.7%

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

   if 1.94999999999999984e29 < y.re

   1. Initial program 42.0%

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

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

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. *-commutative 79.1%

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

      2. *-un-lft-identity 79.1%

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

      3. times-frac 84.7%

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

   5. Applied egg-rr 84.7%

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

      1. clear-num 84.7%

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

      2. frac-times 84.8%

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

      3. *-un-lft-identity 84.8%

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

   7. Applied egg-rr 84.8%

      \[\leadsto \frac{x.im + -1 \cdot \color{blue}{\frac{x.re}{\frac{1}{y.im} \cdot y.re}}}{y.re} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -3.3 \cdot 10^{+64}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq -9 \cdot 10^{-9}:\\ \;\;\;\;\frac{y.re \cdot x.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.re \leq 1.95 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{y.re \cdot x.im}{y.im} - x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{y.re \cdot \frac{1}{y.im}}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{if}\;y.re \leq -3 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.re \leq -1.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq -1.25 \cdot 10^{-10}:\\ \;\;\;\;\frac{y.re \cdot x.im}{y.re \cdot y.re + y.im \cdot y.im}\\ \mathbf{elif}\;y.re \leq 1.16 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{y.re \cdot x.im}{y.im} - x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ (- x.im (/ x.re (/ y.re y.im))) y.re)))
   (if (<= y.re -3e+62)
     t_0
     (if (<= y.re -1.3e+41)
       (/ (- (* x.im (/ y.re y.im)) x.re) y.im)
       (if (<= y.re -1.25e-10)
         (/ (* y.re x.im) (+ (* y.re y.re) (* y.im y.im)))
         (if (<= y.re 1.16e+29)
           (/ (- (/ (* y.re x.im) y.im) x.re) 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_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	double tmp;
	if (y_46_re <= -3e+62) {
		tmp = t_0;
	} else if (y_46_re <= -1.3e+41) {
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	} else if (y_46_re <= -1.25e-10) {
		tmp = (y_46_re * x_46_im) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_re <= 1.16e+29) {
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / 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_46im - (x_46re / (y_46re / y_46im))) / y_46re
    if (y_46re <= (-3d+62)) then
        tmp = t_0
    else if (y_46re <= (-1.3d+41)) then
        tmp = ((x_46im * (y_46re / y_46im)) - x_46re) / y_46im
    else if (y_46re <= (-1.25d-10)) then
        tmp = (y_46re * x_46im) / ((y_46re * y_46re) + (y_46im * y_46im))
    else if (y_46re <= 1.16d+29) then
        tmp = (((y_46re * x_46im) / y_46im) - x_46re) / 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_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	double tmp;
	if (y_46_re <= -3e+62) {
		tmp = t_0;
	} else if (y_46_re <= -1.3e+41) {
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	} else if (y_46_re <= -1.25e-10) {
		tmp = (y_46_re * x_46_im) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	} else if (y_46_re <= 1.16e+29) {
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / 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_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re
	tmp = 0
	if y_46_re <= -3e+62:
		tmp = t_0
	elif y_46_re <= -1.3e+41:
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im
	elif y_46_re <= -1.25e-10:
		tmp = (y_46_re * x_46_im) / ((y_46_re * y_46_re) + (y_46_im * y_46_im))
	elif y_46_re <= 1.16e+29:
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / 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_im - Float64(x_46_re / Float64(y_46_re / y_46_im))) / y_46_re)
	tmp = 0.0
	if (y_46_re <= -3e+62)
		tmp = t_0;
	elseif (y_46_re <= -1.3e+41)
		tmp = Float64(Float64(Float64(x_46_im * Float64(y_46_re / y_46_im)) - x_46_re) / y_46_im);
	elseif (y_46_re <= -1.25e-10)
		tmp = Float64(Float64(y_46_re * x_46_im) / Float64(Float64(y_46_re * y_46_re) + Float64(y_46_im * y_46_im)));
	elseif (y_46_re <= 1.16e+29)
		tmp = Float64(Float64(Float64(Float64(y_46_re * x_46_im) / y_46_im) - x_46_re) / 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_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	tmp = 0.0;
	if (y_46_re <= -3e+62)
		tmp = t_0;
	elseif (y_46_re <= -1.3e+41)
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	elseif (y_46_re <= -1.25e-10)
		tmp = (y_46_re * x_46_im) / ((y_46_re * y_46_re) + (y_46_im * y_46_im));
	elseif (y_46_re <= 1.16e+29)
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / 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$46$im - N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]}, If[LessEqual[y$46$re, -3e+62], t$95$0, If[LessEqual[y$46$re, -1.3e+41], N[(N[(N[(x$46$im * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, -1.25e-10], N[(N[(y$46$re * x$46$im), $MachinePrecision] / N[(N[(y$46$re * y$46$re), $MachinePrecision] + N[(y$46$im * y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.16e+29], N[(N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] / y$46$im), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y.re < -3e62 or 1.16e29 < y.re

