powComplex, real part

Percentage Accurate: 40.0% → 69.3%

Time: 29.8s

Alternatives: 13

Speedup: 2.0×

• 36.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)\\ e^{t\_0 \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(t\_0 \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (log (sqrt (+ (* x.re x.re) (* x.im x.im))))))
   (*
    (exp (- (* t_0 y.re) (* (atan2 x.im x.re) y.im)))
    (cos (+ (* t_0 y.im) (* (atan2 x.im x.re) y.re))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	return exp(((t_0 * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im))) * cos(((t_0 * y_46_im) + (atan2(x_46_im, x_46_re) * 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
    real(8) :: t_0
    t_0 = log(sqrt(((x_46re * x_46re) + (x_46im * x_46im))))
    code = exp(((t_0 * y_46re) - (atan2(x_46im, x_46re) * y_46im))) * cos(((t_0 * y_46im) + (atan2(x_46im, x_46re) * 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) {
	double t_0 = Math.log(Math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	return Math.exp(((t_0 * y_46_re) - (Math.atan2(x_46_im, x_46_re) * y_46_im))) * Math.cos(((t_0 * y_46_im) + (Math.atan2(x_46_im, x_46_re) * y_46_re)));
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = math.log(math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))))
	return math.exp(((t_0 * y_46_re) - (math.atan2(x_46_im, x_46_re) * y_46_im))) * math.cos(((t_0 * y_46_im) + (math.atan2(x_46_im, x_46_re) * y_46_re)))

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im))))
	return Float64(exp(Float64(Float64(t_0 * y_46_re) - Float64(atan(x_46_im, x_46_re) * y_46_im))) * cos(Float64(Float64(t_0 * y_46_im) + Float64(atan(x_46_im, x_46_re) * y_46_re))))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	tmp = exp(((t_0 * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im))) * cos(((t_0 * y_46_im) + (atan2(x_46_im, x_46_re) * y_46_re)));
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, N[(N[Exp[N[(N[(t$95$0 * y$46$re), $MachinePrecision] - N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(N[(t$95$0 * y$46$im), $MachinePrecision] + N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$re), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Initial Program: 40.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)\\ e^{t\_0 \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(t\_0 \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (log (sqrt (+ (* x.re x.re) (* x.im x.im))))))
   (*
    (exp (- (* t_0 y.re) (* (atan2 x.im x.re) y.im)))
    (cos (+ (* t_0 y.im) (* (atan2 x.im x.re) y.re))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	return exp(((t_0 * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im))) * cos(((t_0 * y_46_im) + (atan2(x_46_im, x_46_re) * 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
    real(8) :: t_0
    t_0 = log(sqrt(((x_46re * x_46re) + (x_46im * x_46im))))
    code = exp(((t_0 * y_46re) - (atan2(x_46im, x_46re) * y_46im))) * cos(((t_0 * y_46im) + (atan2(x_46im, x_46re) * 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) {
	double t_0 = Math.log(Math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	return Math.exp(((t_0 * y_46_re) - (Math.atan2(x_46_im, x_46_re) * y_46_im))) * Math.cos(((t_0 * y_46_im) + (Math.atan2(x_46_im, x_46_re) * y_46_re)));
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = math.log(math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))))
	return math.exp(((t_0 * y_46_re) - (math.atan2(x_46_im, x_46_re) * y_46_im))) * math.cos(((t_0 * y_46_im) + (math.atan2(x_46_im, x_46_re) * y_46_re)))

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im))))
	return Float64(exp(Float64(Float64(t_0 * y_46_re) - Float64(atan(x_46_im, x_46_re) * y_46_im))) * cos(Float64(Float64(t_0 * y_46_im) + Float64(atan(x_46_im, x_46_re) * y_46_re))))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	tmp = exp(((t_0 * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im))) * cos(((t_0 * y_46_im) + (atan2(x_46_im, x_46_re) * y_46_re)));
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, N[(N[Exp[N[(N[(t$95$0 * y$46$re), $MachinePrecision] - N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(N[(t$95$0 * y$46$im), $MachinePrecision] + N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$re), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Alternative 1: 69.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(y.im \cdot \log \left(\frac{-1}{x.im}\right)\right)\\ t_1 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_2 := \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, t\_1\right)\right)\\ t_3 := t\_2 \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ t_4 := \cos t\_1\\ t_5 := t\_2 \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ t_6 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_7 := e^{y.re \cdot \log x.re - t\_6}\\ t_8 := t\_4 \cdot e^{y.re \cdot \log x.im - t\_6}\\ t_9 := t\_4 \cdot t\_7\\ t_10 := e^{y.re \cdot \log \left(-x.re\right) - t\_6} \cdot t\_4\\ t_11 := e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - t\_6}\\ t_12 := t\_4 \cdot t\_11\\ t_13 := t\_7 \cdot \cos \left(t\_1 + y.im \cdot \log x.re\right)\\ \mathbf{if}\;x.re \leq -1 \cdot 10^{+120}:\\ \;\;\;\;t\_10\\ \mathbf{elif}\;x.re \leq -1.9 \cdot 10^{-34}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;x.re \leq -4.8 \cdot 10^{-52}:\\ \;\;\;\;t\_10\\ \mathbf{elif}\;x.re \leq -4.3 \cdot 10^{-57}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq -1.12 \cdot 10^{-114}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;x.re \leq -1.6 \cdot 10^{-124}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq -1 \cdot 10^{-154}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;x.re \leq -2.65 \cdot 10^{-163}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x.re \leq -3.2 \cdot 10^{-192}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq -6.4 \cdot 10^{-232}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq -7.2 \cdot 10^{-258}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;x.re \leq -4.5 \cdot 10^{-258}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq -9.5 \cdot 10^{-260}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;x.re \leq -1.6 \cdot 10^{-278}:\\ \;\;\;\;t\_10\\ \mathbf{elif}\;x.re \leq 5 \cdot 10^{-310}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;x.re \leq 1.1 \cdot 10^{-305}:\\ \;\;\;\;t\_9\\ \mathbf{elif}\;x.re \leq 8.2 \cdot 10^{-294}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;x.re \leq 1.05 \cdot 10^{-267}:\\ \;\;\;\;t\_13\\ \mathbf{elif}\;x.re \leq 1.15 \cdot 10^{-261}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;x.re \leq 6.2 \cdot 10^{-242}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 4.1 \cdot 10^{-204}:\\ \;\;\;\;t\_9\\ \mathbf{elif}\;x.re \leq 3.5 \cdot 10^{-196}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 9.5 \cdot 10^{-189}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;x.re \leq 4.5 \cdot 10^{-171}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 3.7 \cdot 10^{-147}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;x.re \leq 6.4 \cdot 10^{-69}:\\ \;\;\;\;t\_13\\ \mathbf{elif}\;x.re \leq 5.3 \cdot 10^{-61}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 3.6 \cdot 10^{-23}:\\ \;\;\;\;t\_12\\ \mathbf{elif}\;x.re \leq 4.15 \cdot 10^{-22}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 2.1 \cdot 10^{+42}:\\ \;\;\;\;t\_12\\ \mathbf{elif}\;x.re \leq 8 \cdot 10^{+130}:\\ \;\;\;\;t\_13\\ \mathbf{elif}\;x.re \leq 8.5 \cdot 10^{+132}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 1.1 \cdot 10^{+176}:\\ \;\;\;\;t\_13\\ \mathbf{elif}\;x.re \leq 2.7 \cdot 10^{+177}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 2.6 \cdot 10^{+252}:\\ \;\;\;\;t\_13\\ \mathbf{elif}\;x.re \leq 4 \cdot 10^{+253}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{+284}:\\ \;\;\;\;t\_9\\ \mathbf{elif}\;x.re \leq 1.12 \cdot 10^{+288}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{+291}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x.re \leq 2.9 \cdot 10^{+291}:\\ \;\;\;\;t\_8\\ \mathbf{else}:\\ \;\;\;\;t\_11\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0
         (*
          (/ (pow (hypot x.re x.im) y.re) (pow (exp y.im) (atan2 x.im x.re)))
          (cos (* y.im (log (/ -1.0 x.im))))))
        (t_1 (* y.re (atan2 x.im x.re)))
        (t_2 (cos (fma (log (hypot x.re x.im)) y.im t_1)))
        (t_3 (* t_2 (pow (hypot x.im x.re) y.re)))
        (t_4 (cos t_1))
        (t_5 (* t_2 (exp (* (atan2 x.im x.re) (- y.im)))))
        (t_6 (* (atan2 x.im x.re) y.im))
        (t_7 (exp (- (* y.re (log x.re)) t_6)))
        (t_8 (* t_4 (exp (- (* y.re (log x.im)) t_6))))
        (t_9 (* t_4 t_7))
        (t_10 (* (exp (- (* y.re (log (- x.re))) t_6)) t_4))
        (t_11
         (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) t_6)))
        (t_12 (* t_4 t_11))
        (t_13 (* t_7 (cos (+ t_1 (* y.im (log x.re)))))))
   (if (<= x.re -1e+120)
     t_10
     (if (<= x.re -1.9e-34)
       t_11
       (if (<= x.re -4.8e-52)
         t_10
         (if (<= x.re -4.3e-57)
           t_3
           (if (<= x.re -1.12e-114)
             t_11
             (if (<= x.re -1.6e-124)
               t_5
               (if (<= x.re -1e-154)
                 t_8
                 (if (<= x.re -2.65e-163)
                   t_0
                   (if (<= x.re -3.2e-192)
                     t_5
                     (if (<= x.re -6.4e-232)
                       t_3
                       (if (<= x.re -7.2e-258)
                         t_11
                         (if (<= x.re -4.5e-258)
                           t_5
                           (if (<= x.re -9.5e-260)
                             t_11
                             (if (<= x.re -1.6e-278)
                               t_10
                               (if (<= x.re 5e-310)
                                 t_11
                                 (if (<= x.re 1.1e-305)
                                   t_9
                                   (if (<= x.re 8.2e-294)
                                     t_11
                                     (if (<= x.re 1.05e-267)
                                       t_13
                                       (if (<= x.re 1.15e-261)
                                         t_11
                                         (if (<= x.re 6.2e-242)
                                           t_5
                                           (if (<= x.re 4.1e-204)
                                             t_9
                                             (if (<= x.re 3.5e-196)
                                               t_5
                                               (if (<= x.re 9.5e-189)
                                                 t_11
                                                 (if (<= x.re 4.5e-171)
                                                   t_3
                                                   (if (<= x.re 3.7e-147)
                                                     t_11
                                                     (if (<= x.re 6.4e-69)
                                                       t_13
                                                       (if (<= x.re 5.3e-61)
                                                         t_3
                                                         (if (<= x.re 3.6e-23)
                                                           t_12
                                                           (if (<=
                                                                x.re
                                                                4.15e-22)
                                                             t_5
                                                             (if (<=
                                                                  x.re
                                                                  2.1e+42)
                                                               t_12
                                                               (if (<=
                                                                    x.re
                                                                    8e+130)
                                                                 t_13
                                                                 (if (<=
                                                                      x.re
                                                                      8.5e+132)
                                                                   t_5
                                                                   (if (<=
                                                                        x.re
                                                                        1.1e+176)
                                                                     t_13
                                                                     (if (<=
                                                                          x.re
                                                                          2.7e+177)
                                                                       t_3
                                                                       (if (<=
                                                                            x.re
                                                                            2.6e+252)
                                                                         t_13
                                                                         (if (<=
                                                                              x.re
                                                                              4e+253)
                                                                           t_11
                                                                           (if (<=
                                                                                x.re
                                                                                2.4e+284)
                                                                             t_9
                                                                             (if (<=
                                                                                  x.re
                                                                                  1.12e+288)
                                                                               t_11
                                                                               (if (<=
                                                                                    x.re
                                                                                    2.4e+291)
                                                                                 t_0
                                                                                 (if (<=
                                                                                      x.re
                                                                                      2.9e+291)
                                                                                   t_8
                                                                                   t_11))))))))))))))))))))))))))))))))))))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = (pow(hypot(x_46_re, x_46_im), y_46_re) / pow(exp(y_46_im), atan2(x_46_im, x_46_re))) * cos((y_46_im * log((-1.0 / x_46_im))));
	double t_1 = y_46_re * atan2(x_46_im, x_46_re);
	double t_2 = cos(fma(log(hypot(x_46_re, x_46_im)), y_46_im, t_1));
	double t_3 = t_2 * pow(hypot(x_46_im, x_46_re), y_46_re);
	double t_4 = cos(t_1);
	double t_5 = t_2 * exp((atan2(x_46_im, x_46_re) * -y_46_im));
	double t_6 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_7 = exp(((y_46_re * log(x_46_re)) - t_6));
	double t_8 = t_4 * exp(((y_46_re * log(x_46_im)) - t_6));
	double t_9 = t_4 * t_7;
	double t_10 = exp(((y_46_re * log(-x_46_re)) - t_6)) * t_4;
	double t_11 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_6));
	double t_12 = t_4 * t_11;
	double t_13 = t_7 * cos((t_1 + (y_46_im * log(x_46_re))));
	double tmp;
	if (x_46_re <= -1e+120) {
		tmp = t_10;
	} else if (x_46_re <= -1.9e-34) {
		tmp = t_11;
	} else if (x_46_re <= -4.8e-52) {
		tmp = t_10;
	} else if (x_46_re <= -4.3e-57) {
		tmp = t_3;
	} else if (x_46_re <= -1.12e-114) {
		tmp = t_11;
	} else if (x_46_re <= -1.6e-124) {
		tmp = t_5;
	} else if (x_46_re <= -1e-154) {
		tmp = t_8;
	} else if (x_46_re <= -2.65e-163) {
		tmp = t_0;
	} else if (x_46_re <= -3.2e-192) {
		tmp = t_5;
	} else if (x_46_re <= -6.4e-232) {
		tmp = t_3;
	} else if (x_46_re <= -7.2e-258) {
		tmp = t_11;
	} else if (x_46_re <= -4.5e-258) {
		tmp = t_5;
	} else if (x_46_re <= -9.5e-260) {
		tmp = t_11;
	} else if (x_46_re <= -1.6e-278) {
		tmp = t_10;
	} else if (x_46_re <= 5e-310) {
		tmp = t_11;
	} else if (x_46_re <= 1.1e-305) {
		tmp = t_9;
	} else if (x_46_re <= 8.2e-294) {
		tmp = t_11;
	} else if (x_46_re <= 1.05e-267) {
		tmp = t_13;
	} else if (x_46_re <= 1.15e-261) {
		tmp = t_11;
	} else if (x_46_re <= 6.2e-242) {
		tmp = t_5;
	} else if (x_46_re <= 4.1e-204) {
		tmp = t_9;
	} else if (x_46_re <= 3.5e-196) {
		tmp = t_5;
	} else if (x_46_re <= 9.5e-189) {
		tmp = t_11;
	} else if (x_46_re <= 4.5e-171) {
		tmp = t_3;
	} else if (x_46_re <= 3.7e-147) {
		tmp = t_11;
	} else if (x_46_re <= 6.4e-69) {
		tmp = t_13;
	} else if (x_46_re <= 5.3e-61) {
		tmp = t_3;
	} else if (x_46_re <= 3.6e-23) {
		tmp = t_12;
	} else if (x_46_re <= 4.15e-22) {
		tmp = t_5;
	} else if (x_46_re <= 2.1e+42) {
		tmp = t_12;
	} else if (x_46_re <= 8e+130) {
		tmp = t_13;
	} else if (x_46_re <= 8.5e+132) {
		tmp = t_5;
	} else if (x_46_re <= 1.1e+176) {
		tmp = t_13;
	} else if (x_46_re <= 2.7e+177) {
		tmp = t_3;
	} else if (x_46_re <= 2.6e+252) {
		tmp = t_13;
	} else if (x_46_re <= 4e+253) {
		tmp = t_11;
	} else if (x_46_re <= 2.4e+284) {
		tmp = t_9;
	} else if (x_46_re <= 1.12e+288) {
		tmp = t_11;
	} else if (x_46_re <= 2.4e+291) {
		tmp = t_0;
	} else if (x_46_re <= 2.9e+291) {
		tmp = t_8;
	} else {
		tmp = t_11;
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(Float64((hypot(x_46_re, x_46_im) ^ y_46_re) / (exp(y_46_im) ^ atan(x_46_im, x_46_re))) * cos(Float64(y_46_im * log(Float64(-1.0 / x_46_im)))))
	t_1 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_2 = cos(fma(log(hypot(x_46_re, x_46_im)), y_46_im, t_1))
	t_3 = Float64(t_2 * (hypot(x_46_im, x_46_re) ^ y_46_re))
	t_4 = cos(t_1)
	t_5 = Float64(t_2 * exp(Float64(atan(x_46_im, x_46_re) * Float64(-y_46_im))))
	t_6 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_7 = exp(Float64(Float64(y_46_re * log(x_46_re)) - t_6))
	t_8 = Float64(t_4 * exp(Float64(Float64(y_46_re * log(x_46_im)) - t_6)))
	t_9 = Float64(t_4 * t_7)
	t_10 = Float64(exp(Float64(Float64(y_46_re * log(Float64(-x_46_re))) - t_6)) * t_4)
	t_11 = exp(Float64(Float64(log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im)))) * y_46_re) - t_6))
	t_12 = Float64(t_4 * t_11)
	t_13 = Float64(t_7 * cos(Float64(t_1 + Float64(y_46_im * log(x_46_re)))))
	tmp = 0.0
	if (x_46_re <= -1e+120)
		tmp = t_10;
	elseif (x_46_re <= -1.9e-34)
		tmp = t_11;
	elseif (x_46_re <= -4.8e-52)
		tmp = t_10;
	elseif (x_46_re <= -4.3e-57)
		tmp = t_3;
	elseif (x_46_re <= -1.12e-114)
		tmp = t_11;
	elseif (x_46_re <= -1.6e-124)
		tmp = t_5;
	elseif (x_46_re <= -1e-154)
		tmp = t_8;
	elseif (x_46_re <= -2.65e-163)
		tmp = t_0;
	elseif (x_46_re <= -3.2e-192)
		tmp = t_5;
	elseif (x_46_re <= -6.4e-232)
		tmp = t_3;
	elseif (x_46_re <= -7.2e-258)
		tmp = t_11;
	elseif (x_46_re <= -4.5e-258)
		tmp = t_5;
	elseif (x_46_re <= -9.5e-260)
		tmp = t_11;
	elseif (x_46_re <= -1.6e-278)
		tmp = t_10;
	elseif (x_46_re <= 5e-310)
		tmp = t_11;
	elseif (x_46_re <= 1.1e-305)
		tmp = t_9;
	elseif (x_46_re <= 8.2e-294)
		tmp = t_11;
	elseif (x_46_re <= 1.05e-267)
		tmp = t_13;
	elseif (x_46_re <= 1.15e-261)
		tmp = t_11;
	elseif (x_46_re <= 6.2e-242)
		tmp = t_5;
	elseif (x_46_re <= 4.1e-204)
		tmp = t_9;
	elseif (x_46_re <= 3.5e-196)
		tmp = t_5;
	elseif (x_46_re <= 9.5e-189)
		tmp = t_11;
	elseif (x_46_re <= 4.5e-171)
		tmp = t_3;
	elseif (x_46_re <= 3.7e-147)
		tmp = t_11;
	elseif (x_46_re <= 6.4e-69)
		tmp = t_13;
	elseif (x_46_re <= 5.3e-61)
		tmp = t_3;
	elseif (x_46_re <= 3.6e-23)
		tmp = t_12;
	elseif (x_46_re <= 4.15e-22)
		tmp = t_5;
	elseif (x_46_re <= 2.1e+42)
		tmp = t_12;
	elseif (x_46_re <= 8e+130)
		tmp = t_13;
	elseif (x_46_re <= 8.5e+132)
		tmp = t_5;
	elseif (x_46_re <= 1.1e+176)
		tmp = t_13;
	elseif (x_46_re <= 2.7e+177)
		tmp = t_3;
	elseif (x_46_re <= 2.6e+252)
		tmp = t_13;
	elseif (x_46_re <= 4e+253)
		tmp = t_11;
	elseif (x_46_re <= 2.4e+284)
		tmp = t_9;
	elseif (x_46_re <= 1.12e+288)
		tmp = t_11;
	elseif (x_46_re <= 2.4e+291)
		tmp = t_0;
	elseif (x_46_re <= 2.9e+291)
		tmp = t_8;
	else
		tmp = t_11;
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[(N[Power[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision], y$46$re], $MachinePrecision] / N[Power[N[Exp[y$46$im], $MachinePrecision], N[ArcTan[x$46$im / x$46$re], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y$46$im * N[Log[N[(-1.0 / x$46$im), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Cos[N[(N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision] * y$46$im + t$95$1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[Power[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[Cos[t$95$1], $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 * N[Exp[N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * (-y$46$im)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$7 = N[Exp[N[(N[(y$46$re * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$8 = N[(t$95$4 * N[Exp[N[(N[(y$46$re * N[Log[x$46$im], $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$4 * t$95$7), $MachinePrecision]}, Block[{t$95$10 = N[(N[Exp[N[(N[(y$46$re * N[Log[(-x$46$re)], $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision]], $MachinePrecision] * t$95$4), $MachinePrecision]}, Block[{t$95$11 = N[Exp[N[(N[(N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * y$46$re), $MachinePrecision] - t$95$6), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$12 = N[(t$95$4 * t$95$11), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$7 * N[Cos[N[(t$95$1 + N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x$46$re, -1e+120], t$95$10, If[LessEqual[x$46$re, -1.9e-34], t$95$11, If[LessEqual[x$46$re, -4.8e-52], t$95$10, If[LessEqual[x$46$re, -4.3e-57], t$95$3, If[LessEqual[x$46$re, -1.12e-114], t$95$11, If[LessEqual[x$46$re, -1.6e-124], t$95$5, If[LessEqual[x$46$re, -1e-154], t$95$8, If[LessEqual[x$46$re, -2.65e-163], t$95$0, If[LessEqual[x$46$re, -3.2e-192], t$95$5, If[LessEqual[x$46$re, -6.4e-232], t$95$3, If[LessEqual[x$46$re, -7.2e-258], t$95$11, If[LessEqual[x$46$re, -4.5e-258], t$95$5, If[LessEqual[x$46$re, -9.5e-260], t$95$11, If[LessEqual[x$46$re, -1.6e-278], t$95$10, If[LessEqual[x$46$re, 5e-310], t$95$11, If[LessEqual[x$46$re, 1.1e-305], t$95$9, If[LessEqual[x$46$re, 8.2e-294], t$95$11, If[LessEqual[x$46$re, 1.05e-267], t$95$13, If[LessEqual[x$46$re, 1.15e-261], t$95$11, If[LessEqual[x$46$re, 6.2e-242], t$95$5, If[LessEqual[x$46$re, 4.1e-204], t$95$9, If[LessEqual[x$46$re, 3.5e-196], t$95$5, If[LessEqual[x$46$re, 9.5e-189], t$95$11, If[LessEqual[x$46$re, 4.5e-171], t$95$3, If[LessEqual[x$46$re, 3.7e-147], t$95$11, If[LessEqual[x$46$re, 6.4e-69], t$95$13, If[LessEqual[x$46$re, 5.3e-61], t$95$3, If[LessEqual[x$46$re, 3.6e-23], t$95$12, If[LessEqual[x$46$re, 4.15e-22], t$95$5, If[LessEqual[x$46$re, 2.1e+42], t$95$12, If[LessEqual[x$46$re, 8e+130], t$95$13, If[LessEqual[x$46$re, 8.5e+132], t$95$5, If[LessEqual[x$46$re, 1.1e+176], t$95$13, If[LessEqual[x$46$re, 2.7e+177], t$95$3, If[LessEqual[x$46$re, 2.6e+252], t$95$13, If[LessEqual[x$46$re, 4e+253], t$95$11, If[LessEqual[x$46$re, 2.4e+284], t$95$9, If[LessEqual[x$46$re, 1.12e+288], t$95$11, If[LessEqual[x$46$re, 2.4e+291], t$95$0, If[LessEqual[x$46$re, 2.9e+291], t$95$8, t$95$11]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x.re < -9.9999999999999998e119 or -1.9000000000000001e-34 < x.re < -4.8000000000000003e-52 or -9.5000000000000001e-260 < x.re < -1.60000000000000009e-278

   1. Initial program 16.7%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 49.1%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around -inf 92.0%

      \[\leadsto e^{\log \color{blue}{\left(-1 \cdot x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 92.0%

         \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 92.0%

      \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -9.9999999999999998e119 < x.re < -1.9000000000000001e-34 or -4.30000000000000022e-57 < x.re < -1.11999999999999995e-114 or -6.39999999999999973e-232 < x.re < -7.19999999999999958e-258 or -4.50000000000000008e-258 < x.re < -9.5000000000000001e-260 or -1.60000000000000009e-278 < x.re < 4.999999999999985e-310 or 1.09999999999999998e-305 < x.re < 8.1999999999999998e-294 or 1.0500000000000001e-267 < x.re < 1.15e-261 or 3.50000000000000004e-196 < x.re < 9.499999999999999e-189 or 4.5000000000000004e-171 < x.re < 3.7000000000000002e-147 or 2.60000000000000018e252 < x.re < 3.9999999999999997e253 or 2.4000000000000001e284 < x.re < 1.12e288 or 2.9000000000000001e291 < x.re

   1. Initial program 52.9%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 72.2%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in y.re around 0 85.5%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{1} \]

   if -4.8000000000000003e-52 < x.re < -4.30000000000000022e-57 or -3.2000000000000002e-192 < x.re < -6.39999999999999973e-232 or 9.499999999999999e-189 < x.re < 4.5000000000000004e-171 or 6.39999999999999997e-69 < x.re < 5.3e-61 or 1.10000000000000004e176 < x.re < 2.69999999999999991e177

   1. Initial program 62.5%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Step-by-step derivation

      1. exp-diff 54.2%

         \[\leadsto \color{blue}{\frac{e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      2. exp-to-pow 54.2%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)}^{y.re}}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      3. hypot-define 54.2%

         \[\leadsto \frac{{\color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}}^{y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      4. *-commutative 54.2%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{e^{\color{blue}{y.im \cdot \tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      5. exp-prod 54.2%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{\color{blue}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      6. fma-define 54.2%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right), y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right)} \]

      7. hypot-define 80.1%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}, y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right) \]

      8. *-commutative 80.1%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, \color{blue}{y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}}\right)\right) \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y.im around 0 71.5%

      \[\leadsto \color{blue}{{\left(\sqrt{{x.im}^{2} + {x.re}^{2}}\right)}^{y.re}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]
   6. Step-by-step derivation

      1. unpow2 71.5%

         \[\leadsto {\left(\sqrt{\color{blue}{x.im \cdot x.im} + {x.re}^{2}}\right)}^{y.re} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

      2. unpow2 71.5%

         \[\leadsto {\left(\sqrt{x.im \cdot x.im + \color{blue}{x.re \cdot x.re}}\right)}^{y.re} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

      3. hypot-undefine 88.4%

         \[\leadsto {\color{blue}{\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}}^{y.re} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

   7. Simplified 88.4%

      \[\leadsto \color{blue}{{\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

   if -1.11999999999999995e-114 < x.re < -1.60000000000000002e-124 or -2.65000000000000008e-163 < x.re < -3.2000000000000002e-192 or -7.19999999999999958e-258 < x.re < -4.50000000000000008e-258 or 1.15e-261 < x.re < 6.20000000000000031e-242 or 4.1000000000000001e-204 < x.re < 3.50000000000000004e-196 or 3.5999999999999998e-23 < x.re < 4.14999999999999981e-22 or 8.0000000000000005e130 < x.re < 8.49999999999999969e132

   1. Initial program 33.3%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Step-by-step derivation

      1. exp-diff 27.8%

         \[\leadsto \color{blue}{\frac{e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      2. exp-to-pow 27.8%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)}^{y.re}}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      3. hypot-define 27.8%

         \[\leadsto \frac{{\color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}}^{y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      4. *-commutative 27.8%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{e^{\color{blue}{y.im \cdot \tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      5. exp-prod 27.8%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{\color{blue}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      6. fma-define 27.8%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right), y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right)} \]

      7. hypot-define 66.7%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}, y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right) \]

      8. *-commutative 66.7%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, \color{blue}{y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}}\right)\right) \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y.re around 0 72.5%

      \[\leadsto \color{blue}{\frac{1}{e^{y.im \cdot \tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]
   6. Step-by-step derivation

      1. rec-exp 72.5%

         \[\leadsto \color{blue}{e^{-y.im \cdot \tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

      2. distribute-rgt-neg-in 72.5%

         \[\leadsto e^{\color{blue}{y.im \cdot \left(-\tan^{-1}_* \frac{x.im}{x.re}\right)}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

   7. Simplified 72.5%

      \[\leadsto \color{blue}{e^{y.im \cdot \left(-\tan^{-1}_* \frac{x.im}{x.re}\right)}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

   if -1.60000000000000002e-124 < x.re < -9.9999999999999997e-155 or 2.4e291 < x.re < 2.9000000000000001e291

   1. Initial program 71.4%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 86.2%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around 0 100.0%

      \[\leadsto e^{\color{blue}{y.re \cdot \log x.im} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto e^{\color{blue}{\log x.im \cdot y.re} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 100.0%

      \[\leadsto e^{\color{blue}{\log x.im \cdot y.re} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -9.9999999999999997e-155 < x.re < -2.65000000000000008e-163 or 1.12e288 < x.re < 2.4e291

   1. Initial program 33.3%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Step-by-step derivation

      1. exp-diff 33.3%

         \[\leadsto \color{blue}{\frac{e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      2. exp-to-pow 33.3%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)}^{y.re}}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      3. hypot-define 33.3%

         \[\leadsto \frac{{\color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}}^{y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      4. *-commutative 33.3%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{e^{\color{blue}{y.im \cdot \tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      5. exp-prod 33.3%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{\color{blue}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      6. fma-define 33.3%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right), y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right)} \]

      7. hypot-define 33.9%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}, y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right) \]

      8. *-commutative 33.9%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, \color{blue}{y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}}\right)\right) \]

   3. Simplified 33.9%

      \[\leadsto \color{blue}{\frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x.im around -inf 40.3%

      \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \color{blue}{\left(-1 \cdot \left(y.im \cdot \log \left(\frac{-1}{x.im}\right)\right) + y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]
   6. Step-by-step derivation

      1. +-commutative 40.3%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \color{blue}{\left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + -1 \cdot \left(y.im \cdot \log \left(\frac{-1}{x.im}\right)\right)\right)} \]

      2. mul-1-neg 40.3%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + \color{blue}{\left(-y.im \cdot \log \left(\frac{-1}{x.im}\right)\right)}\right) \]

      3. unsub-neg 40.3%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \color{blue}{\left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} - y.im \cdot \log \left(\frac{-1}{x.im}\right)\right)} \]

   7. Simplified 40.3%

      \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \color{blue}{\left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} - y.im \cdot \log \left(\frac{-1}{x.im}\right)\right)} \]

   8. Taylor expanded in y.re around 0 73.7%

      \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \color{blue}{\cos \left(-y.im \cdot \log \left(\frac{-1}{x.im}\right)\right)} \]
   9. Step-by-step derivation

      1. cos-neg 73.7%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \color{blue}{\cos \left(y.im \cdot \log \left(\frac{-1}{x.im}\right)\right)} \]

   10. Simplified 73.7%

       \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \color{blue}{\cos \left(y.im \cdot \log \left(\frac{-1}{x.im}\right)\right)} \]

   if 4.999999999999985e-310 < x.re < 1.09999999999999998e-305 or 6.20000000000000031e-242 < x.re < 4.1000000000000001e-204 or 3.9999999999999997e253 < x.re < 2.4000000000000001e284

   1. Initial program 38.5%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 62.7%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around inf 100.0%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if 8.1999999999999998e-294 < x.re < 1.0500000000000001e-267 or 3.7000000000000002e-147 < x.re < 6.39999999999999997e-69 or 2.09999999999999995e42 < x.re < 8.0000000000000005e130 or 8.49999999999999969e132 < x.re < 1.10000000000000004e176 or 2.69999999999999991e177 < x.re < 2.60000000000000018e252

   1. Initial program 41.4%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x.re around inf 69.7%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \color{blue}{x.re} \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

   4. Taylor expanded in x.re around inf 95.2%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log x.re \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

   if 5.3e-61 < x.re < 3.5999999999999998e-23 or 4.14999999999999981e-22 < x.re < 2.09999999999999995e42

   1. Initial program 76.5%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 100.0%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq -1 \cdot 10^{+120}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -1.9 \cdot 10^{-34}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -4.8 \cdot 10^{-52}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -4.3 \cdot 10^{-57}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq -1.12 \cdot 10^{-114}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -1.6 \cdot 10^{-124}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;x.re \leq -1 \cdot 10^{-154}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.im - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -2.65 \cdot 10^{-163}:\\ \;\;\;\;\frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(y.im \cdot \log \left(\frac{-1}{x.im}\right)\right)\\ \mathbf{elif}\;x.re \leq -3.2 \cdot 10^{-192}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;x.re \leq -6.4 \cdot 10^{-232}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq -7.2 \cdot 10^{-258}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -4.5 \cdot 10^{-258}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;x.re \leq -9.5 \cdot 10^{-260}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -1.6 \cdot 10^{-278}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq 5 \cdot 10^{-310}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.1 \cdot 10^{-305}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 8.2 \cdot 10^{-294}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.05 \cdot 10^{-267}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 1.15 \cdot 10^{-261}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 6.2 \cdot 10^{-242}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;x.re \leq 4.1 \cdot 10^{-204}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 3.5 \cdot 10^{-196}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;x.re \leq 9.5 \cdot 10^{-189}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 4.5 \cdot 10^{-171}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq 3.7 \cdot 10^{-147}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 6.4 \cdot 10^{-69}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 5.3 \cdot 10^{-61}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq 3.6 \cdot 10^{-23}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 4.15 \cdot 10^{-22}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;x.re \leq 2.1 \cdot 10^{+42}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 8 \cdot 10^{+130}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 8.5 \cdot 10^{+132}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;x.re \leq 1.1 \cdot 10^{+176}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 2.7 \cdot 10^{+177}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq 2.6 \cdot 10^{+252}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 4 \cdot 10^{+253}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{+284}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.12 \cdot 10^{+288}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{+291}:\\ \;\;\;\;\frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(y.im \cdot \log \left(\frac{-1}{x.im}\right)\right)\\ \mathbf{elif}\;x.re \leq 2.9 \cdot 10^{+291}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.im - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right)\\ t_2 := \log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)\\ t_3 := e^{t\_2 \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ t_4 := y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\\ \mathbf{if}\;\cos \left(t\_2 \cdot y.im + t\_0\right) \cdot t\_3 \leq -\infty:\\ \;\;\;\;\left(\cos t\_4 - y.re \cdot \left(\tan^{-1}_* \frac{x.im}{x.re} \cdot \sin t\_4\right)\right) \cdot t\_3\\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{fma}\left(t\_1, y.re, \tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)\right)} \cdot \cos \left(\mathsf{fma}\left(t\_1, y.im, t\_0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1 (log (hypot x.re x.im)))
        (t_2 (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))
        (t_3 (exp (- (* t_2 y.re) (* (atan2 x.im x.re) y.im))))
        (t_4 (* y.im (log (hypot x.im x.re)))))
   (if (<= (* (cos (+ (* t_2 y.im) t_0)) t_3) (- INFINITY))
     (* (- (cos t_4) (* y.re (* (atan2 x.im x.re) (sin t_4)))) t_3)
     (*
      (exp (fma t_1 y.re (* (atan2 x.im x.re) (- y.im))))
      (cos (fma t_1 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 = y_46_re * atan2(x_46_im, x_46_re);
	double t_1 = log(hypot(x_46_re, x_46_im));
	double t_2 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	double t_3 = exp(((t_2 * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im)));
	double t_4 = y_46_im * log(hypot(x_46_im, x_46_re));
	double tmp;
	if ((cos(((t_2 * y_46_im) + t_0)) * t_3) <= -((double) INFINITY)) {
		tmp = (cos(t_4) - (y_46_re * (atan2(x_46_im, x_46_re) * sin(t_4)))) * t_3;
	} else {
		tmp = exp(fma(t_1, y_46_re, (atan2(x_46_im, x_46_re) * -y_46_im))) * cos(fma(t_1, y_46_im, t_0));
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = log(hypot(x_46_re, x_46_im))
	t_2 = log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im))))
	t_3 = exp(Float64(Float64(t_2 * y_46_re) - Float64(atan(x_46_im, x_46_re) * y_46_im)))
	t_4 = Float64(y_46_im * log(hypot(x_46_im, x_46_re)))
	tmp = 0.0
	if (Float64(cos(Float64(Float64(t_2 * y_46_im) + t_0)) * t_3) <= Float64(-Inf))
		tmp = Float64(Float64(cos(t_4) - Float64(y_46_re * Float64(atan(x_46_im, x_46_re) * sin(t_4)))) * t_3);
	else
		tmp = Float64(exp(fma(t_1, y_46_re, Float64(atan(x_46_im, x_46_re) * Float64(-y_46_im)))) * cos(fma(t_1, y_46_im, t_0)));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[Exp[N[(N[(t$95$2 * y$46$re), $MachinePrecision] - N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(y$46$im * N[Log[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[Cos[N[(N[(t$95$2 * y$46$im), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] * t$95$3), $MachinePrecision], (-Infinity)], N[(N[(N[Cos[t$95$4], $MachinePrecision] - N[(y$46$re * N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * N[Sin[t$95$4], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision], N[(N[Exp[N[(t$95$1 * y$46$re + N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * (-y$46$im)), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(t$95$1 * y$46$im + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))) < -inf.0

   1. Initial program 42.3%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around 0 65.4%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\left(\cos \left(y.im \cdot \log \left(\sqrt{{x.im}^{2} + {x.re}^{2}}\right)\right) + -1 \cdot \left(y.re \cdot \left(\sin \left(y.im \cdot \log \left(\sqrt{{x.im}^{2} + {x.re}^{2}}\right)\right) \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 65.4%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \left(\cos \left(y.im \cdot \log \left(\sqrt{\color{blue}{{x.re}^{2} + {x.im}^{2}}}\right)\right) + -1 \cdot \left(y.re \cdot \left(\sin \left(y.im \cdot \log \left(\sqrt{{x.im}^{2} + {x.re}^{2}}\right)\right) \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)\right) \]

      2. unpow2 65.4%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \left(\cos \left(y.im \cdot \log \left(\sqrt{\color{blue}{x.re \cdot x.re} + {x.im}^{2}}\right)\right) + -1 \cdot \left(y.re \cdot \left(\sin \left(y.im \cdot \log \left(\sqrt{{x.im}^{2} + {x.re}^{2}}\right)\right) \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)\right) \]

      3. unpow2 65.4%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \left(\cos \left(y.im \cdot \log \left(\sqrt{x.re \cdot x.re + \color{blue}{x.im \cdot x.im}}\right)\right) + -1 \cdot \left(y.re \cdot \left(\sin \left(y.im \cdot \log \left(\sqrt{{x.im}^{2} + {x.re}^{2}}\right)\right) \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)\right) \]

      4. hypot-undefine 65.4%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \left(\cos \left(y.im \cdot \log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}\right) + -1 \cdot \left(y.re \cdot \left(\sin \left(y.im \cdot \log \left(\sqrt{{x.im}^{2} + {x.re}^{2}}\right)\right) \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)\right) \]

      5. mul-1-neg 65.4%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \left(\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right)\right) + \color{blue}{\left(-y.re \cdot \left(\sin \left(y.im \cdot \log \left(\sqrt{{x.im}^{2} + {x.re}^{2}}\right)\right) \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)}\right) \]

      6. unsub-neg 65.4%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\left(\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right)\right) - y.re \cdot \left(\sin \left(y.im \cdot \log \left(\sqrt{{x.im}^{2} + {x.re}^{2}}\right)\right) \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)} \]

   5. Simplified 65.4%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\left(\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right) - y.re \cdot \left(\tan^{-1}_* \frac{x.im}{x.re} \cdot \sin \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right)\right)\right)} \]

   if -inf.0 < (*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))

   1. Initial program 44.3%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub-inv 44.3%

         \[\leadsto e^{\color{blue}{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re + \left(-\tan^{-1}_* \frac{x.im}{x.re}\right) \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      2. fma-define 44.3%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right), y.re, \left(-\tan^{-1}_* \frac{x.im}{x.re}\right) \cdot y.im\right)}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      3. hypot-define 44.3%

         \[\leadsto e^{\mathsf{fma}\left(\log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}, y.re, \left(-\tan^{-1}_* \frac{x.im}{x.re}\right) \cdot y.im\right)} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      4. distribute-lft-neg-in 44.3%

         \[\leadsto e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \color{blue}{-\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\right)} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      5. distribute-rgt-neg-out 44.3%

         \[\leadsto e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \color{blue}{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\right)} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      6. fma-define 44.3%

         \[\leadsto e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)\right)} \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right), y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right)} \]

      7. hypot-define 86.3%

         \[\leadsto e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)\right)} \cdot \cos \left(\mathsf{fma}\left(\log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}, y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right) \]

      8. *-commutative 86.3%

         \[\leadsto e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)\right)} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, \color{blue}{y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}}\right)\right) \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)\right)} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \leq -\infty:\\ \;\;\;\;\left(\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right) - y.re \cdot \left(\tan^{-1}_* \frac{x.im}{x.re} \cdot \sin \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right)\right)\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)\right)} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)\\ t_1 := e^{t\_0 \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ t_2 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_3 := \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right)\\ \mathbf{if}\;\cos \left(t\_0 \cdot y.im + t\_2\right) \cdot t\_1 \leq \infty:\\ \;\;\;\;\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right) \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{fma}\left(t\_3, y.re, \tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)\right)} \cdot \cos \left(\mathsf{fma}\left(t\_3, y.im, t\_2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))
        (t_1 (exp (- (* t_0 y.re) (* (atan2 x.im x.re) y.im))))
        (t_2 (* y.re (atan2 x.im x.re)))
        (t_3 (log (hypot x.re x.im))))
   (if (<= (* (cos (+ (* t_0 y.im) t_2)) t_1) INFINITY)
     (* (cos (* y.im (log (hypot x.im x.re)))) t_1)
     (*
      (exp (fma t_3 y.re (* (atan2 x.im x.re) (- y.im))))
      (cos (fma t_3 y.im t_2))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	double t_1 = exp(((t_0 * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im)));
	double t_2 = y_46_re * atan2(x_46_im, x_46_re);
	double t_3 = log(hypot(x_46_re, x_46_im));
	double tmp;
	if ((cos(((t_0 * y_46_im) + t_2)) * t_1) <= ((double) INFINITY)) {
		tmp = cos((y_46_im * log(hypot(x_46_im, x_46_re)))) * t_1;
	} else {
		tmp = exp(fma(t_3, y_46_re, (atan2(x_46_im, x_46_re) * -y_46_im))) * cos(fma(t_3, y_46_im, t_2));
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im))))
	t_1 = exp(Float64(Float64(t_0 * y_46_re) - Float64(atan(x_46_im, x_46_re) * y_46_im)))
	t_2 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_3 = log(hypot(x_46_re, x_46_im))
	tmp = 0.0
	if (Float64(cos(Float64(Float64(t_0 * y_46_im) + t_2)) * t_1) <= Inf)
		tmp = Float64(cos(Float64(y_46_im * log(hypot(x_46_im, x_46_re)))) * t_1);
	else
		tmp = Float64(exp(fma(t_3, y_46_re, Float64(atan(x_46_im, x_46_re) * Float64(-y_46_im)))) * cos(fma(t_3, y_46_im, t_2)));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(t$95$0 * y$46$re), $MachinePrecision] - N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[Cos[N[(N[(t$95$0 * y$46$im), $MachinePrecision] + t$95$2), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision], Infinity], N[(N[Cos[N[(y$46$im * N[Log[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision], N[(N[Exp[N[(t$95$3 * y$46$re + N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * (-y$46$im)), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(t$95$3 * y$46$im + t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))) < +inf.0

   1. Initial program 79.6%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around 0 83.8%

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

      1. unpow2 83.8%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.im \cdot \log \left(\sqrt{\color{blue}{x.im \cdot x.im} + {x.re}^{2}}\right)\right) \]

      2. unpow2 83.8%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.im \cdot \log \left(\sqrt{x.im \cdot x.im + \color{blue}{x.re \cdot x.re}}\right)\right) \]

      3. hypot-undefine 83.8%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.im \cdot \log \color{blue}{\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}\right) \]

   5. Simplified 83.8%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right)} \]

   if +inf.0 < (*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))