   1. Initial program 44.2%

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

   3. Taylor expanded in y.re around inf 84.9%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. associate-/l* 89.1%

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

   5. Simplified 89.1%

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

      1. clear-num 89.1%

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

      2. *-un-lft-identity 89.1%

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

      3. associate-*l/ 89.1%

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

      4. div-inv 89.2%

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

      5. associate-*l/ 89.2%

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

      6. *-un-lft-identity 89.2%

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

   7. Applied egg-rr 89.2%

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

   if -3e62 < y.re < -1.3e41

   1. Initial program 40.4%

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

   3. Taylor expanded in y.re around 0 60.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{x.im \cdot y.re}{{y.im}^{2}}} \]
   4. Step-by-step derivation

      1. +-commutative 60.7%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} + -1 \cdot \frac{x.re}{y.im}} \]

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} - \frac{x.re}{y.im}} \]

      4. unpow2 60.7%

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

      5. associate-/r* 61.3%

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

      6. div-sub 61.3%

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

      7. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   if -1.3e41 < y.re < -1.25000000000000008e-10

   1. Initial program 91.1%

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

   3. Taylor expanded in x.im around inf 83.7%

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

      1. *-commutative 83.7%

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

      2. unpow2 83.7%

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

      3. unpow2 83.7%

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

      4. +-commutative 83.7%

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

   5. Simplified 83.7%

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

   if -1.25000000000000008e-10 < y.re < 1.16e29

   1. Initial program 76.8%

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

   3. Taylor expanded in y.re around 0 77.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{x.im \cdot y.re}{{y.im}^{2}}} \]
   4. Step-by-step derivation

      1. +-commutative 77.4%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} + -1 \cdot \frac{x.re}{y.im}} \]

      2. mul-1-neg 77.4%

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

      3. unsub-neg 77.4%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} - \frac{x.re}{y.im}} \]