   1. Initial program 0.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub-inv 0.0%

         \[\leadsto e^{\color{blue}{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re + \left(-\tan^{-1}_* \frac{x.im}{x.re}\right) \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      2. fma-define 0.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right), y.re, \left(-\tan^{-1}_* \frac{x.im}{x.re}\right) \cdot y.im\right)}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      3. hypot-define 0.0%

         \[\leadsto e^{\mathsf{fma}\left(\log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}, y.re, \left(-\tan^{-1}_* \frac{x.im}{x.re}\right) \cdot y.im\right)} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      4. distribute-lft-neg-in 0.0%

         \[\leadsto e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \color{blue}{-\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\right)} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      5. distribute-rgt-neg-out 0.0%

         \[\leadsto e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \color{blue}{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\right)} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      6. fma-define 0.0%

         \[\leadsto e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)\right)} \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right), y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right)} \]

      7. hypot-define 84.6%

         \[\leadsto e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)\right)} \cdot \cos \left(\mathsf{fma}\left(\log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}, y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right) \]

      8. *-commutative 84.6%

         \[\leadsto e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)\right)} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, \color{blue}{y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}}\right)\right) \]

   3. Simplified 84.6%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)\right)} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \leq \infty:\\ \;\;\;\;\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.re, \tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)\right)} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)\\ t_2 := e^{t\_1 \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{if}\;\cos \left(t\_1 \cdot y.im + t\_0\right) \cdot t\_2 \leq \infty:\\ \;\;\;\;\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right) \cdot t\_2\\ \mathbf{else}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, t\_0\right)\right) \cdot \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1 (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))
        (t_2 (exp (- (* t_1 y.re) (* (atan2 x.im x.re) y.im)))))
   (if (<= (* (cos (+ (* t_1 y.im) t_0)) t_2) INFINITY)
     (* (cos (* y.im (log (hypot x.im x.re)))) t_2)
     (*
      (cos (fma (log (hypot x.re x.im)) y.im t_0))
      (/ (pow (hypot x.re x.im) y.re) (pow (exp y.im) (atan2 x.im x.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 * atan2(x_46_im, x_46_re);
	double t_1 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	double t_2 = exp(((t_1 * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im)));
	double tmp;
	if ((cos(((t_1 * y_46_im) + t_0)) * t_2) <= ((double) INFINITY)) {
		tmp = cos((y_46_im * log(hypot(x_46_im, x_46_re)))) * t_2;
	} else {
		tmp = cos(fma(log(hypot(x_46_re, x_46_im)), y_46_im, t_0)) * (pow(hypot(x_46_re, x_46_im), y_46_re) / pow(exp(y_46_im), atan2(x_46_im, x_46_re)));
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im))))
	t_2 = exp(Float64(Float64(t_1 * y_46_re) - Float64(atan(x_46_im, x_46_re) * y_46_im)))
	tmp = 0.0
	if (Float64(cos(Float64(Float64(t_1 * y_46_im) + t_0)) * t_2) <= Inf)
		tmp = Float64(cos(Float64(y_46_im * log(hypot(x_46_im, x_46_re)))) * t_2);
	else
		tmp = Float64(cos(fma(log(hypot(x_46_re, x_46_im)), y_46_im, t_0)) * Float64((hypot(x_46_re, x_46_im) ^ y_46_re) / (exp(y_46_im) ^ atan(x_46_im, x_46_re))));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(N[(t$95$1 * y$46$re), $MachinePrecision] - N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[Cos[N[(N[(t$95$1 * y$46$im), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] * t$95$2), $MachinePrecision], Infinity], N[(N[Cos[N[(y$46$im * N[Log[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$2), $MachinePrecision], N[(N[Cos[N[(N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision] * y$46$im + t$95$0), $MachinePrecision]], $MachinePrecision] * N[(N[Power[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision], y$46$re], $MachinePrecision] / N[Power[N[Exp[y$46$im], $MachinePrecision], N[ArcTan[x$46$im / x$46$re], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))) < +inf.0

   1. Initial program 79.6%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around 0 83.8%

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

      1. unpow2 83.8%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.im \cdot \log \left(\sqrt{\color{blue}{x.im \cdot x.im} + {x.re}^{2}}\right)\right) \]

      2. unpow2 83.8%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.im \cdot \log \left(\sqrt{x.im \cdot x.im + \color{blue}{x.re \cdot x.re}}\right)\right) \]

      3. hypot-undefine 83.8%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.im \cdot \log \color{blue}{\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}\right) \]

   5. Simplified 83.8%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right)} \]

   if +inf.0 < (*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))

   1. Initial program 0.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Step-by-step derivation

      1. exp-diff 0.0%

         \[\leadsto \color{blue}{\frac{e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      2. exp-to-pow 0.0%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)}^{y.re}}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      3. hypot-define 0.0%

         \[\leadsto \frac{{\color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}}^{y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      4. *-commutative 0.0%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{e^{\color{blue}{y.im \cdot \tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      5. exp-prod 0.0%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{\color{blue}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      6. fma-define 0.0%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right), y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right)} \]

      7. hypot-define 78.5%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}, y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right) \]

      8. *-commutative 78.5%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, \color{blue}{y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}}\right)\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \leq \infty:\\ \;\;\;\;\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)\\ t_2 := e^{t\_1 \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{if}\;\cos \left(t\_1 \cdot y.im + t\_0\right) \cdot t\_2 \leq \infty:\\ \;\;\;\;\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right) \cdot t\_2\\ \mathbf{else}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, t\_0\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1 (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))
        (t_2 (exp (- (* t_1 y.re) (* (atan2 x.im x.re) y.im)))))
   (if (<= (* (cos (+ (* t_1 y.im) t_0)) t_2) INFINITY)
     (* (cos (* y.im (log (hypot x.im x.re)))) t_2)
     (*
      (cos (fma (log (hypot x.re x.im)) y.im t_0))
      (pow (hypot x.im x.re) y.re)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * atan2(x_46_im, x_46_re);
	double t_1 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	double t_2 = exp(((t_1 * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im)));
	double tmp;
	if ((cos(((t_1 * y_46_im) + t_0)) * t_2) <= ((double) INFINITY)) {
		tmp = cos((y_46_im * log(hypot(x_46_im, x_46_re)))) * t_2;
	} else {
		tmp = cos(fma(log(hypot(x_46_re, x_46_im)), y_46_im, t_0)) * pow(hypot(x_46_im, x_46_re), y_46_re);
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im))))
	t_2 = exp(Float64(Float64(t_1 * y_46_re) - Float64(atan(x_46_im, x_46_re) * y_46_im)))
	tmp = 0.0
	if (Float64(cos(Float64(Float64(t_1 * y_46_im) + t_0)) * t_2) <= Inf)
		tmp = Float64(cos(Float64(y_46_im * log(hypot(x_46_im, x_46_re)))) * t_2);
	else
		tmp = Float64(cos(fma(log(hypot(x_46_re, x_46_im)), y_46_im, t_0)) * (hypot(x_46_im, x_46_re) ^ y_46_re));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(N[(t$95$1 * y$46$re), $MachinePrecision] - N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[Cos[N[(N[(t$95$1 * y$46$im), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] * t$95$2), $MachinePrecision], Infinity], N[(N[Cos[N[(y$46$im * N[Log[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$2), $MachinePrecision], N[(N[Cos[N[(N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision] * y$46$im + t$95$0), $MachinePrecision]], $MachinePrecision] * N[Power[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))) < +inf.0

   1. Initial program 79.6%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.re around 0 83.8%

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

      1. unpow2 83.8%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.im \cdot \log \left(\sqrt{\color{blue}{x.im \cdot x.im} + {x.re}^{2}}\right)\right) \]

      2. unpow2 83.8%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.im \cdot \log \left(\sqrt{x.im \cdot x.im + \color{blue}{x.re \cdot x.re}}\right)\right) \]

      3. hypot-undefine 83.8%

         \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.im \cdot \log \color{blue}{\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}\right) \]

   5. Simplified 83.8%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right)} \]

   if +inf.0 < (*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (cos.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))

   1. Initial program 0.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Step-by-step derivation

      1. exp-diff 0.0%

         \[\leadsto \color{blue}{\frac{e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      2. exp-to-pow 0.0%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)}^{y.re}}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      3. hypot-define 0.0%

         \[\leadsto \frac{{\color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}}^{y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      4. *-commutative 0.0%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{e^{\color{blue}{y.im \cdot \tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      5. exp-prod 0.0%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{\color{blue}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      6. fma-define 0.0%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right), y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right)} \]

      7. hypot-define 78.5%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}, y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right) \]

      8. *-commutative 78.5%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, \color{blue}{y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}}\right)\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y.im around 0 41.8%

      \[\leadsto \color{blue}{{\left(\sqrt{{x.im}^{2} + {x.re}^{2}}\right)}^{y.re}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]
   6. Step-by-step derivation

      1. unpow2 41.8%

         \[\leadsto {\left(\sqrt{\color{blue}{x.im \cdot x.im} + {x.re}^{2}}\right)}^{y.re} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

      2. unpow2 41.8%

         \[\leadsto {\left(\sqrt{x.im \cdot x.im + \color{blue}{x.re \cdot x.re}}\right)}^{y.re} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

      3. hypot-undefine 67.4%

         \[\leadsto {\color{blue}{\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}}^{y.re} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

   7. Simplified 67.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \leq \infty:\\ \;\;\;\;\cos \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \cos t\_0\\ t_2 := \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, t\_0\right)\right)\\ t_3 := t\_2 \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ t_4 := t\_2 \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ t_5 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_6 := e^{y.re \cdot \log \left(-x.re\right) - t\_5} \cdot t\_1\\ t_7 := e^{y.re \cdot \log x.re - t\_5}\\ t_8 := e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - t\_5}\\ t_9 := t\_1 \cdot t\_8\\ t_10 := t\_7 \cdot \cos \left(t\_0 + y.im \cdot \log x.re\right)\\ t_11 := t\_1 \cdot t\_7\\ \mathbf{if}\;y.re \leq -0.0122:\\ \;\;\;\;t\_9\\ \mathbf{elif}\;y.re \leq -1.6 \cdot 10^{-122}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y.re \leq -2 \cdot 10^{-128}:\\ \;\;\;\;t\_10\\ \mathbf{elif}\;y.re \leq -1.65 \cdot 10^{-143}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;y.re \leq -6.5 \cdot 10^{-150}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y.re \leq -1.8 \cdot 10^{-169}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y.re \leq -7.3 \cdot 10^{-171}:\\ \;\;\;\;t\_10\\ \mathbf{elif}\;y.re \leq -2.3 \cdot 10^{-178}:\\ \;\;\;\;t\_9\\ \mathbf{elif}\;y.re \leq -1.15 \cdot 10^{-179}:\\ \;\;\;\;t\_1 \cdot e^{y.re \cdot \log x.im - t\_5}\\ \mathbf{elif}\;y.re \leq -1.1 \cdot 10^{-179}:\\ \;\;\;\;t\_1 \cdot e^{y.re \cdot \log \left(x.im + 0.5 \cdot \frac{{x.re}^{2}}{x.im}\right) - t\_5}\\ \mathbf{elif}\;y.re \leq -2.7 \cdot 10^{-211}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y.re \leq -2.4 \cdot 10^{-226}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;y.re \leq -2.4 \cdot 10^{-286}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y.re \leq -5 \cdot 10^{-288}:\\ \;\;\;\;t\_10\\ \mathbf{elif}\;y.re \leq -6.2 \cdot 10^{-291}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y.re \leq 6.4 \cdot 10^{-208}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y.re \leq 10^{-164}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y.re \leq 5.4 \cdot 10^{-160}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y.re \leq 9.2 \cdot 10^{-147}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y.re \leq 3.9 \cdot 10^{-121}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;y.re \leq 9.5 \cdot 10^{-20}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y.re \leq 1.5 \cdot 10^{-13}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y.re \leq 9.5 \cdot 10^{-12}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;y.re \leq 1.1 \cdot 10^{-11}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;y.re \leq 1.2 \cdot 10^{+70}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;y.re \leq 1.02 \cdot 10^{+89}:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;y.re \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;y.re \leq 4.6 \cdot 10^{+152}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y.re \leq 5 \cdot 10^{+174}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y.re \leq 5.6 \cdot 10^{+199}:\\ \;\;\;\;t\_9\\ \mathbf{elif}\;y.re \leq 8.8 \cdot 10^{+204}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y.re \leq 8.5 \cdot 10^{+205}:\\ \;\;\;\;t\_10\\ \mathbf{elif}\;y.re \leq 2.8 \cdot 10^{+210}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y.re \leq 2.4 \cdot 10^{+224}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y.re \leq 10^{+266}:\\ \;\;\;\;t\_9\\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1 (cos t_0))
        (t_2 (cos (fma (log (hypot x.re x.im)) y.im t_0)))
        (t_3 (* t_2 (pow (hypot x.im x.re) y.re)))
        (t_4 (* t_2 (exp (* (atan2 x.im x.re) (- y.im)))))
        (t_5 (* (atan2 x.im x.re) y.im))
        (t_6 (* (exp (- (* y.re (log (- x.re))) t_5)) t_1))
        (t_7 (exp (- (* y.re (log x.re)) t_5)))
        (t_8
         (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) t_5)))
        (t_9 (* t_1 t_8))
        (t_10 (* t_7 (cos (+ t_0 (* y.im (log x.re))))))
        (t_11 (* t_1 t_7)))
   (if (<= y.re -0.0122)
     t_9
     (if (<= y.re -1.6e-122)
       t_4
       (if (<= y.re -2e-128)
         t_10
         (if (<= y.re -1.65e-143)
           t_8
           (if (<= y.re -6.5e-150)
             t_3
             (if (<= y.re -1.8e-169)
               t_4
               (if (<= y.re -7.3e-171)
                 t_10
                 (if (<= y.re -2.3e-178)
                   t_9
                   (if (<= y.re -1.15e-179)
                     (* t_1 (exp (- (* y.re (log x.im)) t_5)))
                     (if (<= y.re -1.1e-179)
                       (*
                        t_1
                        (exp
                         (-
                          (*
                           y.re
                           (log (+ x.im (* 0.5 (/ (pow x.re 2.0) x.im)))))
                          t_5)))
                       (if (<= y.re -2.7e-211)
                         t_3
                         (if (<= y.re -2.4e-226)
                           t_8
                           (if (<= y.re -2.4e-286)
                             t_4
                             (if (<= y.re -5e-288)
                               t_10
                               (if (<= y.re -6.2e-291)
                                 t_6
                                 (if (<= y.re 6.4e-208)
                                   t_4
                                   (if (<= y.re 1e-164)
                                     t_6
                                     (if (<= y.re 5.4e-160)
                                       t_3
                                       (if (<= y.re 9.2e-147)
                                         t_4
                                         (if (<= y.re 3.9e-121)
                                           t_8
                                           (if (<= y.re 9.5e-20)
                                             t_4
                                             (if (<= y.re 1.5e-13)
                                               t_3
                                               (if (<= y.re 9.5e-12)
                                                 t_8
                                                 (if (<= y.re 1.1e-11)
                                                   t_11
                                                   (if (<= y.re 1.2e+70)
                                                     t_8
                                                     (if (<= y.re 1.02e+89)
                                                       t_11
                                                       (if (<= y.re 4.5e+152)
                                                         t_8
                                                         (if (<= y.re 4.6e+152)
                                                           t_6
                                                           (if (<= y.re 5e+174)
                                                             t_3
                                                             (if (<=
                                                                  y.re
                                                                  5.6e+199)
                                                               t_9
                                                               (if (<=
                                                                    y.re
                                                                    8.8e+204)
                                                                 t_4
                                                                 (if (<=
                                                                      y.re
                                                                      8.5e+205)
                                                                   t_10
                                                                   (if (<=
                                                                        y.re
                                                                        2.8e+210)
                                                                     t_6
                                                                     (if (<=
                                                                          y.re
                                                                          2.4e+224)
                                                                       t_4
                                                                       (if (<=
                                                                            y.re
                                                                            1e+266)
                                                                         t_9
                                                                         t_8)))))))))))))))))))))))))))))))))))))

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 * atan2(x_46_im, x_46_re);
	double t_1 = cos(t_0);
	double t_2 = cos(fma(log(hypot(x_46_re, x_46_im)), y_46_im, t_0));
	double t_3 = t_2 * pow(hypot(x_46_im, x_46_re), y_46_re);
	double t_4 = t_2 * exp((atan2(x_46_im, x_46_re) * -y_46_im));
	double t_5 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_6 = exp(((y_46_re * log(-x_46_re)) - t_5)) * t_1;
	double t_7 = exp(((y_46_re * log(x_46_re)) - t_5));
	double t_8 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_5));
	double t_9 = t_1 * t_8;
	double t_10 = t_7 * cos((t_0 + (y_46_im * log(x_46_re))));
	double t_11 = t_1 * t_7;
	double tmp;
	if (y_46_re <= -0.0122) {
		tmp = t_9;
	} else if (y_46_re <= -1.6e-122) {
		tmp = t_4;
	} else if (y_46_re <= -2e-128) {
		tmp = t_10;
	} else if (y_46_re <= -1.65e-143) {
		tmp = t_8;
	} else if (y_46_re <= -6.5e-150) {
		tmp = t_3;
	} else if (y_46_re <= -1.8e-169) {
		tmp = t_4;
	} else if (y_46_re <= -7.3e-171) {
		tmp = t_10;
	} else if (y_46_re <= -2.3e-178) {
		tmp = t_9;
	} else if (y_46_re <= -1.15e-179) {
		tmp = t_1 * exp(((y_46_re * log(x_46_im)) - t_5));
	} else if (y_46_re <= -1.1e-179) {
		tmp = t_1 * exp(((y_46_re * log((x_46_im + (0.5 * (pow(x_46_re, 2.0) / x_46_im))))) - t_5));
	} else if (y_46_re <= -2.7e-211) {
		tmp = t_3;
	} else if (y_46_re <= -2.4e-226) {
		tmp = t_8;
	} else if (y_46_re <= -2.4e-286) {
		tmp = t_4;
	} else if (y_46_re <= -5e-288) {
		tmp = t_10;
	} else if (y_46_re <= -6.2e-291) {
		tmp = t_6;
	} else if (y_46_re <= 6.4e-208) {
		tmp = t_4;
	} else if (y_46_re <= 1e-164) {
		tmp = t_6;
	} else if (y_46_re <= 5.4e-160) {
		tmp = t_3;
	} else if (y_46_re <= 9.2e-147) {
		tmp = t_4;
	} else if (y_46_re <= 3.9e-121) {
		tmp = t_8;
	} else if (y_46_re <= 9.5e-20) {
		tmp = t_4;
	} else if (y_46_re <= 1.5e-13) {
		tmp = t_3;
	} else if (y_46_re <= 9.5e-12) {
		tmp = t_8;
	} else if (y_46_re <= 1.1e-11) {
		tmp = t_11;
	} else if (y_46_re <= 1.2e+70) {
		tmp = t_8;
	} else if (y_46_re <= 1.02e+89) {
		tmp = t_11;
	} else if (y_46_re <= 4.5e+152) {
		tmp = t_8;
	} else if (y_46_re <= 4.6e+152) {
		tmp = t_6;
	} else if (y_46_re <= 5e+174) {
		tmp = t_3;
	} else if (y_46_re <= 5.6e+199) {
		tmp = t_9;
	} else if (y_46_re <= 8.8e+204) {
		tmp = t_4;
	} else if (y_46_re <= 8.5e+205) {
		tmp = t_10;
	} else if (y_46_re <= 2.8e+210) {
		tmp = t_6;
	} else if (y_46_re <= 2.4e+224) {
		tmp = t_4;
	} else if (y_46_re <= 1e+266) {
		tmp = t_9;
	} else {
		tmp = t_8;
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = cos(t_0)
	t_2 = cos(fma(log(hypot(x_46_re, x_46_im)), y_46_im, t_0))
	t_3 = Float64(t_2 * (hypot(x_46_im, x_46_re) ^ y_46_re))
	t_4 = Float64(t_2 * exp(Float64(atan(x_46_im, x_46_re) * Float64(-y_46_im))))
	t_5 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_6 = Float64(exp(Float64(Float64(y_46_re * log(Float64(-x_46_re))) - t_5)) * t_1)
	t_7 = exp(Float64(Float64(y_46_re * log(x_46_re)) - t_5))
	t_8 = exp(Float64(Float64(log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im)))) * y_46_re) - t_5))
	t_9 = Float64(t_1 * t_8)
	t_10 = Float64(t_7 * cos(Float64(t_0 + Float64(y_46_im * log(x_46_re)))))
	t_11 = Float64(t_1 * t_7)
	tmp = 0.0
	if (y_46_re <= -0.0122)
		tmp = t_9;
	elseif (y_46_re <= -1.6e-122)
		tmp = t_4;
	elseif (y_46_re <= -2e-128)
		tmp = t_10;
	elseif (y_46_re <= -1.65e-143)
		tmp = t_8;
	elseif (y_46_re <= -6.5e-150)
		tmp = t_3;
	elseif (y_46_re <= -1.8e-169)
		tmp = t_4;
	elseif (y_46_re <= -7.3e-171)
		tmp = t_10;
	elseif (y_46_re <= -2.3e-178)
		tmp = t_9;
	elseif (y_46_re <= -1.15e-179)
		tmp = Float64(t_1 * exp(Float64(Float64(y_46_re * log(x_46_im)) - t_5)));
	elseif (y_46_re <= -1.1e-179)
		tmp = Float64(t_1 * exp(Float64(Float64(y_46_re * log(Float64(x_46_im + Float64(0.5 * Float64((x_46_re ^ 2.0) / x_46_im))))) - t_5)));
	elseif (y_46_re <= -2.7e-211)
		tmp = t_3;
	elseif (y_46_re <= -2.4e-226)
		tmp = t_8;
	elseif (y_46_re <= -2.4e-286)
		tmp = t_4;
	elseif (y_46_re <= -5e-288)
		tmp = t_10;
	elseif (y_46_re <= -6.2e-291)
		tmp = t_6;
	elseif (y_46_re <= 6.4e-208)
		tmp = t_4;
	elseif (y_46_re <= 1e-164)
		tmp = t_6;
	elseif (y_46_re <= 5.4e-160)
		tmp = t_3;
	elseif (y_46_re <= 9.2e-147)
		tmp = t_4;
	elseif (y_46_re <= 3.9e-121)
		tmp = t_8;
	elseif (y_46_re <= 9.5e-20)
		tmp = t_4;
	elseif (y_46_re <= 1.5e-13)
		tmp = t_3;
	elseif (y_46_re <= 9.5e-12)
		tmp = t_8;
	elseif (y_46_re <= 1.1e-11)
		tmp = t_11;
	elseif (y_46_re <= 1.2e+70)
		tmp = t_8;
	elseif (y_46_re <= 1.02e+89)
		tmp = t_11;
	elseif (y_46_re <= 4.5e+152)
		tmp = t_8;
	elseif (y_46_re <= 4.6e+152)
		tmp = t_6;
	elseif (y_46_re <= 5e+174)
		tmp = t_3;
	elseif (y_46_re <= 5.6e+199)
		tmp = t_9;
	elseif (y_46_re <= 8.8e+204)
		tmp = t_4;
	elseif (y_46_re <= 8.5e+205)
		tmp = t_10;
	elseif (y_46_re <= 2.8e+210)
		tmp = t_6;
	elseif (y_46_re <= 2.4e+224)
		tmp = t_4;
	elseif (y_46_re <= 1e+266)
		tmp = t_9;
	else
		tmp = t_8;
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Cos[t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[Cos[N[(N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision] * y$46$im + t$95$0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[Power[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 * N[Exp[N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * (-y$46$im)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$6 = N[(N[Exp[N[(N[(y$46$re * N[Log[(-x$46$re)], $MachinePrecision]), $MachinePrecision] - t$95$5), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision]}, Block[{t$95$7 = N[Exp[N[(N[(y$46$re * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision] - t$95$5), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$8 = N[Exp[N[(N[(N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * y$46$re), $MachinePrecision] - t$95$5), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$9 = N[(t$95$1 * t$95$8), $MachinePrecision]}, Block[{t$95$10 = N[(t$95$7 * N[Cos[N[(t$95$0 + N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$1 * t$95$7), $MachinePrecision]}, If[LessEqual[y$46$re, -0.0122], t$95$9, If[LessEqual[y$46$re, -1.6e-122], t$95$4, If[LessEqual[y$46$re, -2e-128], t$95$10, If[LessEqual[y$46$re, -1.65e-143], t$95$8, If[LessEqual[y$46$re, -6.5e-150], t$95$3, If[LessEqual[y$46$re, -1.8e-169], t$95$4, If[LessEqual[y$46$re, -7.3e-171], t$95$10, If[LessEqual[y$46$re, -2.3e-178], t$95$9, If[LessEqual[y$46$re, -1.15e-179], N[(t$95$1 * N[Exp[N[(N[(y$46$re * N[Log[x$46$im], $MachinePrecision]), $MachinePrecision] - t$95$5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, -1.1e-179], N[(t$95$1 * N[Exp[N[(N[(y$46$re * N[Log[N[(x$46$im + N[(0.5 * N[(N[Power[x$46$re, 2.0], $MachinePrecision] / x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, -2.7e-211], t$95$3, If[LessEqual[y$46$re, -2.4e-226], t$95$8, If[LessEqual[y$46$re, -2.4e-286], t$95$4, If[LessEqual[y$46$re, -5e-288], t$95$10, If[LessEqual[y$46$re, -6.2e-291], t$95$6, If[LessEqual[y$46$re, 6.4e-208], t$95$4, If[LessEqual[y$46$re, 1e-164], t$95$6, If[LessEqual[y$46$re, 5.4e-160], t$95$3, If[LessEqual[y$46$re, 9.2e-147], t$95$4, If[LessEqual[y$46$re, 3.9e-121], t$95$8, If[LessEqual[y$46$re, 9.5e-20], t$95$4, If[LessEqual[y$46$re, 1.5e-13], t$95$3, If[LessEqual[y$46$re, 9.5e-12], t$95$8, If[LessEqual[y$46$re, 1.1e-11], t$95$11, If[LessEqual[y$46$re, 1.2e+70], t$95$8, If[LessEqual[y$46$re, 1.02e+89], t$95$11, If[LessEqual[y$46$re, 4.5e+152], t$95$8, If[LessEqual[y$46$re, 4.6e+152], t$95$6, If[LessEqual[y$46$re, 5e+174], t$95$3, If[LessEqual[y$46$re, 5.6e+199], t$95$9, If[LessEqual[y$46$re, 8.8e+204], t$95$4, If[LessEqual[y$46$re, 8.5e+205], t$95$10, If[LessEqual[y$46$re, 2.8e+210], t$95$6, If[LessEqual[y$46$re, 2.4e+224], t$95$4, If[LessEqual[y$46$re, 1e+266], t$95$9, t$95$8]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y.re < -0.0122000000000000008 or -7.30000000000000015e-171 < y.re < -2.29999999999999994e-178 or 4.9999999999999997e174 < y.re < 5.6000000000000002e199 or 2.40000000000000001e224 < y.re < 1e266