      4. unpow2 77.4%

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

      5. associate-/r* 80.7%

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

      6. div-sub 81.7%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

      1. associate-*r/ 81.7%

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

      2. *-commutative 81.7%

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

   7. Applied egg-rr 81.7%

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

Alternative 6: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{if}\;y.re \leq -8.1 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.re \leq -3.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq -5.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x.im}{y.re} - y.im \cdot \frac{x.re}{y.re \cdot y.re}\\ \mathbf{elif}\;y.re \leq 2.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{y.re \cdot x.im}{y.im} - x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ (- x.im (/ x.re (/ y.re y.im))) y.re)))
   (if (<= y.re -8.1e+62)
     t_0
     (if (<= y.re -3.8e+40)
       (/ (- (* x.im (/ y.re y.im)) x.re) y.im)
       (if (<= y.re -5.5e-10)
         (- (/ x.im y.re) (* y.im (/ x.re (* y.re y.re))))
         (if (<= y.re 2.5e+29)
           (/ (- (/ (* y.re x.im) y.im) x.re) 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_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	double tmp;
	if (y_46_re <= -8.1e+62) {
		tmp = t_0;
	} else if (y_46_re <= -3.8e+40) {
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	} else if (y_46_re <= -5.5e-10) {
		tmp = (x_46_im / y_46_re) - (y_46_im * (x_46_re / (y_46_re * y_46_re)));
	} else if (y_46_re <= 2.5e+29) {
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / 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_46im - (x_46re / (y_46re / y_46im))) / y_46re
    if (y_46re <= (-8.1d+62)) then
        tmp = t_0
    else if (y_46re <= (-3.8d+40)) then
        tmp = ((x_46im * (y_46re / y_46im)) - x_46re) / y_46im
    else if (y_46re <= (-5.5d-10)) then
        tmp = (x_46im / y_46re) - (y_46im * (x_46re / (y_46re * y_46re)))
    else if (y_46re <= 2.5d+29) then
        tmp = (((y_46re * x_46im) / y_46im) - x_46re) / 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_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	double tmp;
	if (y_46_re <= -8.1e+62) {
		tmp = t_0;
	} else if (y_46_re <= -3.8e+40) {
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	} else if (y_46_re <= -5.5e-10) {
		tmp = (x_46_im / y_46_re) - (y_46_im * (x_46_re / (y_46_re * y_46_re)));
	} else if (y_46_re <= 2.5e+29) {
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / 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_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re
	tmp = 0
	if y_46_re <= -8.1e+62:
		tmp = t_0
	elif y_46_re <= -3.8e+40:
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im
	elif y_46_re <= -5.5e-10:
		tmp = (x_46_im / y_46_re) - (y_46_im * (x_46_re / (y_46_re * y_46_re)))
	elif y_46_re <= 2.5e+29:
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / 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_im - Float64(x_46_re / Float64(y_46_re / y_46_im))) / y_46_re)
	tmp = 0.0
	if (y_46_re <= -8.1e+62)
		tmp = t_0;
	elseif (y_46_re <= -3.8e+40)
		tmp = Float64(Float64(Float64(x_46_im * Float64(y_46_re / y_46_im)) - x_46_re) / y_46_im);
	elseif (y_46_re <= -5.5e-10)
		tmp = Float64(Float64(x_46_im / y_46_re) - Float64(y_46_im * Float64(x_46_re / Float64(y_46_re * y_46_re))));
	elseif (y_46_re <= 2.5e+29)
		tmp = Float64(Float64(Float64(Float64(y_46_re * x_46_im) / y_46_im) - x_46_re) / 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_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	tmp = 0.0;
	if (y_46_re <= -8.1e+62)
		tmp = t_0;
	elseif (y_46_re <= -3.8e+40)
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	elseif (y_46_re <= -5.5e-10)
		tmp = (x_46_im / y_46_re) - (y_46_im * (x_46_re / (y_46_re * y_46_re)));
	elseif (y_46_re <= 2.5e+29)
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / 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$46$im - N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]}, If[LessEqual[y$46$re, -8.1e+62], t$95$0, If[LessEqual[y$46$re, -3.8e+40], N[(N[(N[(x$46$im * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, -5.5e-10], N[(N[(x$46$im / y$46$re), $MachinePrecision] - N[(y$46$im * N[(x$46$re / N[(y$46$re * y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 2.5e+29], N[(N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] / y$46$im), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y.re < -8.09999999999999998e62 or 2.5e29 < y.re

   1. Initial program 44.2%

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

   3. Taylor expanded in y.re around inf 84.9%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. associate-/l* 89.1%

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

   5. Simplified 89.1%

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

      1. clear-num 89.1%

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

      2. *-un-lft-identity 89.1%

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

      3. associate-*l/ 89.1%

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

      4. div-inv 89.2%

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

      5. associate-*l/ 89.2%

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

      6. *-un-lft-identity 89.2%

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

   7. Applied egg-rr 89.2%

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

   if -8.09999999999999998e62 < y.re < -3.80000000000000004e40

   1. Initial program 40.4%

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

   3. Taylor expanded in y.re around 0 60.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{x.im \cdot y.re}{{y.im}^{2}}} \]
   4. Step-by-step derivation

      1. +-commutative 60.7%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} + -1 \cdot \frac{x.re}{y.im}} \]

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} - \frac{x.re}{y.im}} \]

      4. unpow2 60.7%

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

      5. associate-/r* 61.3%

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

      6. div-sub 61.3%

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

      7. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   if -3.80000000000000004e40 < y.re < -5.4999999999999996e-10

   1. Initial program 91.1%

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

   3. Taylor expanded in y.im around 0 67.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re \cdot y.im}{{y.re}^{2}} + \frac{x.im}{y.re}} \]
   4. Step-by-step derivation

      1. +-commutative 67.8%

         \[\leadsto \color{blue}{\frac{x.im}{y.re} + -1 \cdot \frac{x.re \cdot y.im}{{y.re}^{2}}} \]

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

         \[\leadsto \color{blue}{\frac{x.im}{y.re} - \frac{x.re \cdot y.im}{{y.re}^{2}}} \]