   1. Initial program 50.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 81.1%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   if -0.0122000000000000008 < y.re < -1.6000000000000001e-122 or -6.49999999999999997e-150 < y.re < -1.80000000000000001e-169 or -2.4e-226 < y.re < -2.39999999999999993e-286 or -6.20000000000000023e-291 < y.re < 6.4000000000000003e-208 or 5.40000000000000019e-160 < y.re < 9.19999999999999962e-147 or 3.9e-121 < y.re < 9.5e-20 or 5.6000000000000002e199 < y.re < 8.80000000000000046e204 or 2.8000000000000002e210 < y.re < 2.40000000000000001e224

   1. Initial program 47.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Step-by-step derivation

      1. exp-diff 45.8%

         \[\leadsto \color{blue}{\frac{e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      2. exp-to-pow 45.8%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)}^{y.re}}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      3. hypot-define 45.8%

         \[\leadsto \frac{{\color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}}^{y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      4. *-commutative 45.8%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{e^{\color{blue}{y.im \cdot \tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      5. exp-prod 45.8%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{\color{blue}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      6. fma-define 45.8%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right), y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right)} \]

      7. hypot-define 93.2%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}, y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right) \]

      8. *-commutative 93.2%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, \color{blue}{y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}}\right)\right) \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y.re around 0 94.3%

      \[\leadsto \color{blue}{\frac{1}{e^{y.im \cdot \tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]
   6. Step-by-step derivation

      1. rec-exp 94.3%

         \[\leadsto \color{blue}{e^{-y.im \cdot \tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

      2. distribute-rgt-neg-in 94.3%

         \[\leadsto e^{\color{blue}{y.im \cdot \left(-\tan^{-1}_* \frac{x.im}{x.re}\right)}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

   7. Simplified 94.3%

      \[\leadsto \color{blue}{e^{y.im \cdot \left(-\tan^{-1}_* \frac{x.im}{x.re}\right)}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

   if -1.6000000000000001e-122 < y.re < -2.00000000000000011e-128 or -1.80000000000000001e-169 < y.re < -7.30000000000000015e-171 or -2.39999999999999993e-286 < y.re < -5.00000000000000011e-288 or 8.80000000000000046e204 < y.re < 8.49999999999999997e205

   1. Initial program 40.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x.re around inf 50.9%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \color{blue}{x.re} \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

   4. Taylor expanded in x.re around inf 90.2%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log x.re \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

   if -2.00000000000000011e-128 < y.re < -1.65e-143 or -2.6999999999999999e-211 < y.re < -2.4e-226 or 9.19999999999999962e-147 < y.re < 3.9e-121 or 1.49999999999999992e-13 < y.re < 9.4999999999999995e-12 or 1.1000000000000001e-11 < y.re < 1.19999999999999993e70 or 1.0199999999999999e89 < y.re < 4.5000000000000001e152 or 1e266 < y.re

   1. Initial program 47.9%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 81.3%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in y.re around 0 95.9%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{1} \]

   if -1.65e-143 < y.re < -6.49999999999999997e-150 or -1.10000000000000002e-179 < y.re < -2.6999999999999999e-211 or 9.99999999999999962e-165 < y.re < 5.40000000000000019e-160 or 9.5e-20 < y.re < 1.49999999999999992e-13 or 4.5999999999999997e152 < y.re < 4.9999999999999997e174

   1. Initial program 31.3%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Step-by-step derivation

      1. exp-diff 31.3%

         \[\leadsto \color{blue}{\frac{e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      2. exp-to-pow 31.3%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)}^{y.re}}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      3. hypot-define 31.3%

         \[\leadsto \frac{{\color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}}^{y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      4. *-commutative 31.3%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{e^{\color{blue}{y.im \cdot \tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      5. exp-prod 31.3%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{\color{blue}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      6. fma-define 31.3%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right), y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right)} \]

      7. hypot-define 75.0%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}, y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right) \]

      8. *-commutative 75.0%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, \color{blue}{y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}}\right)\right) \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{\frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y.im around 0 57.2%

      \[\leadsto \color{blue}{{\left(\sqrt{{x.im}^{2} + {x.re}^{2}}\right)}^{y.re}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]
   6. Step-by-step derivation

      1. unpow2 57.2%

         \[\leadsto {\left(\sqrt{\color{blue}{x.im \cdot x.im} + {x.re}^{2}}\right)}^{y.re} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

      2. unpow2 57.2%

         \[\leadsto {\left(\sqrt{x.im \cdot x.im + \color{blue}{x.re \cdot x.re}}\right)}^{y.re} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

      3. hypot-undefine 81.4%

         \[\leadsto {\color{blue}{\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}}^{y.re} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

   7. Simplified 81.4%

      \[\leadsto \color{blue}{{\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

   if -2.29999999999999994e-178 < y.re < -1.14999999999999994e-179

   1. Initial program 0.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 3.1%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around 0 100.0%

      \[\leadsto e^{\color{blue}{y.re \cdot \log x.im} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto e^{\color{blue}{\log x.im \cdot y.re} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 100.0%

      \[\leadsto e^{\color{blue}{\log x.im \cdot y.re} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -1.14999999999999994e-179 < y.re < -1.10000000000000002e-179

   1. Initial program 0.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 3.1%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around 0 3.1%

      \[\leadsto e^{\log \color{blue}{\left(x.im + 0.5 \cdot \frac{{x.re}^{2}}{x.im}\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -5.00000000000000011e-288 < y.re < -6.20000000000000023e-291 or 6.4000000000000003e-208 < y.re < 9.99999999999999962e-165 or 4.5000000000000001e152 < y.re < 4.5999999999999997e152 or 8.49999999999999997e205 < y.re < 2.8000000000000002e210

   1. Initial program 0.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 38.5%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around -inf 75.4%

      \[\leadsto e^{\log \color{blue}{\left(-1 \cdot x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 75.4%

         \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 75.4%

      \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if 9.4999999999999995e-12 < y.re < 1.1000000000000001e-11 or 1.19999999999999993e70 < y.re < 1.0199999999999999e89

   1. Initial program 0.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 51.2%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around inf 100.0%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
3. Recombined 9 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y.re \leq -0.0122:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq -1.6 \cdot 10^{-122}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;y.re \leq -2 \cdot 10^{-128}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;y.re \leq -1.65 \cdot 10^{-143}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq -6.5 \cdot 10^{-150}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;y.re \leq -1.8 \cdot 10^{-169}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;y.re \leq -7.3 \cdot 10^{-171}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;y.re \leq -2.3 \cdot 10^{-178}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq -1.15 \cdot 10^{-179}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.im - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq -1.1 \cdot 10^{-179}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log \left(x.im + 0.5 \cdot \frac{{x.re}^{2}}{x.im}\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq -2.7 \cdot 10^{-211}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;y.re \leq -2.4 \cdot 10^{-226}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq -2.4 \cdot 10^{-286}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;y.re \leq -5 \cdot 10^{-288}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;y.re \leq -6.2 \cdot 10^{-291}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;y.re \leq 6.4 \cdot 10^{-208}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;y.re \leq 10^{-164}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;y.re \leq 5.4 \cdot 10^{-160}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;y.re \leq 9.2 \cdot 10^{-147}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;y.re \leq 3.9 \cdot 10^{-121}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq 9.5 \cdot 10^{-20}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;y.re \leq 1.5 \cdot 10^{-13}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;y.re \leq 9.5 \cdot 10^{-12}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq 1.1 \cdot 10^{-11}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq 1.2 \cdot 10^{+70}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq 1.02 \cdot 10^{+89}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq 4.6 \cdot 10^{+152}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;y.re \leq 5 \cdot 10^{+174}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;y.re \leq 5.6 \cdot 10^{+199}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;y.re \leq 8.8 \cdot 10^{+204}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;y.re \leq 8.5 \cdot 10^{+205}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;y.re \leq 2.8 \cdot 10^{+210}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;y.re \leq 2.4 \cdot 10^{+224}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot \left(-y.im\right)}\\ \mathbf{elif}\;y.re \leq 10^{+266}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \cos t\_0\\ t_2 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_3 := e^{y.re \cdot \log x.re - t\_2}\\ t_4 := t\_3 \cdot \cos \left(t\_0 + y.im \cdot \log x.re\right)\\ t_5 := \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, t\_0\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ t_6 := t\_1 \cdot t\_3\\ t_7 := e^{y.re \cdot \log \left(-x.re\right) - t\_2} \cdot t\_1\\ t_8 := e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - t\_2}\\ \mathbf{if}\;x.re \leq -7 \cdot 10^{+119}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -2 \cdot 10^{-46}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;x.re \leq -7 \cdot 10^{-53}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -4.3 \cdot 10^{-57}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq -2 \cdot 10^{-115}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;x.re \leq -1.95 \cdot 10^{-115}:\\ \;\;\;\;t\_1 \cdot e^{y.re \cdot \log \left(x.im + 0.5 \cdot \frac{{x.re}^{2}}{x.im}\right) - t\_2}\\ \mathbf{elif}\;x.re \leq -1.78 \cdot 10^{-124}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq -7.5 \cdot 10^{-149}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;x.re \leq -4.3 \cdot 10^{-160}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq -1.15 \cdot 10^{-192}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;x.re \leq -9.8 \cdot 10^{-234}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq -7.6 \cdot 10^{-260}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;x.re \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 9 \cdot 10^{-306}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq 2.35 \cdot 10^{-297}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;x.re \leq 9 \cdot 10^{-267}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 2.6 \cdot 10^{-242}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 3.05 \cdot 10^{-192}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 9 \cdot 10^{-189}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;x.re \leq 5.5 \cdot 10^{-171}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 1.55 \cdot 10^{-148}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;x.re \leq 5.3 \cdot 10^{-73}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 1.36 \cdot 10^{-61}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;t\_1 \cdot t\_8\\ \mathbf{elif}\;x.re \leq 6.8 \cdot 10^{+132}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 7.5 \cdot 10^{+132}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 9.2 \cdot 10^{+175}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 2.7 \cdot 10^{+177}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 2.6 \cdot 10^{+252}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 4 \cdot 10^{+253}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{+284}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq 2.5 \cdot 10^{+284} \lor \neg \left(x.re \leq 3.8 \cdot 10^{+293}\right):\\ \;\;\;\;t\_8\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1 (cos t_0))
        (t_2 (* (atan2 x.im x.re) y.im))
        (t_3 (exp (- (* y.re (log x.re)) t_2)))
        (t_4 (* t_3 (cos (+ t_0 (* y.im (log x.re))))))
        (t_5
         (*
          (cos (fma (log (hypot x.re x.im)) y.im t_0))
          (pow (hypot x.im x.re) y.re)))
        (t_6 (* t_1 t_3))
        (t_7 (* (exp (- (* y.re (log (- x.re))) t_2)) t_1))
        (t_8
         (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) t_2))))
   (if (<= x.re -7e+119)
     t_7
     (if (<= x.re -2e-46)
       t_8
       (if (<= x.re -7e-53)
         t_7
         (if (<= x.re -4.3e-57)
           t_5
           (if (<= x.re -2e-115)
             t_8
             (if (<= x.re -1.95e-115)
               (*
                t_1
                (exp
                 (-
                  (* y.re (log (+ x.im (* 0.5 (/ (pow x.re 2.0) x.im)))))
                  t_2)))
               (if (<= x.re -1.78e-124)
                 t_5
                 (if (<= x.re -7.5e-149)
                   t_8
                   (if (<= x.re -4.3e-160)
                     t_5
                     (if (<= x.re -1.15e-192)
                       t_8
                       (if (<= x.re -9.8e-234)
                         t_5
                         (if (<= x.re -7.6e-260)
                           t_8
                           (if (<= x.re -5e-310)
                             t_7
                             (if (<= x.re 9e-306)
                               t_6
                               (if (<= x.re 2.35e-297)
                                 t_8
                                 (if (<= x.re 9e-267)
                                   t_4
                                   (if (<= x.re 2.6e-242)
                                     t_5
                                     (if (<= x.re 3.05e-192)
                                       t_4
                                       (if (<= x.re 9e-189)
                                         t_8
                                         (if (<= x.re 5.5e-171)
                                           t_5
                                           (if (<= x.re 1.55e-148)
                                             t_8
                                             (if (<= x.re 5.3e-73)
                                               t_4
                                               (if (<= x.re 1.36e-61)
                                                 t_5
                                                 (if (<= x.re 4.2e+42)
                                                   (* t_1 t_8)
                                                   (if (<= x.re 6.8e+132)
                                                     t_4
                                                     (if (<= x.re 7.5e+132)
                                                       t_5
                                                       (if (<= x.re 9.2e+175)
                                                         t_4
                                                         (if (<= x.re 2.7e+177)
                                                           t_5
                                                           (if (<=
                                                                x.re
                                                                2.6e+252)
                                                             t_4
                                                             (if (<=
                                                                  x.re
                                                                  4e+253)
                                                               t_8
                                                               (if (<=
                                                                    x.re
                                                                    2.4e+284)
                                                                 t_6
                                                                 (if (or (<=
                                                                          x.re
                                                                          2.5e+284)
                                                                         (not
                                                                          (<=
                                                                           x.re
                                                                           3.8e+293)))
                                                                   t_8
                                                                   t_4))))))))))))))))))))))))))))))))))