      4. *-commutative 67.8%

         \[\leadsto \frac{x.im}{y.re} - \frac{\color{blue}{y.im \cdot x.re}}{{y.re}^{2}} \]

      5. unpow2 67.8%

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

      6. associate-/l* 75.6%

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

   5. Simplified 75.6%

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

   if -5.4999999999999996e-10 < y.re < 2.5e29

   1. Initial program 76.8%

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

   3. Taylor expanded in y.re around 0 77.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{x.im \cdot y.re}{{y.im}^{2}}} \]
   4. Step-by-step derivation

      1. +-commutative 77.4%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} + -1 \cdot \frac{x.re}{y.im}} \]

      2. mul-1-neg 77.4%

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

      3. unsub-neg 77.4%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} - \frac{x.re}{y.im}} \]

      4. unpow2 77.4%

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

      5. associate-/r* 80.7%

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

      6. div-sub 81.7%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

      1. associate-*r/ 81.7%

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

      2. *-commutative 81.7%

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

   7. Applied egg-rr 81.7%

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

Alternative 7: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{if}\;y.re \leq -2.5 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y.re \leq -5.4 \cdot 10^{+38}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq -2 \cdot 10^{-10}:\\ \;\;\;\;\frac{x.im - \frac{x.re \cdot y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 6.4 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{y.re \cdot x.im}{y.im} - x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (/ (- x.im (/ x.re (/ y.re y.im))) y.re)))
   (if (<= y.re -2.5e+62)
     t_0
     (if (<= y.re -5.4e+38)
       (/ (- (* x.im (/ y.re y.im)) x.re) y.im)
       (if (<= y.re -2e-10)
         (/ (- x.im (/ (* x.re y.im) y.re)) y.re)
         (if (<= y.re 6.4e+32)
           (/ (- (/ (* y.re x.im) y.im) x.re) 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_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	double tmp;
	if (y_46_re <= -2.5e+62) {
		tmp = t_0;
	} else if (y_46_re <= -5.4e+38) {
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	} else if (y_46_re <= -2e-10) {
		tmp = (x_46_im - ((x_46_re * y_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_re <= 6.4e+32) {
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / 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_46im - (x_46re / (y_46re / y_46im))) / y_46re
    if (y_46re <= (-2.5d+62)) then
        tmp = t_0
    else if (y_46re <= (-5.4d+38)) then
        tmp = ((x_46im * (y_46re / y_46im)) - x_46re) / y_46im
    else if (y_46re <= (-2d-10)) then
        tmp = (x_46im - ((x_46re * y_46im) / y_46re)) / y_46re
    else if (y_46re <= 6.4d+32) then
        tmp = (((y_46re * x_46im) / y_46im) - x_46re) / 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_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	double tmp;
	if (y_46_re <= -2.5e+62) {
		tmp = t_0;
	} else if (y_46_re <= -5.4e+38) {
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	} else if (y_46_re <= -2e-10) {
		tmp = (x_46_im - ((x_46_re * y_46_im) / y_46_re)) / y_46_re;
	} else if (y_46_re <= 6.4e+32) {
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / 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_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re
	tmp = 0
	if y_46_re <= -2.5e+62:
		tmp = t_0
	elif y_46_re <= -5.4e+38:
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im
	elif y_46_re <= -2e-10:
		tmp = (x_46_im - ((x_46_re * y_46_im) / y_46_re)) / y_46_re
	elif y_46_re <= 6.4e+32:
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / 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_im - Float64(x_46_re / Float64(y_46_re / y_46_im))) / y_46_re)
	tmp = 0.0
	if (y_46_re <= -2.5e+62)
		tmp = t_0;
	elseif (y_46_re <= -5.4e+38)
		tmp = Float64(Float64(Float64(x_46_im * Float64(y_46_re / y_46_im)) - x_46_re) / y_46_im);
	elseif (y_46_re <= -2e-10)
		tmp = Float64(Float64(x_46_im - Float64(Float64(x_46_re * y_46_im) / y_46_re)) / y_46_re);
	elseif (y_46_re <= 6.4e+32)
		tmp = Float64(Float64(Float64(Float64(y_46_re * x_46_im) / y_46_im) - x_46_re) / 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_im - (x_46_re / (y_46_re / y_46_im))) / y_46_re;
	tmp = 0.0;
	if (y_46_re <= -2.5e+62)
		tmp = t_0;
	elseif (y_46_re <= -5.4e+38)
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	elseif (y_46_re <= -2e-10)
		tmp = (x_46_im - ((x_46_re * y_46_im) / y_46_re)) / y_46_re;
	elseif (y_46_re <= 6.4e+32)
		tmp = (((y_46_re * x_46_im) / y_46_im) - x_46_re) / 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$46$im - N[(x$46$re / N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]}, If[LessEqual[y$46$re, -2.5e+62], t$95$0, If[LessEqual[y$46$re, -5.4e+38], N[(N[(N[(x$46$im * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], If[LessEqual[y$46$re, -2e-10], N[(N[(x$46$im - N[(N[(x$46$re * y$46$im), $MachinePrecision] / y$46$re), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision], If[LessEqual[y$46$re, 6.4e+32], N[(N[(N[(N[(y$46$re * x$46$im), $MachinePrecision] / y$46$im), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y.re < -2.50000000000000014e62 or 6.3999999999999998e32 < y.re