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 * atan2(x_46_im, x_46_re);
	double t_1 = cos(t_0);
	double t_2 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_3 = exp(((y_46_re * log(x_46_re)) - t_2));
	double t_4 = t_3 * cos((t_0 + (y_46_im * log(x_46_re))));
	double t_5 = cos(fma(log(hypot(x_46_re, x_46_im)), y_46_im, t_0)) * pow(hypot(x_46_im, x_46_re), y_46_re);
	double t_6 = t_1 * t_3;
	double t_7 = exp(((y_46_re * log(-x_46_re)) - t_2)) * t_1;
	double t_8 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_2));
	double tmp;
	if (x_46_re <= -7e+119) {
		tmp = t_7;
	} else if (x_46_re <= -2e-46) {
		tmp = t_8;
	} else if (x_46_re <= -7e-53) {
		tmp = t_7;
	} else if (x_46_re <= -4.3e-57) {
		tmp = t_5;
	} else if (x_46_re <= -2e-115) {
		tmp = t_8;
	} else if (x_46_re <= -1.95e-115) {
		tmp = t_1 * exp(((y_46_re * log((x_46_im + (0.5 * (pow(x_46_re, 2.0) / x_46_im))))) - t_2));
	} else if (x_46_re <= -1.78e-124) {
		tmp = t_5;
	} else if (x_46_re <= -7.5e-149) {
		tmp = t_8;
	} else if (x_46_re <= -4.3e-160) {
		tmp = t_5;
	} else if (x_46_re <= -1.15e-192) {
		tmp = t_8;
	} else if (x_46_re <= -9.8e-234) {
		tmp = t_5;
	} else if (x_46_re <= -7.6e-260) {
		tmp = t_8;
	} else if (x_46_re <= -5e-310) {
		tmp = t_7;
	} else if (x_46_re <= 9e-306) {
		tmp = t_6;
	} else if (x_46_re <= 2.35e-297) {
		tmp = t_8;
	} else if (x_46_re <= 9e-267) {
		tmp = t_4;
	} else if (x_46_re <= 2.6e-242) {
		tmp = t_5;
	} else if (x_46_re <= 3.05e-192) {
		tmp = t_4;
	} else if (x_46_re <= 9e-189) {
		tmp = t_8;
	} else if (x_46_re <= 5.5e-171) {
		tmp = t_5;
	} else if (x_46_re <= 1.55e-148) {
		tmp = t_8;
	} else if (x_46_re <= 5.3e-73) {
		tmp = t_4;
	} else if (x_46_re <= 1.36e-61) {
		tmp = t_5;
	} else if (x_46_re <= 4.2e+42) {
		tmp = t_1 * t_8;
	} else if (x_46_re <= 6.8e+132) {
		tmp = t_4;
	} else if (x_46_re <= 7.5e+132) {
		tmp = t_5;
	} else if (x_46_re <= 9.2e+175) {
		tmp = t_4;
	} else if (x_46_re <= 2.7e+177) {
		tmp = t_5;
	} else if (x_46_re <= 2.6e+252) {
		tmp = t_4;
	} else if (x_46_re <= 4e+253) {
		tmp = t_8;
	} else if (x_46_re <= 2.4e+284) {
		tmp = t_6;
	} else if ((x_46_re <= 2.5e+284) || !(x_46_re <= 3.8e+293)) {
		tmp = t_8;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = cos(t_0)
	t_2 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_3 = exp(Float64(Float64(y_46_re * log(x_46_re)) - t_2))
	t_4 = Float64(t_3 * cos(Float64(t_0 + Float64(y_46_im * log(x_46_re)))))
	t_5 = Float64(cos(fma(log(hypot(x_46_re, x_46_im)), y_46_im, t_0)) * (hypot(x_46_im, x_46_re) ^ y_46_re))
	t_6 = Float64(t_1 * t_3)
	t_7 = Float64(exp(Float64(Float64(y_46_re * log(Float64(-x_46_re))) - t_2)) * t_1)
	t_8 = exp(Float64(Float64(log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im)))) * y_46_re) - t_2))
	tmp = 0.0
	if (x_46_re <= -7e+119)
		tmp = t_7;
	elseif (x_46_re <= -2e-46)
		tmp = t_8;
	elseif (x_46_re <= -7e-53)
		tmp = t_7;
	elseif (x_46_re <= -4.3e-57)
		tmp = t_5;
	elseif (x_46_re <= -2e-115)
		tmp = t_8;
	elseif (x_46_re <= -1.95e-115)
		tmp = Float64(t_1 * exp(Float64(Float64(y_46_re * log(Float64(x_46_im + Float64(0.5 * Float64((x_46_re ^ 2.0) / x_46_im))))) - t_2)));
	elseif (x_46_re <= -1.78e-124)
		tmp = t_5;
	elseif (x_46_re <= -7.5e-149)
		tmp = t_8;
	elseif (x_46_re <= -4.3e-160)
		tmp = t_5;
	elseif (x_46_re <= -1.15e-192)
		tmp = t_8;
	elseif (x_46_re <= -9.8e-234)
		tmp = t_5;
	elseif (x_46_re <= -7.6e-260)
		tmp = t_8;
	elseif (x_46_re <= -5e-310)
		tmp = t_7;
	elseif (x_46_re <= 9e-306)
		tmp = t_6;
	elseif (x_46_re <= 2.35e-297)
		tmp = t_8;
	elseif (x_46_re <= 9e-267)
		tmp = t_4;
	elseif (x_46_re <= 2.6e-242)
		tmp = t_5;
	elseif (x_46_re <= 3.05e-192)
		tmp = t_4;
	elseif (x_46_re <= 9e-189)
		tmp = t_8;
	elseif (x_46_re <= 5.5e-171)
		tmp = t_5;
	elseif (x_46_re <= 1.55e-148)
		tmp = t_8;
	elseif (x_46_re <= 5.3e-73)
		tmp = t_4;
	elseif (x_46_re <= 1.36e-61)
		tmp = t_5;
	elseif (x_46_re <= 4.2e+42)
		tmp = Float64(t_1 * t_8);
	elseif (x_46_re <= 6.8e+132)
		tmp = t_4;
	elseif (x_46_re <= 7.5e+132)
		tmp = t_5;
	elseif (x_46_re <= 9.2e+175)
		tmp = t_4;
	elseif (x_46_re <= 2.7e+177)
		tmp = t_5;
	elseif (x_46_re <= 2.6e+252)
		tmp = t_4;
	elseif (x_46_re <= 4e+253)
		tmp = t_8;
	elseif (x_46_re <= 2.4e+284)
		tmp = t_6;
	elseif ((x_46_re <= 2.5e+284) || !(x_46_re <= 3.8e+293))
		tmp = t_8;
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Cos[t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$3 = N[Exp[N[(N[(y$46$re * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * N[Cos[N[(t$95$0 + N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[Cos[N[(N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision] * y$46$im + t$95$0), $MachinePrecision]], $MachinePrecision] * N[Power[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$1 * t$95$3), $MachinePrecision]}, Block[{t$95$7 = N[(N[Exp[N[(N[(y$46$re * N[Log[(-x$46$re)], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision]}, Block[{t$95$8 = N[Exp[N[(N[(N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * y$46$re), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x$46$re, -7e+119], t$95$7, If[LessEqual[x$46$re, -2e-46], t$95$8, If[LessEqual[x$46$re, -7e-53], t$95$7, If[LessEqual[x$46$re, -4.3e-57], t$95$5, If[LessEqual[x$46$re, -2e-115], t$95$8, If[LessEqual[x$46$re, -1.95e-115], N[(t$95$1 * N[Exp[N[(N[(y$46$re * N[Log[N[(x$46$im + N[(0.5 * N[(N[Power[x$46$re, 2.0], $MachinePrecision] / x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x$46$re, -1.78e-124], t$95$5, If[LessEqual[x$46$re, -7.5e-149], t$95$8, If[LessEqual[x$46$re, -4.3e-160], t$95$5, If[LessEqual[x$46$re, -1.15e-192], t$95$8, If[LessEqual[x$46$re, -9.8e-234], t$95$5, If[LessEqual[x$46$re, -7.6e-260], t$95$8, If[LessEqual[x$46$re, -5e-310], t$95$7, If[LessEqual[x$46$re, 9e-306], t$95$6, If[LessEqual[x$46$re, 2.35e-297], t$95$8, If[LessEqual[x$46$re, 9e-267], t$95$4, If[LessEqual[x$46$re, 2.6e-242], t$95$5, If[LessEqual[x$46$re, 3.05e-192], t$95$4, If[LessEqual[x$46$re, 9e-189], t$95$8, If[LessEqual[x$46$re, 5.5e-171], t$95$5, If[LessEqual[x$46$re, 1.55e-148], t$95$8, If[LessEqual[x$46$re, 5.3e-73], t$95$4, If[LessEqual[x$46$re, 1.36e-61], t$95$5, If[LessEqual[x$46$re, 4.2e+42], N[(t$95$1 * t$95$8), $MachinePrecision], If[LessEqual[x$46$re, 6.8e+132], t$95$4, If[LessEqual[x$46$re, 7.5e+132], t$95$5, If[LessEqual[x$46$re, 9.2e+175], t$95$4, If[LessEqual[x$46$re, 2.7e+177], t$95$5, If[LessEqual[x$46$re, 2.6e+252], t$95$4, If[LessEqual[x$46$re, 4e+253], t$95$8, If[LessEqual[x$46$re, 2.4e+284], t$95$6, If[Or[LessEqual[x$46$re, 2.5e+284], N[Not[LessEqual[x$46$re, 3.8e+293]], $MachinePrecision]], t$95$8, t$95$4]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x.re < -7.0000000000000001e119 or -2.00000000000000005e-46 < x.re < -6.99999999999999987e-53 or -7.6000000000000006e-260 < x.re < -4.999999999999985e-310

   1. Initial program 22.6%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 52.0%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around -inf 90.9%

      \[\leadsto e^{\log \color{blue}{\left(-1 \cdot x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 90.9%

         \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 90.9%

      \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -7.0000000000000001e119 < x.re < -2.00000000000000005e-46 or -4.30000000000000022e-57 < x.re < -2.0000000000000001e-115 or -1.78e-124 < x.re < -7.49999999999999995e-149 or -4.30000000000000014e-160 < x.re < -1.15000000000000009e-192 or -9.80000000000000015e-234 < x.re < -7.6000000000000006e-260 or 9.00000000000000009e-306 < x.re < 2.34999999999999993e-297 or 3.05e-192 < x.re < 8.9999999999999992e-189 or 5.50000000000000037e-171 < x.re < 1.5500000000000001e-148 or 2.60000000000000018e252 < x.re < 3.9999999999999997e253 or 2.4000000000000001e284 < x.re < 2.5e284 or 3.80000000000000014e293 < x.re

   1. Initial program 48.6%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 70.2%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in y.re around 0 84.4%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{1} \]

   if -6.99999999999999987e-53 < x.re < -4.30000000000000022e-57 or -1.9499999999999999e-115 < x.re < -1.78e-124 or -7.49999999999999995e-149 < x.re < -4.30000000000000014e-160 or -1.15000000000000009e-192 < x.re < -9.80000000000000015e-234 or 8.9999999999999999e-267 < x.re < 2.60000000000000017e-242 or 8.9999999999999992e-189 < x.re < 5.50000000000000037e-171 or 5.29999999999999972e-73 < x.re < 1.35999999999999995e-61 or 6.80000000000000051e132 < x.re < 7.50000000000000017e132 or 9.1999999999999998e175 < x.re < 2.69999999999999991e177

   1. Initial program 63.2%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Step-by-step derivation

      1. exp-diff 55.3%

         \[\leadsto \color{blue}{\frac{e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      2. exp-to-pow 55.3%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)}^{y.re}}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      3. hypot-define 55.3%

         \[\leadsto \frac{{\color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}}^{y.re}}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      4. *-commutative 55.3%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{e^{\color{blue}{y.im \cdot \tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      5. exp-prod 55.3%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{\color{blue}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}}} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

      6. fma-define 55.3%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right), y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right)} \]

      7. hypot-define 84.8%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \color{blue}{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}, y.im, \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\right) \]

      8. *-commutative 84.8%

         \[\leadsto \frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, \color{blue}{y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}}\right)\right) \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{\frac{{\left(\mathsf{hypot}\left(x.re, x.im\right)\right)}^{y.re}}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y.im around 0 64.1%

      \[\leadsto \color{blue}{{\left(\sqrt{{x.im}^{2} + {x.re}^{2}}\right)}^{y.re}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]
   6. Step-by-step derivation

      1. unpow2 64.1%

         \[\leadsto {\left(\sqrt{\color{blue}{x.im \cdot x.im} + {x.re}^{2}}\right)}^{y.re} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

      2. unpow2 64.1%

         \[\leadsto {\left(\sqrt{x.im \cdot x.im + \color{blue}{x.re \cdot x.re}}\right)}^{y.re} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

      3. hypot-undefine 82.5%

         \[\leadsto {\color{blue}{\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}}^{y.re} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

   7. Simplified 82.5%

      \[\leadsto \color{blue}{{\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}} \cdot \cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \]

   if -2.0000000000000001e-115 < x.re < -1.9499999999999999e-115

   1. Initial program 0.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 0.0%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around 0 1.6%

      \[\leadsto e^{\log \color{blue}{\left(x.im + 0.5 \cdot \frac{{x.re}^{2}}{x.im}\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -4.999999999999985e-310 < x.re < 9.00000000000000009e-306 or 3.9999999999999997e253 < x.re < 2.4000000000000001e284

   1. Initial program 25.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 51.6%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around inf 100.0%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if 2.34999999999999993e-297 < x.re < 8.9999999999999999e-267 or 2.60000000000000017e-242 < x.re < 3.05e-192 or 1.5500000000000001e-148 < x.re < 5.29999999999999972e-73 or 4.19999999999999991e42 < x.re < 6.80000000000000051e132 or 7.50000000000000017e132 < x.re < 9.1999999999999998e175 or 2.69999999999999991e177 < x.re < 2.60000000000000018e252 or 2.5e284 < x.re < 3.80000000000000014e293

   1. Initial program 40.3%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x.re around inf 66.1%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \color{blue}{x.re} \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

   4. Taylor expanded in x.re around inf 93.4%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log x.re \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

   if 1.35999999999999995e-61 < x.re < 4.19999999999999991e42

   1. Initial program 72.2%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 94.4%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq -7 \cdot 10^{+119}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -2 \cdot 10^{-46}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -7 \cdot 10^{-53}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -4.3 \cdot 10^{-57}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq -2 \cdot 10^{-115}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -1.95 \cdot 10^{-115}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log \left(x.im + 0.5 \cdot \frac{{x.re}^{2}}{x.im}\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -1.78 \cdot 10^{-124}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq -7.5 \cdot 10^{-149}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -4.3 \cdot 10^{-160}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq -1.15 \cdot 10^{-192}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -9.8 \cdot 10^{-234}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq -7.6 \cdot 10^{-260}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -5 \cdot 10^{-310}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq 9 \cdot 10^{-306}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.35 \cdot 10^{-297}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 9 \cdot 10^{-267}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 2.6 \cdot 10^{-242}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq 3.05 \cdot 10^{-192}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 9 \cdot 10^{-189}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 5.5 \cdot 10^{-171}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq 1.55 \cdot 10^{-148}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 5.3 \cdot 10^{-73}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 1.36 \cdot 10^{-61}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 6.8 \cdot 10^{+132}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 7.5 \cdot 10^{+132}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq 9.2 \cdot 10^{+175}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 2.7 \cdot 10^{+177}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(\log \left(\mathsf{hypot}\left(x.re, x.im\right)\right), y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \cdot {\left(\mathsf{hypot}\left(x.im, x.re\right)\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq 2.6 \cdot 10^{+252}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 4 \cdot 10^{+253}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{+284}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.5 \cdot 10^{+284} \lor \neg \left(x.re \leq 3.8 \cdot 10^{+293}\right):\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \cos t\_0\\ t_2 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_3 := e^{y.re \cdot \log x.re - t\_2}\\ t_4 := t\_1 \cdot t\_3\\ t_5 := t\_3 \cdot \cos \left(t\_0 + y.im \cdot \log x.re\right)\\ t_6 := e^{y.re \cdot \log \left(-x.re\right) - t\_2} \cdot t\_1\\ t_7 := e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - t\_2}\\ \mathbf{if}\;x.re \leq -9.5 \cdot 10^{+119}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq -4 \cdot 10^{-46}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -6.6 \cdot 10^{-49}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq -9.5 \cdot 10^{-95}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -5.3 \cdot 10^{-121}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq -4.5 \cdot 10^{-154}:\\ \;\;\;\;t\_1 \cdot e^{y.re \cdot \log x.im - t\_2}\\ \mathbf{elif}\;x.re \leq -9.5 \cdot 10^{-206}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -6 \cdot 10^{-233}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq -1.14 \cdot 10^{-259}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq 2.5 \cdot 10^{-304}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 5 \cdot 10^{-296}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 7.2 \cdot 10^{-268}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 3.95 \cdot 10^{-262}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 1.76 \cdot 10^{-246}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 2.15 \cdot 10^{-237}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 3 \cdot 10^{-192}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 9.5 \cdot 10^{-189}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 10^{-187}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 2.5 \cdot 10^{-174}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 5.5 \cdot 10^{-171}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 6.2 \cdot 10^{-148}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 1.75 \cdot 10^{-65}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 8 \cdot 10^{-60}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 7.5 \cdot 10^{-39}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 0.00048:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 4.8 \cdot 10^{+42}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 2.3 \cdot 10^{+132}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 8.5 \cdot 10^{+132}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 2.6 \cdot 10^{+252}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 4 \cdot 10^{+253}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{+284}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 2.5 \cdot 10^{+284} \lor \neg \left(x.re \leq 3.8 \cdot 10^{+293}\right):\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1 (cos t_0))
        (t_2 (* (atan2 x.im x.re) y.im))
        (t_3 (exp (- (* y.re (log x.re)) t_2)))
        (t_4 (* t_1 t_3))
        (t_5 (* t_3 (cos (+ t_0 (* y.im (log x.re))))))
        (t_6 (* (exp (- (* y.re (log (- x.re))) t_2)) t_1))
        (t_7
         (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) t_2))))
   (if (<= x.re -9.5e+119)
     t_6
     (if (<= x.re -4e-46)
       t_7
       (if (<= x.re -6.6e-49)
         t_6
         (if (<= x.re -9.5e-95)
           t_7
           (if (<= x.re -5.3e-121)
             t_6
             (if (<= x.re -4.5e-154)
               (* t_1 (exp (- (* y.re (log x.im)) t_2)))
               (if (<= x.re -9.5e-206)
                 t_7
                 (if (<= x.re -6e-233)
                   t_6
                   (if (<= x.re -1.14e-259)
                     t_7
                     (if (<= x.re -5e-310)
                       t_6
                       (if (<= x.re 2.5e-304)
                         t_4
                         (if (<= x.re 5e-296)
                           t_7
                           (if (<= x.re 7.2e-268)
                             t_5
                             (if (<= x.re 3.95e-262)
                               t_7
                               (if (<= x.re 1.76e-246)
                                 t_4
                                 (if (<= x.re 2.15e-237)
                                   t_7
                                   (if (<= x.re 3e-192)
                                     t_5
                                     (if (<= x.re 9.5e-189)
                                       t_7
                                       (if (<= x.re 1e-187)
                                         t_4
                                         (if (<= x.re 2.5e-174)
                                           t_7
                                           (if (<= x.re 5.5e-171)
                                             t_4
                                             (if (<= x.re 6.2e-148)
                                               t_7
                                               (if (<= x.re 1.75e-65)
                                                 t_5
                                                 (if (<= x.re 8e-60)
                                                   t_7
                                                   (if (<= x.re 7.5e-39)
                                                     t_4
                                                     (if (<= x.re 0.00048)
                                                       t_7
                                                       (if (<= x.re 4.8e+42)
                                                         t_4
                                                         (if (<= x.re 2.3e+132)
                                                           t_5
                                                           (if (<=
                                                                x.re
                                                                8.5e+132)
                                                             t_7
                                                             (if (<=
                                                                  x.re
                                                                  2.6e+252)
                                                               t_5
                                                               (if (<=
                                                                    x.re
                                                                    4e+253)
                                                                 t_7
                                                                 (if (<=
                                                                      x.re
                                                                      2.4e+284)
                                                                   t_4
                                                                   (if (or (<=
                                                                            x.re
                                                                            2.5e+284)
                                                                           (not
                                                                            (<=
                                                                             x.re
                                                                             3.8e+293)))
                                                                     t_7
                                                                     t_5)))))))))))))))))))))))))))))))))))