   1. Initial program 44.2%

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

   3. Taylor expanded in y.re around inf 84.9%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. associate-/l* 89.1%

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

   5. Simplified 89.1%

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

      1. clear-num 89.1%

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

      2. *-un-lft-identity 89.1%

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

      3. associate-*l/ 89.1%

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

      4. div-inv 89.2%

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

      5. associate-*l/ 89.2%

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

      6. *-un-lft-identity 89.2%

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

   7. Applied egg-rr 89.2%

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

   if -2.50000000000000014e62 < y.re < -5.39999999999999992e38

   1. Initial program 50.3%

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

   3. Taylor expanded in y.re around 0 67.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{x.im \cdot y.re}{{y.im}^{2}}} \]
   4. Step-by-step derivation

      1. +-commutative 67.3%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} + -1 \cdot \frac{x.re}{y.im}} \]

      2. mul-1-neg 67.3%

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

      3. unsub-neg 67.3%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} - \frac{x.re}{y.im}} \]

      4. unpow2 67.3%

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

      5. associate-/r* 67.7%

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

      6. div-sub 67.7%

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

      7. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   if -5.39999999999999992e38 < y.re < -2.00000000000000007e-10

   1. Initial program 90.3%

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

      1. clear-num 90.3%

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

   4. Applied egg-rr 90.3%

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

   5. Taylor expanded in y.re around inf 73.4%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   6. Step-by-step derivation

      1. mul-1-neg 73.4%

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

      2. associate-*r/ 70.1%

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

      3. sub-neg 70.1%

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

      4. associate-*r/ 73.4%

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

      5. *-commutative 73.4%

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

   7. Simplified 73.4%

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

   if -2.00000000000000007e-10 < y.re < 6.3999999999999998e32

   1. Initial program 76.8%

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

   3. Taylor expanded in y.re around 0 77.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{x.im \cdot y.re}{{y.im}^{2}}} \]
   4. Step-by-step derivation

      1. +-commutative 77.4%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} + -1 \cdot \frac{x.re}{y.im}} \]

      2. mul-1-neg 77.4%

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

      3. unsub-neg 77.4%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} - \frac{x.re}{y.im}} \]

      4. unpow2 77.4%

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

      5. associate-/r* 80.7%

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

      6. div-sub 81.7%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

      1. associate-*r/ 81.7%

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

      2. *-commutative 81.7%

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

   7. Applied egg-rr 81.7%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -2.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \mathbf{elif}\;y.re \leq -5.4 \cdot 10^{+38}:\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \mathbf{elif}\;y.re \leq -2 \cdot 10^{-10}:\\ \;\;\;\;\frac{x.im - \frac{x.re \cdot y.im}{y.re}}{y.re}\\ \mathbf{elif}\;y.re \leq 6.4 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{y.re \cdot x.im}{y.im} - x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - \frac{x.re}{\frac{y.re}{y.im}}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -2.22 \cdot 10^{-32} \lor \neg \left(y.im \leq 8.2 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -2.22e-32) (not (<= y.im 8.2e+46)))
   (/ (- (* x.im (/ y.re y.im)) x.re) y.im)
   (/ (- x.im (* x.re (/ y.im y.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_im <= -2.22e-32) || !(y_46_im <= 8.2e+46)) {
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	} else {
		tmp = (x_46_im - (x_46_re * (y_46_im / y_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_46im <= (-2.22d-32)) .or. (.not. (y_46im <= 8.2d+46))) then
        tmp = ((x_46im * (y_46re / y_46im)) - x_46re) / y_46im
    else
        tmp = (x_46im - (x_46re * (y_46im / y_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_im <= -2.22e-32) || !(y_46_im <= 8.2e+46)) {
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	} else {
		tmp = (x_46_im - (x_46_re * (y_46_im / y_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_im <= -2.22e-32) or not (y_46_im <= 8.2e+46):
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im
	else:
		tmp = (x_46_im - (x_46_re * (y_46_im / y_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_im <= -2.22e-32) || !(y_46_im <= 8.2e+46))
		tmp = Float64(Float64(Float64(x_46_im * Float64(y_46_re / y_46_im)) - x_46_re) / y_46_im);
	else
		tmp = Float64(Float64(x_46_im - Float64(x_46_re * Float64(y_46_im / y_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_im <= -2.22e-32) || ~((y_46_im <= 8.2e+46)))
		tmp = ((x_46_im * (y_46_re / y_46_im)) - x_46_re) / y_46_im;
	else
		tmp = (x_46_im - (x_46_re * (y_46_im / y_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[Or[LessEqual[y$46$im, -2.22e-32], N[Not[LessEqual[y$46$im, 8.2e+46]], $MachinePrecision]], N[(N[(N[(x$46$im * N[(y$46$re / y$46$im), $MachinePrecision]), $MachinePrecision] - x$46$re), $MachinePrecision] / y$46$im), $MachinePrecision], N[(N[(x$46$im - N[(x$46$re * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.im < -2.21999999999999995e-32 or 8.19999999999999999e46 < y.im

   1. Initial program 52.5%

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

   3. Taylor expanded in y.re around 0 73.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x.re}{y.im} + \frac{x.im \cdot y.re}{{y.im}^{2}}} \]
   4. Step-by-step derivation

      1. +-commutative 73.0%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} + -1 \cdot \frac{x.re}{y.im}} \]

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

         \[\leadsto \color{blue}{\frac{x.im \cdot y.re}{{y.im}^{2}} - \frac{x.re}{y.im}} \]

      4. unpow2 73.0%

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

      5. associate-/r* 74.8%

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

      6. div-sub 74.8%

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

      7. associate-/l* 77.9%

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

   5. Simplified 77.9%

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

   if -2.21999999999999995e-32 < y.im < 8.19999999999999999e46

   1. Initial program 70.4%

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

   3. Taylor expanded in y.re around inf 85.5%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. mul-1-neg 85.5%

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

      2. unsub-neg 85.5%

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

      3. associate-/l* 86.8%

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

   5. Simplified 86.8%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -2.22 \cdot 10^{-32} \lor \neg \left(y.im \leq 8.2 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{x.im \cdot \frac{y.re}{y.im} - x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -2.9 \cdot 10^{-28} \lor \neg \left(y.im \leq 5.8 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{-x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -2.9e-28) (not (<= y.im 5.8e+46)))
   (/ (- x.re) y.im)
   (/ (- x.im (* x.re (/ y.im y.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_im <= -2.9e-28) || !(y_46_im <= 5.8e+46)) {
		tmp = -x_46_re / y_46_im;
	} else {
		tmp = (x_46_im - (x_46_re * (y_46_im / y_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_46im <= (-2.9d-28)) .or. (.not. (y_46im <= 5.8d+46))) then
        tmp = -x_46re / y_46im
    else
        tmp = (x_46im - (x_46re * (y_46im / y_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_im <= -2.9e-28) || !(y_46_im <= 5.8e+46)) {
		tmp = -x_46_re / y_46_im;
	} else {
		tmp = (x_46_im - (x_46_re * (y_46_im / y_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_im <= -2.9e-28) or not (y_46_im <= 5.8e+46):
		tmp = -x_46_re / y_46_im
	else:
		tmp = (x_46_im - (x_46_re * (y_46_im / y_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_im <= -2.9e-28) || !(y_46_im <= 5.8e+46))
		tmp = Float64(Float64(-x_46_re) / y_46_im);
	else
		tmp = Float64(Float64(x_46_im - Float64(x_46_re * Float64(y_46_im / y_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_im <= -2.9e-28) || ~((y_46_im <= 5.8e+46)))
		tmp = -x_46_re / y_46_im;
	else
		tmp = (x_46_im - (x_46_re * (y_46_im / y_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[Or[LessEqual[y$46$im, -2.9e-28], N[Not[LessEqual[y$46$im, 5.8e+46]], $MachinePrecision]], N[((-x$46$re) / y$46$im), $MachinePrecision], N[(N[(x$46$im - N[(x$46$re * N[(y$46$im / y$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y$46$re), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.im < -2.90000000000000013e-28 or 5.8000000000000004e46 < y.im