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 * atan2(x_46_im, x_46_re);
	double t_1 = cos(t_0);
	double t_2 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_3 = exp(((y_46_re * log(x_46_re)) - t_2));
	double t_4 = t_1 * t_3;
	double t_5 = t_3 * cos((t_0 + (y_46_im * log(x_46_re))));
	double t_6 = exp(((y_46_re * log(-x_46_re)) - t_2)) * t_1;
	double t_7 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_2));
	double tmp;
	if (x_46_re <= -9.5e+119) {
		tmp = t_6;
	} else if (x_46_re <= -4e-46) {
		tmp = t_7;
	} else if (x_46_re <= -6.6e-49) {
		tmp = t_6;
	} else if (x_46_re <= -9.5e-95) {
		tmp = t_7;
	} else if (x_46_re <= -5.3e-121) {
		tmp = t_6;
	} else if (x_46_re <= -4.5e-154) {
		tmp = t_1 * exp(((y_46_re * log(x_46_im)) - t_2));
	} else if (x_46_re <= -9.5e-206) {
		tmp = t_7;
	} else if (x_46_re <= -6e-233) {
		tmp = t_6;
	} else if (x_46_re <= -1.14e-259) {
		tmp = t_7;
	} else if (x_46_re <= -5e-310) {
		tmp = t_6;
	} else if (x_46_re <= 2.5e-304) {
		tmp = t_4;
	} else if (x_46_re <= 5e-296) {
		tmp = t_7;
	} else if (x_46_re <= 7.2e-268) {
		tmp = t_5;
	} else if (x_46_re <= 3.95e-262) {
		tmp = t_7;
	} else if (x_46_re <= 1.76e-246) {
		tmp = t_4;
	} else if (x_46_re <= 2.15e-237) {
		tmp = t_7;
	} else if (x_46_re <= 3e-192) {
		tmp = t_5;
	} else if (x_46_re <= 9.5e-189) {
		tmp = t_7;
	} else if (x_46_re <= 1e-187) {
		tmp = t_4;
	} else if (x_46_re <= 2.5e-174) {
		tmp = t_7;
	} else if (x_46_re <= 5.5e-171) {
		tmp = t_4;
	} else if (x_46_re <= 6.2e-148) {
		tmp = t_7;
	} else if (x_46_re <= 1.75e-65) {
		tmp = t_5;
	} else if (x_46_re <= 8e-60) {
		tmp = t_7;
	} else if (x_46_re <= 7.5e-39) {
		tmp = t_4;
	} else if (x_46_re <= 0.00048) {
		tmp = t_7;
	} else if (x_46_re <= 4.8e+42) {
		tmp = t_4;
	} else if (x_46_re <= 2.3e+132) {
		tmp = t_5;
	} else if (x_46_re <= 8.5e+132) {
		tmp = t_7;
	} else if (x_46_re <= 2.6e+252) {
		tmp = t_5;
	} else if (x_46_re <= 4e+253) {
		tmp = t_7;
	} else if (x_46_re <= 2.4e+284) {
		tmp = t_4;
	} else if ((x_46_re <= 2.5e+284) || !(x_46_re <= 3.8e+293)) {
		tmp = t_7;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = y_46re * atan2(x_46im, x_46re)
    t_1 = cos(t_0)
    t_2 = atan2(x_46im, x_46re) * y_46im
    t_3 = exp(((y_46re * log(x_46re)) - t_2))
    t_4 = t_1 * t_3
    t_5 = t_3 * cos((t_0 + (y_46im * log(x_46re))))
    t_6 = exp(((y_46re * log(-x_46re)) - t_2)) * t_1
    t_7 = exp(((log(sqrt(((x_46re * x_46re) + (x_46im * x_46im)))) * y_46re) - t_2))
    if (x_46re <= (-9.5d+119)) then
        tmp = t_6
    else if (x_46re <= (-4d-46)) then
        tmp = t_7
    else if (x_46re <= (-6.6d-49)) then
        tmp = t_6
    else if (x_46re <= (-9.5d-95)) then
        tmp = t_7
    else if (x_46re <= (-5.3d-121)) then
        tmp = t_6
    else if (x_46re <= (-4.5d-154)) then
        tmp = t_1 * exp(((y_46re * log(x_46im)) - t_2))
    else if (x_46re <= (-9.5d-206)) then
        tmp = t_7
    else if (x_46re <= (-6d-233)) then
        tmp = t_6
    else if (x_46re <= (-1.14d-259)) then
        tmp = t_7
    else if (x_46re <= (-5d-310)) then
        tmp = t_6
    else if (x_46re <= 2.5d-304) then
        tmp = t_4
    else if (x_46re <= 5d-296) then
        tmp = t_7
    else if (x_46re <= 7.2d-268) then
        tmp = t_5
    else if (x_46re <= 3.95d-262) then
        tmp = t_7
    else if (x_46re <= 1.76d-246) then
        tmp = t_4
    else if (x_46re <= 2.15d-237) then
        tmp = t_7
    else if (x_46re <= 3d-192) then
        tmp = t_5
    else if (x_46re <= 9.5d-189) then
        tmp = t_7
    else if (x_46re <= 1d-187) then
        tmp = t_4
    else if (x_46re <= 2.5d-174) then
        tmp = t_7
    else if (x_46re <= 5.5d-171) then
        tmp = t_4
    else if (x_46re <= 6.2d-148) then
        tmp = t_7
    else if (x_46re <= 1.75d-65) then
        tmp = t_5
    else if (x_46re <= 8d-60) then
        tmp = t_7
    else if (x_46re <= 7.5d-39) then
        tmp = t_4
    else if (x_46re <= 0.00048d0) then
        tmp = t_7
    else if (x_46re <= 4.8d+42) then
        tmp = t_4
    else if (x_46re <= 2.3d+132) then
        tmp = t_5
    else if (x_46re <= 8.5d+132) then
        tmp = t_7
    else if (x_46re <= 2.6d+252) then
        tmp = t_5
    else if (x_46re <= 4d+253) then
        tmp = t_7
    else if (x_46re <= 2.4d+284) then
        tmp = t_4
    else if ((x_46re <= 2.5d+284) .or. (.not. (x_46re <= 3.8d+293))) then
        tmp = t_7
    else
        tmp = t_5
    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 * Math.atan2(x_46_im, x_46_re);
	double t_1 = Math.cos(t_0);
	double t_2 = Math.atan2(x_46_im, x_46_re) * y_46_im;
	double t_3 = Math.exp(((y_46_re * Math.log(x_46_re)) - t_2));
	double t_4 = t_1 * t_3;
	double t_5 = t_3 * Math.cos((t_0 + (y_46_im * Math.log(x_46_re))));
	double t_6 = Math.exp(((y_46_re * Math.log(-x_46_re)) - t_2)) * t_1;
	double t_7 = Math.exp(((Math.log(Math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_2));
	double tmp;
	if (x_46_re <= -9.5e+119) {
		tmp = t_6;
	} else if (x_46_re <= -4e-46) {
		tmp = t_7;
	} else if (x_46_re <= -6.6e-49) {
		tmp = t_6;
	} else if (x_46_re <= -9.5e-95) {
		tmp = t_7;
	} else if (x_46_re <= -5.3e-121) {
		tmp = t_6;
	} else if (x_46_re <= -4.5e-154) {
		tmp = t_1 * Math.exp(((y_46_re * Math.log(x_46_im)) - t_2));
	} else if (x_46_re <= -9.5e-206) {
		tmp = t_7;
	} else if (x_46_re <= -6e-233) {
		tmp = t_6;
	} else if (x_46_re <= -1.14e-259) {
		tmp = t_7;
	} else if (x_46_re <= -5e-310) {
		tmp = t_6;
	} else if (x_46_re <= 2.5e-304) {
		tmp = t_4;
	} else if (x_46_re <= 5e-296) {
		tmp = t_7;
	} else if (x_46_re <= 7.2e-268) {
		tmp = t_5;
	} else if (x_46_re <= 3.95e-262) {
		tmp = t_7;
	} else if (x_46_re <= 1.76e-246) {
		tmp = t_4;
	} else if (x_46_re <= 2.15e-237) {
		tmp = t_7;
	} else if (x_46_re <= 3e-192) {
		tmp = t_5;
	} else if (x_46_re <= 9.5e-189) {
		tmp = t_7;
	} else if (x_46_re <= 1e-187) {
		tmp = t_4;
	} else if (x_46_re <= 2.5e-174) {
		tmp = t_7;
	} else if (x_46_re <= 5.5e-171) {
		tmp = t_4;
	} else if (x_46_re <= 6.2e-148) {
		tmp = t_7;
	} else if (x_46_re <= 1.75e-65) {
		tmp = t_5;
	} else if (x_46_re <= 8e-60) {
		tmp = t_7;
	} else if (x_46_re <= 7.5e-39) {
		tmp = t_4;
	} else if (x_46_re <= 0.00048) {
		tmp = t_7;
	} else if (x_46_re <= 4.8e+42) {
		tmp = t_4;
	} else if (x_46_re <= 2.3e+132) {
		tmp = t_5;
	} else if (x_46_re <= 8.5e+132) {
		tmp = t_7;
	} else if (x_46_re <= 2.6e+252) {
		tmp = t_5;
	} else if (x_46_re <= 4e+253) {
		tmp = t_7;
	} else if (x_46_re <= 2.4e+284) {
		tmp = t_4;
	} else if ((x_46_re <= 2.5e+284) || !(x_46_re <= 3.8e+293)) {
		tmp = t_7;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = y_46_re * math.atan2(x_46_im, x_46_re)
	t_1 = math.cos(t_0)
	t_2 = math.atan2(x_46_im, x_46_re) * y_46_im
	t_3 = math.exp(((y_46_re * math.log(x_46_re)) - t_2))
	t_4 = t_1 * t_3
	t_5 = t_3 * math.cos((t_0 + (y_46_im * math.log(x_46_re))))
	t_6 = math.exp(((y_46_re * math.log(-x_46_re)) - t_2)) * t_1
	t_7 = math.exp(((math.log(math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_2))
	tmp = 0
	if x_46_re <= -9.5e+119:
		tmp = t_6
	elif x_46_re <= -4e-46:
		tmp = t_7
	elif x_46_re <= -6.6e-49:
		tmp = t_6
	elif x_46_re <= -9.5e-95:
		tmp = t_7
	elif x_46_re <= -5.3e-121:
		tmp = t_6
	elif x_46_re <= -4.5e-154:
		tmp = t_1 * math.exp(((y_46_re * math.log(x_46_im)) - t_2))
	elif x_46_re <= -9.5e-206:
		tmp = t_7
	elif x_46_re <= -6e-233:
		tmp = t_6
	elif x_46_re <= -1.14e-259:
		tmp = t_7
	elif x_46_re <= -5e-310:
		tmp = t_6
	elif x_46_re <= 2.5e-304:
		tmp = t_4
	elif x_46_re <= 5e-296:
		tmp = t_7
	elif x_46_re <= 7.2e-268:
		tmp = t_5
	elif x_46_re <= 3.95e-262:
		tmp = t_7
	elif x_46_re <= 1.76e-246:
		tmp = t_4
	elif x_46_re <= 2.15e-237:
		tmp = t_7
	elif x_46_re <= 3e-192:
		tmp = t_5
	elif x_46_re <= 9.5e-189:
		tmp = t_7
	elif x_46_re <= 1e-187:
		tmp = t_4
	elif x_46_re <= 2.5e-174:
		tmp = t_7
	elif x_46_re <= 5.5e-171:
		tmp = t_4
	elif x_46_re <= 6.2e-148:
		tmp = t_7
	elif x_46_re <= 1.75e-65:
		tmp = t_5
	elif x_46_re <= 8e-60:
		tmp = t_7
	elif x_46_re <= 7.5e-39:
		tmp = t_4
	elif x_46_re <= 0.00048:
		tmp = t_7
	elif x_46_re <= 4.8e+42:
		tmp = t_4
	elif x_46_re <= 2.3e+132:
		tmp = t_5
	elif x_46_re <= 8.5e+132:
		tmp = t_7
	elif x_46_re <= 2.6e+252:
		tmp = t_5
	elif x_46_re <= 4e+253:
		tmp = t_7
	elif x_46_re <= 2.4e+284:
		tmp = t_4
	elif (x_46_re <= 2.5e+284) or not (x_46_re <= 3.8e+293):
		tmp = t_7
	else:
		tmp = t_5
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = cos(t_0)
	t_2 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_3 = exp(Float64(Float64(y_46_re * log(x_46_re)) - t_2))
	t_4 = Float64(t_1 * t_3)
	t_5 = Float64(t_3 * cos(Float64(t_0 + Float64(y_46_im * log(x_46_re)))))
	t_6 = Float64(exp(Float64(Float64(y_46_re * log(Float64(-x_46_re))) - t_2)) * t_1)
	t_7 = exp(Float64(Float64(log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im)))) * y_46_re) - t_2))
	tmp = 0.0
	if (x_46_re <= -9.5e+119)
		tmp = t_6;
	elseif (x_46_re <= -4e-46)
		tmp = t_7;
	elseif (x_46_re <= -6.6e-49)
		tmp = t_6;
	elseif (x_46_re <= -9.5e-95)
		tmp = t_7;
	elseif (x_46_re <= -5.3e-121)
		tmp = t_6;
	elseif (x_46_re <= -4.5e-154)
		tmp = Float64(t_1 * exp(Float64(Float64(y_46_re * log(x_46_im)) - t_2)));
	elseif (x_46_re <= -9.5e-206)
		tmp = t_7;
	elseif (x_46_re <= -6e-233)
		tmp = t_6;
	elseif (x_46_re <= -1.14e-259)
		tmp = t_7;
	elseif (x_46_re <= -5e-310)
		tmp = t_6;
	elseif (x_46_re <= 2.5e-304)
		tmp = t_4;
	elseif (x_46_re <= 5e-296)
		tmp = t_7;
	elseif (x_46_re <= 7.2e-268)
		tmp = t_5;
	elseif (x_46_re <= 3.95e-262)
		tmp = t_7;
	elseif (x_46_re <= 1.76e-246)
		tmp = t_4;
	elseif (x_46_re <= 2.15e-237)
		tmp = t_7;
	elseif (x_46_re <= 3e-192)
		tmp = t_5;
	elseif (x_46_re <= 9.5e-189)
		tmp = t_7;
	elseif (x_46_re <= 1e-187)
		tmp = t_4;
	elseif (x_46_re <= 2.5e-174)
		tmp = t_7;
	elseif (x_46_re <= 5.5e-171)
		tmp = t_4;
	elseif (x_46_re <= 6.2e-148)
		tmp = t_7;
	elseif (x_46_re <= 1.75e-65)
		tmp = t_5;
	elseif (x_46_re <= 8e-60)
		tmp = t_7;
	elseif (x_46_re <= 7.5e-39)
		tmp = t_4;
	elseif (x_46_re <= 0.00048)
		tmp = t_7;
	elseif (x_46_re <= 4.8e+42)
		tmp = t_4;
	elseif (x_46_re <= 2.3e+132)
		tmp = t_5;
	elseif (x_46_re <= 8.5e+132)
		tmp = t_7;
	elseif (x_46_re <= 2.6e+252)
		tmp = t_5;
	elseif (x_46_re <= 4e+253)
		tmp = t_7;
	elseif (x_46_re <= 2.4e+284)
		tmp = t_4;
	elseif ((x_46_re <= 2.5e+284) || !(x_46_re <= 3.8e+293))
		tmp = t_7;
	else
		tmp = t_5;
	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 * atan2(x_46_im, x_46_re);
	t_1 = cos(t_0);
	t_2 = atan2(x_46_im, x_46_re) * y_46_im;
	t_3 = exp(((y_46_re * log(x_46_re)) - t_2));
	t_4 = t_1 * t_3;
	t_5 = t_3 * cos((t_0 + (y_46_im * log(x_46_re))));
	t_6 = exp(((y_46_re * log(-x_46_re)) - t_2)) * t_1;
	t_7 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_2));
	tmp = 0.0;
	if (x_46_re <= -9.5e+119)
		tmp = t_6;
	elseif (x_46_re <= -4e-46)
		tmp = t_7;
	elseif (x_46_re <= -6.6e-49)
		tmp = t_6;
	elseif (x_46_re <= -9.5e-95)
		tmp = t_7;
	elseif (x_46_re <= -5.3e-121)
		tmp = t_6;
	elseif (x_46_re <= -4.5e-154)
		tmp = t_1 * exp(((y_46_re * log(x_46_im)) - t_2));
	elseif (x_46_re <= -9.5e-206)
		tmp = t_7;
	elseif (x_46_re <= -6e-233)
		tmp = t_6;
	elseif (x_46_re <= -1.14e-259)
		tmp = t_7;
	elseif (x_46_re <= -5e-310)
		tmp = t_6;
	elseif (x_46_re <= 2.5e-304)
		tmp = t_4;
	elseif (x_46_re <= 5e-296)
		tmp = t_7;
	elseif (x_46_re <= 7.2e-268)
		tmp = t_5;
	elseif (x_46_re <= 3.95e-262)
		tmp = t_7;
	elseif (x_46_re <= 1.76e-246)
		tmp = t_4;
	elseif (x_46_re <= 2.15e-237)
		tmp = t_7;
	elseif (x_46_re <= 3e-192)
		tmp = t_5;
	elseif (x_46_re <= 9.5e-189)
		tmp = t_7;
	elseif (x_46_re <= 1e-187)
		tmp = t_4;
	elseif (x_46_re <= 2.5e-174)
		tmp = t_7;
	elseif (x_46_re <= 5.5e-171)
		tmp = t_4;
	elseif (x_46_re <= 6.2e-148)
		tmp = t_7;
	elseif (x_46_re <= 1.75e-65)
		tmp = t_5;
	elseif (x_46_re <= 8e-60)
		tmp = t_7;
	elseif (x_46_re <= 7.5e-39)
		tmp = t_4;
	elseif (x_46_re <= 0.00048)
		tmp = t_7;
	elseif (x_46_re <= 4.8e+42)
		tmp = t_4;
	elseif (x_46_re <= 2.3e+132)
		tmp = t_5;
	elseif (x_46_re <= 8.5e+132)
		tmp = t_7;
	elseif (x_46_re <= 2.6e+252)
		tmp = t_5;
	elseif (x_46_re <= 4e+253)
		tmp = t_7;
	elseif (x_46_re <= 2.4e+284)
		tmp = t_4;
	elseif ((x_46_re <= 2.5e+284) || ~((x_46_re <= 3.8e+293)))
		tmp = t_7;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Cos[t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$3 = N[Exp[N[(N[(y$46$re * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 * N[Cos[N[(t$95$0 + N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[Exp[N[(N[(y$46$re * N[Log[(-x$46$re)], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision]}, Block[{t$95$7 = N[Exp[N[(N[(N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * y$46$re), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x$46$re, -9.5e+119], t$95$6, If[LessEqual[x$46$re, -4e-46], t$95$7, If[LessEqual[x$46$re, -6.6e-49], t$95$6, If[LessEqual[x$46$re, -9.5e-95], t$95$7, If[LessEqual[x$46$re, -5.3e-121], t$95$6, If[LessEqual[x$46$re, -4.5e-154], N[(t$95$1 * N[Exp[N[(N[(y$46$re * N[Log[x$46$im], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x$46$re, -9.5e-206], t$95$7, If[LessEqual[x$46$re, -6e-233], t$95$6, If[LessEqual[x$46$re, -1.14e-259], t$95$7, If[LessEqual[x$46$re, -5e-310], t$95$6, If[LessEqual[x$46$re, 2.5e-304], t$95$4, If[LessEqual[x$46$re, 5e-296], t$95$7, If[LessEqual[x$46$re, 7.2e-268], t$95$5, If[LessEqual[x$46$re, 3.95e-262], t$95$7, If[LessEqual[x$46$re, 1.76e-246], t$95$4, If[LessEqual[x$46$re, 2.15e-237], t$95$7, If[LessEqual[x$46$re, 3e-192], t$95$5, If[LessEqual[x$46$re, 9.5e-189], t$95$7, If[LessEqual[x$46$re, 1e-187], t$95$4, If[LessEqual[x$46$re, 2.5e-174], t$95$7, If[LessEqual[x$46$re, 5.5e-171], t$95$4, If[LessEqual[x$46$re, 6.2e-148], t$95$7, If[LessEqual[x$46$re, 1.75e-65], t$95$5, If[LessEqual[x$46$re, 8e-60], t$95$7, If[LessEqual[x$46$re, 7.5e-39], t$95$4, If[LessEqual[x$46$re, 0.00048], t$95$7, If[LessEqual[x$46$re, 4.8e+42], t$95$4, If[LessEqual[x$46$re, 2.3e+132], t$95$5, If[LessEqual[x$46$re, 8.5e+132], t$95$7, If[LessEqual[x$46$re, 2.6e+252], t$95$5, If[LessEqual[x$46$re, 4e+253], t$95$7, If[LessEqual[x$46$re, 2.4e+284], t$95$4, If[Or[LessEqual[x$46$re, 2.5e+284], N[Not[LessEqual[x$46$re, 3.8e+293]], $MachinePrecision]], t$95$7, t$95$5]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x.re < -9.4999999999999994e119 or -4.00000000000000009e-46 < x.re < -6.6e-49 or -9.49999999999999998e-95 < x.re < -5.2999999999999996e-121 or -9.49999999999999979e-206 < x.re < -5.99999999999999997e-233 or -1.14e-259 < x.re < -4.999999999999985e-310

   1. Initial program 29.7%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 57.2%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around -inf 90.9%

      \[\leadsto e^{\log \color{blue}{\left(-1 \cdot x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 90.9%

         \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 90.9%

      \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -9.4999999999999994e119 < x.re < -4.00000000000000009e-46 or -6.6e-49 < x.re < -9.49999999999999998e-95 or -4.4999999999999997e-154 < x.re < -9.49999999999999979e-206 or -5.99999999999999997e-233 < x.re < -1.14e-259 or 2.49999999999999983e-304 < x.re < 5.0000000000000003e-296 or 7.2000000000000002e-268 < x.re < 3.94999999999999994e-262 or 1.75999999999999993e-246 < x.re < 2.14999999999999991e-237 or 2.9999999999999999e-192 < x.re < 9.499999999999999e-189 or 1e-187 < x.re < 2.5000000000000001e-174 or 5.50000000000000037e-171 < x.re < 6.2000000000000003e-148 or 1.75000000000000002e-65 < x.re < 7.9999999999999998e-60 or 7.49999999999999971e-39 < x.re < 4.80000000000000012e-4 or 2.3000000000000002e132 < x.re < 8.49999999999999969e132 or 2.60000000000000018e252 < x.re < 3.9999999999999997e253 or 2.4000000000000001e284 < x.re < 2.5e284 or 3.80000000000000014e293 < x.re

   1. Initial program 52.3%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 69.9%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in y.re around 0 81.5%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{1} \]

   if -5.2999999999999996e-121 < x.re < -4.4999999999999997e-154

   1. Initial program 75.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 75.4%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around 0 87.5%

      \[\leadsto e^{\color{blue}{y.re \cdot \log x.im} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto e^{\color{blue}{\log x.im \cdot y.re} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 87.5%

      \[\leadsto e^{\color{blue}{\log x.im \cdot y.re} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -4.999999999999985e-310 < x.re < 2.49999999999999983e-304 or 3.94999999999999994e-262 < x.re < 1.75999999999999993e-246 or 9.499999999999999e-189 < x.re < 1e-187 or 2.5000000000000001e-174 < x.re < 5.50000000000000037e-171 or 7.9999999999999998e-60 < x.re < 7.49999999999999971e-39 or 4.80000000000000012e-4 < x.re < 4.7999999999999997e42 or 3.9999999999999997e253 < x.re < 2.4000000000000001e284

   1. Initial program 59.1%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 69.0%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around inf 95.5%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if 5.0000000000000003e-296 < x.re < 7.2000000000000002e-268 or 2.14999999999999991e-237 < x.re < 2.9999999999999999e-192 or 6.2000000000000003e-148 < x.re < 1.75000000000000002e-65 or 4.7999999999999997e42 < x.re < 2.3000000000000002e132 or 8.49999999999999969e132 < x.re < 2.60000000000000018e252 or 2.5e284 < x.re < 3.80000000000000014e293

   1. Initial program 39.5%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x.re around inf 65.3%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \color{blue}{x.re} \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

   4. Taylor expanded in x.re around inf 92.7%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log x.re \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq -9.5 \cdot 10^{+119}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -4 \cdot 10^{-46}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -6.6 \cdot 10^{-49}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -9.5 \cdot 10^{-95}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -5.3 \cdot 10^{-121}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -4.5 \cdot 10^{-154}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.im - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -9.5 \cdot 10^{-206}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -6 \cdot 10^{-233}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -1.14 \cdot 10^{-259}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -5 \cdot 10^{-310}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq 2.5 \cdot 10^{-304}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 5 \cdot 10^{-296}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 7.2 \cdot 10^{-268}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 3.95 \cdot 10^{-262}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.76 \cdot 10^{-246}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.15 \cdot 10^{-237}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 3 \cdot 10^{-192}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 9.5 \cdot 10^{-189}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 10^{-187}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.5 \cdot 10^{-174}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 5.5 \cdot 10^{-171}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 6.2 \cdot 10^{-148}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.75 \cdot 10^{-65}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 8 \cdot 10^{-60}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 7.5 \cdot 10^{-39}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 0.00048:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 4.8 \cdot 10^{+42}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.3 \cdot 10^{+132}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 8.5 \cdot 10^{+132}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.6 \cdot 10^{+252}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 4 \cdot 10^{+253}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{+284}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.5 \cdot 10^{+284} \lor \neg \left(x.re \leq 3.8 \cdot 10^{+293}\right):\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \cos t\_0\\ t_2 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_3 := e^{y.re \cdot \log x.re - t\_2}\\ t_4 := t\_1 \cdot t\_3\\ t_5 := t\_3 \cdot \cos \left(t\_0 + y.im \cdot \log x.re\right)\\ t_6 := e^{y.re \cdot \log \left(-x.re\right) - t\_2} \cdot t\_1\\ t_7 := e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - t\_2}\\ \mathbf{if}\;x.re \leq -2 \cdot 10^{+120}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq -1.9 \cdot 10^{-47}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -1.65 \cdot 10^{-47}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq -7.5 \cdot 10^{-93}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -5.3 \cdot 10^{-121}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq -4.5 \cdot 10^{-154}:\\ \;\;\;\;t\_1 \cdot e^{y.re \cdot \log x.im - t\_2}\\ \mathbf{elif}\;x.re \leq -6.5 \cdot 10^{-205}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -4.8 \cdot 10^{-230}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq -1.1 \cdot 10^{-259}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq 1.3 \cdot 10^{-306}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 1.22 \cdot 10^{-294}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 2.15 \cdot 10^{-266}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 3.15 \cdot 10^{-259}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 2.1 \cdot 10^{-245}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 3.6 \cdot 10^{-241}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 3.6 \cdot 10^{-191}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 1.1 \cdot 10^{-188}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 3 \cdot 10^{-188}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 1.35 \cdot 10^{-174}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 5.5 \cdot 10^{-171}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 1.25 \cdot 10^{-147}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 1.25 \cdot 10^{-64}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 1.3 \cdot 10^{+42}:\\ \;\;\;\;t\_1 \cdot t\_7\\ \mathbf{elif}\;x.re \leq 1.7 \cdot 10^{+132}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 7.5 \cdot 10^{+132}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 2.6 \cdot 10^{+252}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 4 \cdot 10^{+253}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{+284}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 2.5 \cdot 10^{+284} \lor \neg \left(x.re \leq 3.8 \cdot 10^{+293}\right):\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1 (cos t_0))
        (t_2 (* (atan2 x.im x.re) y.im))
        (t_3 (exp (- (* y.re (log x.re)) t_2)))
        (t_4 (* t_1 t_3))
        (t_5 (* t_3 (cos (+ t_0 (* y.im (log x.re))))))
        (t_6 (* (exp (- (* y.re (log (- x.re))) t_2)) t_1))
        (t_7
         (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) t_2))))
   (if (<= x.re -2e+120)
     t_6
     (if (<= x.re -1.9e-47)
       t_7
       (if (<= x.re -1.65e-47)
         t_6
         (if (<= x.re -7.5e-93)
           t_7
           (if (<= x.re -5.3e-121)
             t_6
             (if (<= x.re -4.5e-154)
               (* t_1 (exp (- (* y.re (log x.im)) t_2)))
               (if (<= x.re -6.5e-205)
                 t_7
                 (if (<= x.re -4.8e-230)
                   t_6
                   (if (<= x.re -1.1e-259)
                     t_7
                     (if (<= x.re -5e-310)
                       t_6
                       (if (<= x.re 1.3e-306)
                         t_4
                         (if (<= x.re 1.22e-294)
                           t_7
                           (if (<= x.re 2.15e-266)
                             t_5
                             (if (<= x.re 3.15e-259)
                               t_7
                               (if (<= x.re 2.1e-245)
                                 t_4
                                 (if (<= x.re 3.6e-241)
                                   t_7
                                   (if (<= x.re 3.6e-191)
                                     t_5
                                     (if (<= x.re 1.1e-188)
                                       t_7
                                       (if (<= x.re 3e-188)
                                         t_4
                                         (if (<= x.re 1.35e-174)
                                           t_7
                                           (if (<= x.re 5.5e-171)
                                             t_4
                                             (if (<= x.re 1.25e-147)
                                               t_7
                                               (if (<= x.re 1.25e-64)
                                                 t_5
                                                 (if (<= x.re 1.3e+42)
                                                   (* t_1 t_7)
                                                   (if (<= x.re 1.7e+132)
                                                     t_5
                                                     (if (<= x.re 7.5e+132)
                                                       t_7
                                                       (if (<= x.re 2.6e+252)
                                                         t_5
                                                         (if (<= x.re 4e+253)
                                                           t_7
                                                           (if (<=
                                                                x.re
                                                                2.4e+284)
                                                             t_4
                                                             (if (or (<=
                                                                      x.re
                                                                      2.5e+284)
                                                                     (not
                                                                      (<=
                                                                       x.re
                                                                       3.8e+293)))
                                                               t_7
                                                               t_5))))))))))))))))))))))))))))))))

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 * atan2(x_46_im, x_46_re);
	double t_1 = cos(t_0);
	double t_2 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_3 = exp(((y_46_re * log(x_46_re)) - t_2));
	double t_4 = t_1 * t_3;
	double t_5 = t_3 * cos((t_0 + (y_46_im * log(x_46_re))));
	double t_6 = exp(((y_46_re * log(-x_46_re)) - t_2)) * t_1;
	double t_7 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_2));
	double tmp;
	if (x_46_re <= -2e+120) {
		tmp = t_6;
	} else if (x_46_re <= -1.9e-47) {
		tmp = t_7;
	} else if (x_46_re <= -1.65e-47) {
		tmp = t_6;
	} else if (x_46_re <= -7.5e-93) {
		tmp = t_7;
	} else if (x_46_re <= -5.3e-121) {
		tmp = t_6;
	} else if (x_46_re <= -4.5e-154) {
		tmp = t_1 * exp(((y_46_re * log(x_46_im)) - t_2));
	} else if (x_46_re <= -6.5e-205) {
		tmp = t_7;
	} else if (x_46_re <= -4.8e-230) {
		tmp = t_6;
	} else if (x_46_re <= -1.1e-259) {
		tmp = t_7;
	} else if (x_46_re <= -5e-310) {
		tmp = t_6;
	} else if (x_46_re <= 1.3e-306) {
		tmp = t_4;
	} else if (x_46_re <= 1.22e-294) {
		tmp = t_7;
	} else if (x_46_re <= 2.15e-266) {
		tmp = t_5;
	} else if (x_46_re <= 3.15e-259) {
		tmp = t_7;
	} else if (x_46_re <= 2.1e-245) {
		tmp = t_4;
	} else if (x_46_re <= 3.6e-241) {
		tmp = t_7;
	} else if (x_46_re <= 3.6e-191) {
		tmp = t_5;
	} else if (x_46_re <= 1.1e-188) {
		tmp = t_7;
	} else if (x_46_re <= 3e-188) {
		tmp = t_4;
	} else if (x_46_re <= 1.35e-174) {
		tmp = t_7;
	} else if (x_46_re <= 5.5e-171) {
		tmp = t_4;
	} else if (x_46_re <= 1.25e-147) {
		tmp = t_7;
	} else if (x_46_re <= 1.25e-64) {
		tmp = t_5;
	} else if (x_46_re <= 1.3e+42) {
		tmp = t_1 * t_7;
	} else if (x_46_re <= 1.7e+132) {
		tmp = t_5;
	} else if (x_46_re <= 7.5e+132) {
		tmp = t_7;
	} else if (x_46_re <= 2.6e+252) {
		tmp = t_5;
	} else if (x_46_re <= 4e+253) {
		tmp = t_7;
	} else if (x_46_re <= 2.4e+284) {
		tmp = t_4;
	} else if ((x_46_re <= 2.5e+284) || !(x_46_re <= 3.8e+293)) {
		tmp = t_7;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = y_46re * atan2(x_46im, x_46re)
    t_1 = cos(t_0)
    t_2 = atan2(x_46im, x_46re) * y_46im
    t_3 = exp(((y_46re * log(x_46re)) - t_2))
    t_4 = t_1 * t_3
    t_5 = t_3 * cos((t_0 + (y_46im * log(x_46re))))
    t_6 = exp(((y_46re * log(-x_46re)) - t_2)) * t_1
    t_7 = exp(((log(sqrt(((x_46re * x_46re) + (x_46im * x_46im)))) * y_46re) - t_2))
    if (x_46re <= (-2d+120)) then
        tmp = t_6
    else if (x_46re <= (-1.9d-47)) then
        tmp = t_7
    else if (x_46re <= (-1.65d-47)) then
        tmp = t_6
    else if (x_46re <= (-7.5d-93)) then
        tmp = t_7
    else if (x_46re <= (-5.3d-121)) then
        tmp = t_6
    else if (x_46re <= (-4.5d-154)) then
        tmp = t_1 * exp(((y_46re * log(x_46im)) - t_2))
    else if (x_46re <= (-6.5d-205)) then
        tmp = t_7
    else if (x_46re <= (-4.8d-230)) then
        tmp = t_6
    else if (x_46re <= (-1.1d-259)) then
        tmp = t_7
    else if (x_46re <= (-5d-310)) then
        tmp = t_6
    else if (x_46re <= 1.3d-306) then
        tmp = t_4
    else if (x_46re <= 1.22d-294) then
        tmp = t_7
    else if (x_46re <= 2.15d-266) then
        tmp = t_5
    else if (x_46re <= 3.15d-259) then
        tmp = t_7
    else if (x_46re <= 2.1d-245) then
        tmp = t_4
    else if (x_46re <= 3.6d-241) then
        tmp = t_7
    else if (x_46re <= 3.6d-191) then
        tmp = t_5
    else if (x_46re <= 1.1d-188) then
        tmp = t_7
    else if (x_46re <= 3d-188) then
        tmp = t_4
    else if (x_46re <= 1.35d-174) then
        tmp = t_7
    else if (x_46re <= 5.5d-171) then
        tmp = t_4
    else if (x_46re <= 1.25d-147) then
        tmp = t_7
    else if (x_46re <= 1.25d-64) then
        tmp = t_5
    else if (x_46re <= 1.3d+42) then
        tmp = t_1 * t_7
    else if (x_46re <= 1.7d+132) then
        tmp = t_5
    else if (x_46re <= 7.5d+132) then
        tmp = t_7
    else if (x_46re <= 2.6d+252) then
        tmp = t_5
    else if (x_46re <= 4d+253) then
        tmp = t_7
    else if (x_46re <= 2.4d+284) then
        tmp = t_4
    else if ((x_46re <= 2.5d+284) .or. (.not. (x_46re <= 3.8d+293))) then
        tmp = t_7
    else
        tmp = t_5
    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 * Math.atan2(x_46_im, x_46_re);
	double t_1 = Math.cos(t_0);
	double t_2 = Math.atan2(x_46_im, x_46_re) * y_46_im;
	double t_3 = Math.exp(((y_46_re * Math.log(x_46_re)) - t_2));
	double t_4 = t_1 * t_3;
	double t_5 = t_3 * Math.cos((t_0 + (y_46_im * Math.log(x_46_re))));
	double t_6 = Math.exp(((y_46_re * Math.log(-x_46_re)) - t_2)) * t_1;
	double t_7 = Math.exp(((Math.log(Math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_2));
	double tmp;
	if (x_46_re <= -2e+120) {
		tmp = t_6;
	} else if (x_46_re <= -1.9e-47) {
		tmp = t_7;
	} else if (x_46_re <= -1.65e-47) {
		tmp = t_6;
	} else if (x_46_re <= -7.5e-93) {
		tmp = t_7;
	} else if (x_46_re <= -5.3e-121) {
		tmp = t_6;
	} else if (x_46_re <= -4.5e-154) {
		tmp = t_1 * Math.exp(((y_46_re * Math.log(x_46_im)) - t_2));
	} else if (x_46_re <= -6.5e-205) {
		tmp = t_7;
	} else if (x_46_re <= -4.8e-230) {
		tmp = t_6;
	} else if (x_46_re <= -1.1e-259) {
		tmp = t_7;
	} else if (x_46_re <= -5e-310) {
		tmp = t_6;
	} else if (x_46_re <= 1.3e-306) {
		tmp = t_4;
	} else if (x_46_re <= 1.22e-294) {
		tmp = t_7;
	} else if (x_46_re <= 2.15e-266) {
		tmp = t_5;
	} else if (x_46_re <= 3.15e-259) {
		tmp = t_7;
	} else if (x_46_re <= 2.1e-245) {
		tmp = t_4;
	} else if (x_46_re <= 3.6e-241) {
		tmp = t_7;
	} else if (x_46_re <= 3.6e-191) {
		tmp = t_5;
	} else if (x_46_re <= 1.1e-188) {
		tmp = t_7;
	} else if (x_46_re <= 3e-188) {
		tmp = t_4;
	} else if (x_46_re <= 1.35e-174) {
		tmp = t_7;
	} else if (x_46_re <= 5.5e-171) {
		tmp = t_4;
	} else if (x_46_re <= 1.25e-147) {
		tmp = t_7;
	} else if (x_46_re <= 1.25e-64) {
		tmp = t_5;
	} else if (x_46_re <= 1.3e+42) {
		tmp = t_1 * t_7;
	} else if (x_46_re <= 1.7e+132) {
		tmp = t_5;
	} else if (x_46_re <= 7.5e+132) {
		tmp = t_7;
	} else if (x_46_re <= 2.6e+252) {
		tmp = t_5;
	} else if (x_46_re <= 4e+253) {
		tmp = t_7;
	} else if (x_46_re <= 2.4e+284) {
		tmp = t_4;
	} else if ((x_46_re <= 2.5e+284) || !(x_46_re <= 3.8e+293)) {
		tmp = t_7;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = y_46_re * math.atan2(x_46_im, x_46_re)
	t_1 = math.cos(t_0)
	t_2 = math.atan2(x_46_im, x_46_re) * y_46_im
	t_3 = math.exp(((y_46_re * math.log(x_46_re)) - t_2))
	t_4 = t_1 * t_3
	t_5 = t_3 * math.cos((t_0 + (y_46_im * math.log(x_46_re))))
	t_6 = math.exp(((y_46_re * math.log(-x_46_re)) - t_2)) * t_1
	t_7 = math.exp(((math.log(math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_2))
	tmp = 0
	if x_46_re <= -2e+120:
		tmp = t_6
	elif x_46_re <= -1.9e-47:
		tmp = t_7
	elif x_46_re <= -1.65e-47:
		tmp = t_6
	elif x_46_re <= -7.5e-93:
		tmp = t_7
	elif x_46_re <= -5.3e-121:
		tmp = t_6
	elif x_46_re <= -4.5e-154:
		tmp = t_1 * math.exp(((y_46_re * math.log(x_46_im)) - t_2))
	elif x_46_re <= -6.5e-205:
		tmp = t_7
	elif x_46_re <= -4.8e-230:
		tmp = t_6
	elif x_46_re <= -1.1e-259:
		tmp = t_7
	elif x_46_re <= -5e-310:
		tmp = t_6
	elif x_46_re <= 1.3e-306:
		tmp = t_4
	elif x_46_re <= 1.22e-294:
		tmp = t_7
	elif x_46_re <= 2.15e-266:
		tmp = t_5
	elif x_46_re <= 3.15e-259:
		tmp = t_7
	elif x_46_re <= 2.1e-245:
		tmp = t_4
	elif x_46_re <= 3.6e-241:
		tmp = t_7
	elif x_46_re <= 3.6e-191:
		tmp = t_5
	elif x_46_re <= 1.1e-188:
		tmp = t_7
	elif x_46_re <= 3e-188:
		tmp = t_4
	elif x_46_re <= 1.35e-174:
		tmp = t_7
	elif x_46_re <= 5.5e-171:
		tmp = t_4
	elif x_46_re <= 1.25e-147:
		tmp = t_7
	elif x_46_re <= 1.25e-64:
		tmp = t_5
	elif x_46_re <= 1.3e+42:
		tmp = t_1 * t_7
	elif x_46_re <= 1.7e+132:
		tmp = t_5
	elif x_46_re <= 7.5e+132:
		tmp = t_7
	elif x_46_re <= 2.6e+252:
		tmp = t_5
	elif x_46_re <= 4e+253:
		tmp = t_7
	elif x_46_re <= 2.4e+284:
		tmp = t_4
	elif (x_46_re <= 2.5e+284) or not (x_46_re <= 3.8e+293):
		tmp = t_7
	else:
		tmp = t_5
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = cos(t_0)
	t_2 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_3 = exp(Float64(Float64(y_46_re * log(x_46_re)) - t_2))
	t_4 = Float64(t_1 * t_3)
	t_5 = Float64(t_3 * cos(Float64(t_0 + Float64(y_46_im * log(x_46_re)))))
	t_6 = Float64(exp(Float64(Float64(y_46_re * log(Float64(-x_46_re))) - t_2)) * t_1)
	t_7 = exp(Float64(Float64(log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im)))) * y_46_re) - t_2))
	tmp = 0.0
	if (x_46_re <= -2e+120)
		tmp = t_6;
	elseif (x_46_re <= -1.9e-47)
		tmp = t_7;
	elseif (x_46_re <= -1.65e-47)
		tmp = t_6;
	elseif (x_46_re <= -7.5e-93)
		tmp = t_7;
	elseif (x_46_re <= -5.3e-121)
		tmp = t_6;
	elseif (x_46_re <= -4.5e-154)
		tmp = Float64(t_1 * exp(Float64(Float64(y_46_re * log(x_46_im)) - t_2)));
	elseif (x_46_re <= -6.5e-205)
		tmp = t_7;
	elseif (x_46_re <= -4.8e-230)
		tmp = t_6;
	elseif (x_46_re <= -1.1e-259)
		tmp = t_7;
	elseif (x_46_re <= -5e-310)
		tmp = t_6;
	elseif (x_46_re <= 1.3e-306)
		tmp = t_4;
	elseif (x_46_re <= 1.22e-294)
		tmp = t_7;
	elseif (x_46_re <= 2.15e-266)
		tmp = t_5;
	elseif (x_46_re <= 3.15e-259)
		tmp = t_7;
	elseif (x_46_re <= 2.1e-245)
		tmp = t_4;
	elseif (x_46_re <= 3.6e-241)
		tmp = t_7;
	elseif (x_46_re <= 3.6e-191)
		tmp = t_5;
	elseif (x_46_re <= 1.1e-188)
		tmp = t_7;
	elseif (x_46_re <= 3e-188)
		tmp = t_4;
	elseif (x_46_re <= 1.35e-174)
		tmp = t_7;
	elseif (x_46_re <= 5.5e-171)
		tmp = t_4;
	elseif (x_46_re <= 1.25e-147)
		tmp = t_7;
	elseif (x_46_re <= 1.25e-64)
		tmp = t_5;
	elseif (x_46_re <= 1.3e+42)
		tmp = Float64(t_1 * t_7);
	elseif (x_46_re <= 1.7e+132)
		tmp = t_5;
	elseif (x_46_re <= 7.5e+132)
		tmp = t_7;
	elseif (x_46_re <= 2.6e+252)
		tmp = t_5;
	elseif (x_46_re <= 4e+253)
		tmp = t_7;
	elseif (x_46_re <= 2.4e+284)
		tmp = t_4;
	elseif ((x_46_re <= 2.5e+284) || !(x_46_re <= 3.8e+293))
		tmp = t_7;
	else
		tmp = t_5;
	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 * atan2(x_46_im, x_46_re);
	t_1 = cos(t_0);
	t_2 = atan2(x_46_im, x_46_re) * y_46_im;
	t_3 = exp(((y_46_re * log(x_46_re)) - t_2));
	t_4 = t_1 * t_3;
	t_5 = t_3 * cos((t_0 + (y_46_im * log(x_46_re))));
	t_6 = exp(((y_46_re * log(-x_46_re)) - t_2)) * t_1;
	t_7 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_2));
	tmp = 0.0;
	if (x_46_re <= -2e+120)
		tmp = t_6;
	elseif (x_46_re <= -1.9e-47)
		tmp = t_7;
	elseif (x_46_re <= -1.65e-47)
		tmp = t_6;
	elseif (x_46_re <= -7.5e-93)
		tmp = t_7;
	elseif (x_46_re <= -5.3e-121)
		tmp = t_6;
	elseif (x_46_re <= -4.5e-154)
		tmp = t_1 * exp(((y_46_re * log(x_46_im)) - t_2));
	elseif (x_46_re <= -6.5e-205)
		tmp = t_7;
	elseif (x_46_re <= -4.8e-230)
		tmp = t_6;
	elseif (x_46_re <= -1.1e-259)
		tmp = t_7;
	elseif (x_46_re <= -5e-310)
		tmp = t_6;
	elseif (x_46_re <= 1.3e-306)
		tmp = t_4;
	elseif (x_46_re <= 1.22e-294)
		tmp = t_7;
	elseif (x_46_re <= 2.15e-266)
		tmp = t_5;
	elseif (x_46_re <= 3.15e-259)
		tmp = t_7;
	elseif (x_46_re <= 2.1e-245)
		tmp = t_4;
	elseif (x_46_re <= 3.6e-241)
		tmp = t_7;
	elseif (x_46_re <= 3.6e-191)
		tmp = t_5;
	elseif (x_46_re <= 1.1e-188)
		tmp = t_7;
	elseif (x_46_re <= 3e-188)
		tmp = t_4;
	elseif (x_46_re <= 1.35e-174)
		tmp = t_7;
	elseif (x_46_re <= 5.5e-171)
		tmp = t_4;
	elseif (x_46_re <= 1.25e-147)
		tmp = t_7;
	elseif (x_46_re <= 1.25e-64)
		tmp = t_5;
	elseif (x_46_re <= 1.3e+42)
		tmp = t_1 * t_7;
	elseif (x_46_re <= 1.7e+132)
		tmp = t_5;
	elseif (x_46_re <= 7.5e+132)
		tmp = t_7;
	elseif (x_46_re <= 2.6e+252)
		tmp = t_5;
	elseif (x_46_re <= 4e+253)
		tmp = t_7;
	elseif (x_46_re <= 2.4e+284)
		tmp = t_4;
	elseif ((x_46_re <= 2.5e+284) || ~((x_46_re <= 3.8e+293)))
		tmp = t_7;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Cos[t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$3 = N[Exp[N[(N[(y$46$re * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 * N[Cos[N[(t$95$0 + N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[Exp[N[(N[(y$46$re * N[Log[(-x$46$re)], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision]}, Block[{t$95$7 = N[Exp[N[(N[(N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * y$46$re), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x$46$re, -2e+120], t$95$6, If[LessEqual[x$46$re, -1.9e-47], t$95$7, If[LessEqual[x$46$re, -1.65e-47], t$95$6, If[LessEqual[x$46$re, -7.5e-93], t$95$7, If[LessEqual[x$46$re, -5.3e-121], t$95$6, If[LessEqual[x$46$re, -4.5e-154], N[(t$95$1 * N[Exp[N[(N[(y$46$re * N[Log[x$46$im], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x$46$re, -6.5e-205], t$95$7, If[LessEqual[x$46$re, -4.8e-230], t$95$6, If[LessEqual[x$46$re, -1.1e-259], t$95$7, If[LessEqual[x$46$re, -5e-310], t$95$6, If[LessEqual[x$46$re, 1.3e-306], t$95$4, If[LessEqual[x$46$re, 1.22e-294], t$95$7, If[LessEqual[x$46$re, 2.15e-266], t$95$5, If[LessEqual[x$46$re, 3.15e-259], t$95$7, If[LessEqual[x$46$re, 2.1e-245], t$95$4, If[LessEqual[x$46$re, 3.6e-241], t$95$7, If[LessEqual[x$46$re, 3.6e-191], t$95$5, If[LessEqual[x$46$re, 1.1e-188], t$95$7, If[LessEqual[x$46$re, 3e-188], t$95$4, If[LessEqual[x$46$re, 1.35e-174], t$95$7, If[LessEqual[x$46$re, 5.5e-171], t$95$4, If[LessEqual[x$46$re, 1.25e-147], t$95$7, If[LessEqual[x$46$re, 1.25e-64], t$95$5, If[LessEqual[x$46$re, 1.3e+42], N[(t$95$1 * t$95$7), $MachinePrecision], If[LessEqual[x$46$re, 1.7e+132], t$95$5, If[LessEqual[x$46$re, 7.5e+132], t$95$7, If[LessEqual[x$46$re, 2.6e+252], t$95$5, If[LessEqual[x$46$re, 4e+253], t$95$7, If[LessEqual[x$46$re, 2.4e+284], t$95$4, If[Or[LessEqual[x$46$re, 2.5e+284], N[Not[LessEqual[x$46$re, 3.8e+293]], $MachinePrecision]], t$95$7, t$95$5]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x.re < -2e120 or -1.90000000000000007e-47 < x.re < -1.65000000000000002e-47 or -7.50000000000000034e-93 < x.re < -5.2999999999999996e-121 or -6.49999999999999956e-205 < x.re < -4.8000000000000004e-230 or -1.10000000000000005e-259 < x.re < -4.999999999999985e-310

   1. Initial program 29.7%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 57.2%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around -inf 90.9%

      \[\leadsto e^{\log \color{blue}{\left(-1 \cdot x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 90.9%

         \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 90.9%

      \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -2e120 < x.re < -1.90000000000000007e-47 or -1.65000000000000002e-47 < x.re < -7.50000000000000034e-93 or -4.4999999999999997e-154 < x.re < -6.49999999999999956e-205 or -4.8000000000000004e-230 < x.re < -1.10000000000000005e-259 or 1.3e-306 < x.re < 1.21999999999999995e-294 or 2.15000000000000014e-266 < x.re < 3.1500000000000001e-259 or 2.1000000000000001e-245 < x.re < 3.5999999999999999e-241 or 3.60000000000000019e-191 < x.re < 1.1e-188 or 3.00000000000000017e-188 < x.re < 1.34999999999999994e-174 or 5.50000000000000037e-171 < x.re < 1.25000000000000003e-147 or 1.70000000000000013e132 < x.re < 7.50000000000000017e132 or 2.60000000000000018e252 < x.re < 3.9999999999999997e253 or 2.4000000000000001e284 < x.re < 2.5e284 or 3.80000000000000014e293 < x.re