   1. Initial program 52.5%

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

      1. clear-num 52.4%

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

   4. Applied egg-rr 52.4%

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

   5. Taylor expanded in y.re around 0 68.7%

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{y.im}{x.re}}} \]
   6. Step-by-step derivation

      1. mul-1-neg 68.7%

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

      2. neg-sub0 68.7%

         \[\leadsto \frac{1}{\color{blue}{0 - \frac{y.im}{x.re}}} \]

   7. Simplified 68.7%

      \[\leadsto \frac{1}{\color{blue}{0 - \frac{y.im}{x.re}}} \]
   8. Step-by-step derivation

      1. sub0-neg 68.7%

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

      2. distribute-frac-neg2 68.7%

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

      3. clear-num 69.6%

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

   9. Applied egg-rr 69.6%

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

   if -2.90000000000000013e-28 < y.im < 5.8000000000000004e46

   1. Initial program 70.4%

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

   3. Taylor expanded in y.re around inf 85.5%

      \[\leadsto \color{blue}{\frac{x.im + -1 \cdot \frac{x.re \cdot y.im}{y.re}}{y.re}} \]
   4. Step-by-step derivation

      1. mul-1-neg 85.5%

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

      2. unsub-neg 85.5%

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

      3. associate-/l* 86.8%

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

   5. Simplified 86.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -2.9 \cdot 10^{-28} \lor \neg \left(y.im \leq 5.8 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{-x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im - x.re \cdot \frac{y.im}{y.re}}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -1.02 \cdot 10^{-30} \lor \neg \left(y.im \leq 5.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{-x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -1.02e-30) (not (<= y.im 5.2e-15)))
   (/ (- x.re) y.im)
   (/ x.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_im <= -1.02e-30) || !(y_46_im <= 5.2e-15)) {
		tmp = -x_46_re / y_46_im;
	} else {
		tmp = x_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_46im <= (-1.02d-30)) .or. (.not. (y_46im <= 5.2d-15))) then
        tmp = -x_46re / y_46im
    else
        tmp = x_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_im <= -1.02e-30) || !(y_46_im <= 5.2e-15)) {
		tmp = -x_46_re / y_46_im;
	} else {
		tmp = x_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_im <= -1.02e-30) or not (y_46_im <= 5.2e-15):
		tmp = -x_46_re / y_46_im
	else:
		tmp = x_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_im <= -1.02e-30) || !(y_46_im <= 5.2e-15))
		tmp = Float64(Float64(-x_46_re) / y_46_im);
	else
		tmp = Float64(x_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_im <= -1.02e-30) || ~((y_46_im <= 5.2e-15)))
		tmp = -x_46_re / y_46_im;
	else
		tmp = x_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[Or[LessEqual[y$46$im, -1.02e-30], N[Not[LessEqual[y$46$im, 5.2e-15]], $MachinePrecision]], N[((-x$46$re) / y$46$im), $MachinePrecision], N[(x$46$im / y$46$re), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.im < -1.0199999999999999e-30 or 5.20000000000000009e-15 < y.im

   1. Initial program 55.0%

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

      1. clear-num 54.9%

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

   4. Applied egg-rr 54.9%

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

   5. Taylor expanded in y.re around 0 66.3%

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{y.im}{x.re}}} \]
   6. Step-by-step derivation

      1. mul-1-neg 66.3%

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

      2. neg-sub0 66.3%

         \[\leadsto \frac{1}{\color{blue}{0 - \frac{y.im}{x.re}}} \]

   7. Simplified 66.3%

      \[\leadsto \frac{1}{\color{blue}{0 - \frac{y.im}{x.re}}} \]
   8. Step-by-step derivation

      1. sub0-neg 66.3%

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

      2. distribute-frac-neg2 66.3%

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

      3. clear-num 67.1%

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

   9. Applied egg-rr 67.1%

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

   if -1.0199999999999999e-30 < y.im < 5.20000000000000009e-15

   1. Initial program 69.4%

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

   3. Taylor expanded in y.re around inf 74.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -1.02 \cdot 10^{-30} \lor \neg \left(y.im \leq 5.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{-x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y.im \leq -4 \cdot 10^{+151} \lor \neg \left(y.im \leq 1.22 \cdot 10^{+216}\right):\\ \;\;\;\;\frac{x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (if (or (<= y.im -4e+151) (not (<= y.im 1.22e+216)))
   (/ x.re y.im)
   (/ x.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_im <= -4e+151) || !(y_46_im <= 1.22e+216)) {
		tmp = x_46_re / y_46_im;
	} else {
		tmp = x_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_46im <= (-4d+151)) .or. (.not. (y_46im <= 1.22d+216))) then
        tmp = x_46re / y_46im
    else
        tmp = x_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_im <= -4e+151) || !(y_46_im <= 1.22e+216)) {
		tmp = x_46_re / y_46_im;
	} else {
		tmp = x_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_im <= -4e+151) or not (y_46_im <= 1.22e+216):
		tmp = x_46_re / y_46_im
	else:
		tmp = x_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_im <= -4e+151) || !(y_46_im <= 1.22e+216))
		tmp = Float64(x_46_re / y_46_im);
	else
		tmp = Float64(x_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_im <= -4e+151) || ~((y_46_im <= 1.22e+216)))
		tmp = x_46_re / y_46_im;
	else
		tmp = x_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[Or[LessEqual[y$46$im, -4e+151], N[Not[LessEqual[y$46$im, 1.22e+216]], $MachinePrecision]], N[(x$46$re / y$46$im), $MachinePrecision], N[(x$46$im / y$46$re), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y.im < -4.00000000000000007e151 or 1.22e216 < y.im

   1. Initial program 41.9%

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

      1. clear-num 41.9%

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

   4. Applied egg-rr 41.9%

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

   5. Taylor expanded in y.re around 0 82.5%

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{y.im}{x.re}}} \]
   6. Step-by-step derivation

      1. mul-1-neg 82.5%

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

      2. neg-sub0 82.5%

         \[\leadsto \frac{1}{\color{blue}{0 - \frac{y.im}{x.re}}} \]

   7. Simplified 82.5%

      \[\leadsto \frac{1}{\color{blue}{0 - \frac{y.im}{x.re}}} \]
   8. Step-by-step derivation

      1. add-sqr-sqrt 46.6%

         \[\leadsto \frac{1}{\color{blue}{\sqrt{0 - \frac{y.im}{x.re}} \cdot \sqrt{0 - \frac{y.im}{x.re}}}} \]

      2. sqrt-unprod 55.3%

         \[\leadsto \frac{1}{\color{blue}{\sqrt{\left(0 - \frac{y.im}{x.re}\right) \cdot \left(0 - \frac{y.im}{x.re}\right)}}} \]

      3. sub0-neg 55.3%

         \[\leadsto \frac{1}{\sqrt{\color{blue}{\left(-\frac{y.im}{x.re}\right)} \cdot \left(0 - \frac{y.im}{x.re}\right)}} \]

      4. sub0-neg 55.3%

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

      5. sqr-neg 55.3%

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

      6. sqrt-unprod 13.4%

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

      7. add-sqr-sqrt 39.9%

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

      8. clear-num 39.8%

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

   9. Applied egg-rr 39.8%

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

   if -4.00000000000000007e151 < y.im < 1.22e216

   1. Initial program 66.8%

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

   3. Taylor expanded in y.re around inf 54.2%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.im \leq -4 \cdot 10^{+151} \lor \neg \left(y.im \leq 1.22 \cdot 10^{+216}\right):\\ \;\;\;\;\frac{x.re}{y.im}\\ \mathbf{else}:\\ \;\;\;\;\frac{x.im}{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.8% accurate, 5.0× speedup

Math

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

FPCore

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

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_re;
}

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_46re
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_re;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.1%

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

3. Taylor expanded in y.re around inf 46.1%

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

Reproduce

herbie shell --seed 2024107 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, imaginary part"
  :precision binary64
  (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))