   1. Initial program 51.3%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 68.6%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in y.re around 0 81.7%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{1} \]

   if -5.2999999999999996e-121 < x.re < -4.4999999999999997e-154

   1. Initial program 75.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 75.4%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around 0 87.5%

      \[\leadsto e^{\color{blue}{y.re \cdot \log x.im} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto e^{\color{blue}{\log x.im \cdot y.re} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 87.5%

      \[\leadsto e^{\color{blue}{\log x.im \cdot y.re} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -4.999999999999985e-310 < x.re < 1.3e-306 or 3.1500000000000001e-259 < x.re < 2.1000000000000001e-245 or 1.1e-188 < x.re < 3.00000000000000017e-188 or 1.34999999999999994e-174 < x.re < 5.50000000000000037e-171 or 3.9999999999999997e253 < x.re < 2.4000000000000001e284

   1. Initial program 36.4%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 38.1%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around inf 90.9%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if 1.21999999999999995e-294 < x.re < 2.15000000000000014e-266 or 3.5999999999999999e-241 < x.re < 3.60000000000000019e-191 or 1.25000000000000003e-147 < x.re < 1.25000000000000008e-64 or 1.29999999999999995e42 < x.re < 1.70000000000000013e132 or 7.50000000000000017e132 < x.re < 2.60000000000000018e252 or 2.5e284 < x.re < 3.80000000000000014e293

   1. Initial program 39.5%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x.re around inf 65.3%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \color{blue}{x.re} \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

   4. Taylor expanded in x.re around inf 92.7%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log x.re \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

   if 1.25000000000000008e-64 < x.re < 1.29999999999999995e42

   1. Initial program 71.4%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 90.5%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq -2 \cdot 10^{+120}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -1.9 \cdot 10^{-47}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -1.65 \cdot 10^{-47}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -7.5 \cdot 10^{-93}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -5.3 \cdot 10^{-121}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -4.5 \cdot 10^{-154}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.im - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -6.5 \cdot 10^{-205}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -4.8 \cdot 10^{-230}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -1.1 \cdot 10^{-259}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -5 \cdot 10^{-310}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq 1.3 \cdot 10^{-306}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.22 \cdot 10^{-294}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.15 \cdot 10^{-266}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 3.15 \cdot 10^{-259}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.1 \cdot 10^{-245}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 3.6 \cdot 10^{-241}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 3.6 \cdot 10^{-191}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 1.1 \cdot 10^{-188}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 3 \cdot 10^{-188}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.35 \cdot 10^{-174}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 5.5 \cdot 10^{-171}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.25 \cdot 10^{-147}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.25 \cdot 10^{-64}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 1.3 \cdot 10^{+42}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.7 \cdot 10^{+132}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 7.5 \cdot 10^{+132}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.6 \cdot 10^{+252}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 4 \cdot 10^{+253}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{+284}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.5 \cdot 10^{+284} \lor \neg \left(x.re \leq 3.8 \cdot 10^{+293}\right):\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_1 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_2 := \cos t\_1\\ t_3 := e^{y.re \cdot \log x.re - t\_0}\\ t_4 := t\_3 \cdot \cos \left(t\_1 + y.im \cdot \log x.re\right)\\ t_5 := t\_2 \cdot t\_3\\ t_6 := e^{y.re \cdot \log \left(-x.re\right) - t\_0} \cdot t\_2\\ t_7 := e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - t\_0}\\ \mathbf{if}\;x.re \leq -3 \cdot 10^{+121}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq -1.06 \cdot 10^{-38}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -1.75 \cdot 10^{-47}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq -2 \cdot 10^{-115}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -4.5 \cdot 10^{-154}:\\ \;\;\;\;t\_2 \cdot e^{y.re \cdot \log \left(x.im + 0.5 \cdot \frac{{x.re}^{2}}{x.im}\right) - t\_0}\\ \mathbf{elif}\;x.re \leq -1.9 \cdot 10^{-204}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -2.35 \cdot 10^{-231}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq -9 \cdot 10^{-260}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x.re \leq 1.02 \cdot 10^{-306}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 3.8 \cdot 10^{-296}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 7.4 \cdot 10^{-267}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 2.7 \cdot 10^{-265}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 2 \cdot 10^{-245}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 1.02 \cdot 10^{-242}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 9 \cdot 10^{-192}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 1.3 \cdot 10^{-188}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 4.2 \cdot 10^{-188}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 3.1 \cdot 10^{-175}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 5.8 \cdot 10^{-171}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 3 \cdot 10^{-149}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 9.8 \cdot 10^{-65}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 5.5 \cdot 10^{+42}:\\ \;\;\;\;t\_2 \cdot t\_7\\ \mathbf{elif}\;x.re \leq 5.2 \cdot 10^{+132}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 2.6 \cdot 10^{+252}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 4 \cdot 10^{+253}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{+284}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 2.5 \cdot 10^{+284} \lor \neg \left(x.re \leq 3.8 \cdot 10^{+293}\right):\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* (atan2 x.im x.re) y.im))
        (t_1 (* y.re (atan2 x.im x.re)))
        (t_2 (cos t_1))
        (t_3 (exp (- (* y.re (log x.re)) t_0)))
        (t_4 (* t_3 (cos (+ t_1 (* y.im (log x.re))))))
        (t_5 (* t_2 t_3))
        (t_6 (* (exp (- (* y.re (log (- x.re))) t_0)) t_2))
        (t_7
         (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) t_0))))
   (if (<= x.re -3e+121)
     t_6
     (if (<= x.re -1.06e-38)
       t_7
       (if (<= x.re -1.75e-47)
         t_6
         (if (<= x.re -2e-115)
           t_7
           (if (<= x.re -4.5e-154)
             (*
              t_2
              (exp
               (-
                (* y.re (log (+ x.im (* 0.5 (/ (pow x.re 2.0) x.im)))))
                t_0)))
             (if (<= x.re -1.9e-204)
               t_7
               (if (<= x.re -2.35e-231)
                 t_6
                 (if (<= x.re -9e-260)
                   t_7
                   (if (<= x.re -5e-310)
                     t_6
                     (if (<= x.re 1.02e-306)
                       t_5
                       (if (<= x.re 3.8e-296)
                         t_7
                         (if (<= x.re 7.4e-267)
                           t_4
                           (if (<= x.re 2.7e-265)
                             t_7
                             (if (<= x.re 2e-245)
                               t_5
                               (if (<= x.re 1.02e-242)
                                 t_7
                                 (if (<= x.re 9e-192)
                                   t_4
                                   (if (<= x.re 1.3e-188)
                                     t_7
                                     (if (<= x.re 4.2e-188)
                                       t_5
                                       (if (<= x.re 3.1e-175)
                                         t_7
                                         (if (<= x.re 5.8e-171)
                                           t_5
                                           (if (<= x.re 3e-149)
                                             t_7
                                             (if (<= x.re 9.8e-65)
                                               t_4
                                               (if (<= x.re 5.5e+42)
                                                 (* t_2 t_7)
                                                 (if (<= x.re 5.2e+132)
                                                   t_4
                                                   (if (<= x.re 2.2e+133)
                                                     t_7
                                                     (if (<= x.re 2.6e+252)
                                                       t_4
                                                       (if (<= x.re 4e+253)
                                                         t_7
                                                         (if (<= x.re 2.4e+284)
                                                           t_5
                                                           (if (or (<=
                                                                    x.re
                                                                    2.5e+284)
                                                                   (not
                                                                    (<=
                                                                     x.re
                                                                     3.8e+293)))
                                                             t_7
                                                             t_4)))))))))))))))))))))))))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_1 = y_46_re * atan2(x_46_im, x_46_re);
	double t_2 = cos(t_1);
	double t_3 = exp(((y_46_re * log(x_46_re)) - t_0));
	double t_4 = t_3 * cos((t_1 + (y_46_im * log(x_46_re))));
	double t_5 = t_2 * t_3;
	double t_6 = exp(((y_46_re * log(-x_46_re)) - t_0)) * t_2;
	double t_7 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_0));
	double tmp;
	if (x_46_re <= -3e+121) {
		tmp = t_6;
	} else if (x_46_re <= -1.06e-38) {
		tmp = t_7;
	} else if (x_46_re <= -1.75e-47) {
		tmp = t_6;
	} else if (x_46_re <= -2e-115) {
		tmp = t_7;
	} else if (x_46_re <= -4.5e-154) {
		tmp = t_2 * exp(((y_46_re * log((x_46_im + (0.5 * (pow(x_46_re, 2.0) / x_46_im))))) - t_0));
	} else if (x_46_re <= -1.9e-204) {
		tmp = t_7;
	} else if (x_46_re <= -2.35e-231) {
		tmp = t_6;
	} else if (x_46_re <= -9e-260) {
		tmp = t_7;
	} else if (x_46_re <= -5e-310) {
		tmp = t_6;
	} else if (x_46_re <= 1.02e-306) {
		tmp = t_5;
	} else if (x_46_re <= 3.8e-296) {
		tmp = t_7;
	} else if (x_46_re <= 7.4e-267) {
		tmp = t_4;
	} else if (x_46_re <= 2.7e-265) {
		tmp = t_7;
	} else if (x_46_re <= 2e-245) {
		tmp = t_5;
	} else if (x_46_re <= 1.02e-242) {
		tmp = t_7;
	} else if (x_46_re <= 9e-192) {
		tmp = t_4;
	} else if (x_46_re <= 1.3e-188) {
		tmp = t_7;
	} else if (x_46_re <= 4.2e-188) {
		tmp = t_5;
	} else if (x_46_re <= 3.1e-175) {
		tmp = t_7;
	} else if (x_46_re <= 5.8e-171) {
		tmp = t_5;
	} else if (x_46_re <= 3e-149) {
		tmp = t_7;
	} else if (x_46_re <= 9.8e-65) {
		tmp = t_4;
	} else if (x_46_re <= 5.5e+42) {
		tmp = t_2 * t_7;
	} else if (x_46_re <= 5.2e+132) {
		tmp = t_4;
	} else if (x_46_re <= 2.2e+133) {
		tmp = t_7;
	} else if (x_46_re <= 2.6e+252) {
		tmp = t_4;
	} else if (x_46_re <= 4e+253) {
		tmp = t_7;
	} else if (x_46_re <= 2.4e+284) {
		tmp = t_5;
	} else if ((x_46_re <= 2.5e+284) || !(x_46_re <= 3.8e+293)) {
		tmp = t_7;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = atan2(x_46im, x_46re) * y_46im
    t_1 = y_46re * atan2(x_46im, x_46re)
    t_2 = cos(t_1)
    t_3 = exp(((y_46re * log(x_46re)) - t_0))
    t_4 = t_3 * cos((t_1 + (y_46im * log(x_46re))))
    t_5 = t_2 * t_3
    t_6 = exp(((y_46re * log(-x_46re)) - t_0)) * t_2
    t_7 = exp(((log(sqrt(((x_46re * x_46re) + (x_46im * x_46im)))) * y_46re) - t_0))
    if (x_46re <= (-3d+121)) then
        tmp = t_6
    else if (x_46re <= (-1.06d-38)) then
        tmp = t_7
    else if (x_46re <= (-1.75d-47)) then
        tmp = t_6
    else if (x_46re <= (-2d-115)) then
        tmp = t_7
    else if (x_46re <= (-4.5d-154)) then
        tmp = t_2 * exp(((y_46re * log((x_46im + (0.5d0 * ((x_46re ** 2.0d0) / x_46im))))) - t_0))
    else if (x_46re <= (-1.9d-204)) then
        tmp = t_7
    else if (x_46re <= (-2.35d-231)) then
        tmp = t_6
    else if (x_46re <= (-9d-260)) then
        tmp = t_7
    else if (x_46re <= (-5d-310)) then
        tmp = t_6
    else if (x_46re <= 1.02d-306) then
        tmp = t_5
    else if (x_46re <= 3.8d-296) then
        tmp = t_7
    else if (x_46re <= 7.4d-267) then
        tmp = t_4
    else if (x_46re <= 2.7d-265) then
        tmp = t_7
    else if (x_46re <= 2d-245) then
        tmp = t_5
    else if (x_46re <= 1.02d-242) then
        tmp = t_7
    else if (x_46re <= 9d-192) then
        tmp = t_4
    else if (x_46re <= 1.3d-188) then
        tmp = t_7
    else if (x_46re <= 4.2d-188) then
        tmp = t_5
    else if (x_46re <= 3.1d-175) then
        tmp = t_7
    else if (x_46re <= 5.8d-171) then
        tmp = t_5
    else if (x_46re <= 3d-149) then
        tmp = t_7
    else if (x_46re <= 9.8d-65) then
        tmp = t_4
    else if (x_46re <= 5.5d+42) then
        tmp = t_2 * t_7
    else if (x_46re <= 5.2d+132) then
        tmp = t_4
    else if (x_46re <= 2.2d+133) then
        tmp = t_7
    else if (x_46re <= 2.6d+252) then
        tmp = t_4
    else if (x_46re <= 4d+253) then
        tmp = t_7
    else if (x_46re <= 2.4d+284) then
        tmp = t_5
    else if ((x_46re <= 2.5d+284) .or. (.not. (x_46re <= 3.8d+293))) then
        tmp = t_7
    else
        tmp = t_4
    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 = Math.atan2(x_46_im, x_46_re) * y_46_im;
	double t_1 = y_46_re * Math.atan2(x_46_im, x_46_re);
	double t_2 = Math.cos(t_1);
	double t_3 = Math.exp(((y_46_re * Math.log(x_46_re)) - t_0));
	double t_4 = t_3 * Math.cos((t_1 + (y_46_im * Math.log(x_46_re))));
	double t_5 = t_2 * t_3;
	double t_6 = Math.exp(((y_46_re * Math.log(-x_46_re)) - t_0)) * t_2;
	double t_7 = Math.exp(((Math.log(Math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_0));
	double tmp;
	if (x_46_re <= -3e+121) {
		tmp = t_6;
	} else if (x_46_re <= -1.06e-38) {
		tmp = t_7;
	} else if (x_46_re <= -1.75e-47) {
		tmp = t_6;
	} else if (x_46_re <= -2e-115) {
		tmp = t_7;
	} else if (x_46_re <= -4.5e-154) {
		tmp = t_2 * Math.exp(((y_46_re * Math.log((x_46_im + (0.5 * (Math.pow(x_46_re, 2.0) / x_46_im))))) - t_0));
	} else if (x_46_re <= -1.9e-204) {
		tmp = t_7;
	} else if (x_46_re <= -2.35e-231) {
		tmp = t_6;
	} else if (x_46_re <= -9e-260) {
		tmp = t_7;
	} else if (x_46_re <= -5e-310) {
		tmp = t_6;
	} else if (x_46_re <= 1.02e-306) {
		tmp = t_5;
	} else if (x_46_re <= 3.8e-296) {
		tmp = t_7;
	} else if (x_46_re <= 7.4e-267) {
		tmp = t_4;
	} else if (x_46_re <= 2.7e-265) {
		tmp = t_7;
	} else if (x_46_re <= 2e-245) {
		tmp = t_5;
	} else if (x_46_re <= 1.02e-242) {
		tmp = t_7;
	} else if (x_46_re <= 9e-192) {
		tmp = t_4;
	} else if (x_46_re <= 1.3e-188) {
		tmp = t_7;
	} else if (x_46_re <= 4.2e-188) {
		tmp = t_5;
	} else if (x_46_re <= 3.1e-175) {
		tmp = t_7;
	} else if (x_46_re <= 5.8e-171) {
		tmp = t_5;
	} else if (x_46_re <= 3e-149) {
		tmp = t_7;
	} else if (x_46_re <= 9.8e-65) {
		tmp = t_4;
	} else if (x_46_re <= 5.5e+42) {
		tmp = t_2 * t_7;
	} else if (x_46_re <= 5.2e+132) {
		tmp = t_4;
	} else if (x_46_re <= 2.2e+133) {
		tmp = t_7;
	} else if (x_46_re <= 2.6e+252) {
		tmp = t_4;
	} else if (x_46_re <= 4e+253) {
		tmp = t_7;
	} else if (x_46_re <= 2.4e+284) {
		tmp = t_5;
	} else if ((x_46_re <= 2.5e+284) || !(x_46_re <= 3.8e+293)) {
		tmp = t_7;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = math.atan2(x_46_im, x_46_re) * y_46_im
	t_1 = y_46_re * math.atan2(x_46_im, x_46_re)
	t_2 = math.cos(t_1)
	t_3 = math.exp(((y_46_re * math.log(x_46_re)) - t_0))
	t_4 = t_3 * math.cos((t_1 + (y_46_im * math.log(x_46_re))))
	t_5 = t_2 * t_3
	t_6 = math.exp(((y_46_re * math.log(-x_46_re)) - t_0)) * t_2
	t_7 = math.exp(((math.log(math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_0))
	tmp = 0
	if x_46_re <= -3e+121:
		tmp = t_6
	elif x_46_re <= -1.06e-38:
		tmp = t_7
	elif x_46_re <= -1.75e-47:
		tmp = t_6
	elif x_46_re <= -2e-115:
		tmp = t_7
	elif x_46_re <= -4.5e-154:
		tmp = t_2 * math.exp(((y_46_re * math.log((x_46_im + (0.5 * (math.pow(x_46_re, 2.0) / x_46_im))))) - t_0))
	elif x_46_re <= -1.9e-204:
		tmp = t_7
	elif x_46_re <= -2.35e-231:
		tmp = t_6
	elif x_46_re <= -9e-260:
		tmp = t_7
	elif x_46_re <= -5e-310:
		tmp = t_6
	elif x_46_re <= 1.02e-306:
		tmp = t_5
	elif x_46_re <= 3.8e-296:
		tmp = t_7
	elif x_46_re <= 7.4e-267:
		tmp = t_4
	elif x_46_re <= 2.7e-265:
		tmp = t_7
	elif x_46_re <= 2e-245:
		tmp = t_5
	elif x_46_re <= 1.02e-242:
		tmp = t_7
	elif x_46_re <= 9e-192:
		tmp = t_4
	elif x_46_re <= 1.3e-188:
		tmp = t_7
	elif x_46_re <= 4.2e-188:
		tmp = t_5
	elif x_46_re <= 3.1e-175:
		tmp = t_7
	elif x_46_re <= 5.8e-171:
		tmp = t_5
	elif x_46_re <= 3e-149:
		tmp = t_7
	elif x_46_re <= 9.8e-65:
		tmp = t_4
	elif x_46_re <= 5.5e+42:
		tmp = t_2 * t_7
	elif x_46_re <= 5.2e+132:
		tmp = t_4
	elif x_46_re <= 2.2e+133:
		tmp = t_7
	elif x_46_re <= 2.6e+252:
		tmp = t_4
	elif x_46_re <= 4e+253:
		tmp = t_7
	elif x_46_re <= 2.4e+284:
		tmp = t_5
	elif (x_46_re <= 2.5e+284) or not (x_46_re <= 3.8e+293):
		tmp = t_7
	else:
		tmp = t_4
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_1 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_2 = cos(t_1)
	t_3 = exp(Float64(Float64(y_46_re * log(x_46_re)) - t_0))
	t_4 = Float64(t_3 * cos(Float64(t_1 + Float64(y_46_im * log(x_46_re)))))
	t_5 = Float64(t_2 * t_3)
	t_6 = Float64(exp(Float64(Float64(y_46_re * log(Float64(-x_46_re))) - t_0)) * t_2)
	t_7 = exp(Float64(Float64(log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im)))) * y_46_re) - t_0))
	tmp = 0.0
	if (x_46_re <= -3e+121)
		tmp = t_6;
	elseif (x_46_re <= -1.06e-38)
		tmp = t_7;
	elseif (x_46_re <= -1.75e-47)
		tmp = t_6;
	elseif (x_46_re <= -2e-115)
		tmp = t_7;
	elseif (x_46_re <= -4.5e-154)
		tmp = Float64(t_2 * exp(Float64(Float64(y_46_re * log(Float64(x_46_im + Float64(0.5 * Float64((x_46_re ^ 2.0) / x_46_im))))) - t_0)));
	elseif (x_46_re <= -1.9e-204)
		tmp = t_7;
	elseif (x_46_re <= -2.35e-231)
		tmp = t_6;
	elseif (x_46_re <= -9e-260)
		tmp = t_7;
	elseif (x_46_re <= -5e-310)
		tmp = t_6;
	elseif (x_46_re <= 1.02e-306)
		tmp = t_5;
	elseif (x_46_re <= 3.8e-296)
		tmp = t_7;
	elseif (x_46_re <= 7.4e-267)
		tmp = t_4;
	elseif (x_46_re <= 2.7e-265)
		tmp = t_7;
	elseif (x_46_re <= 2e-245)
		tmp = t_5;
	elseif (x_46_re <= 1.02e-242)
		tmp = t_7;
	elseif (x_46_re <= 9e-192)
		tmp = t_4;
	elseif (x_46_re <= 1.3e-188)
		tmp = t_7;
	elseif (x_46_re <= 4.2e-188)
		tmp = t_5;
	elseif (x_46_re <= 3.1e-175)
		tmp = t_7;
	elseif (x_46_re <= 5.8e-171)
		tmp = t_5;
	elseif (x_46_re <= 3e-149)
		tmp = t_7;
	elseif (x_46_re <= 9.8e-65)
		tmp = t_4;
	elseif (x_46_re <= 5.5e+42)
		tmp = Float64(t_2 * t_7);
	elseif (x_46_re <= 5.2e+132)
		tmp = t_4;
	elseif (x_46_re <= 2.2e+133)
		tmp = t_7;
	elseif (x_46_re <= 2.6e+252)
		tmp = t_4;
	elseif (x_46_re <= 4e+253)
		tmp = t_7;
	elseif (x_46_re <= 2.4e+284)
		tmp = t_5;
	elseif ((x_46_re <= 2.5e+284) || !(x_46_re <= 3.8e+293))
		tmp = t_7;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = atan2(x_46_im, x_46_re) * y_46_im;
	t_1 = y_46_re * atan2(x_46_im, x_46_re);
	t_2 = cos(t_1);
	t_3 = exp(((y_46_re * log(x_46_re)) - t_0));
	t_4 = t_3 * cos((t_1 + (y_46_im * log(x_46_re))));
	t_5 = t_2 * t_3;
	t_6 = exp(((y_46_re * log(-x_46_re)) - t_0)) * t_2;
	t_7 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_0));
	tmp = 0.0;
	if (x_46_re <= -3e+121)
		tmp = t_6;
	elseif (x_46_re <= -1.06e-38)
		tmp = t_7;
	elseif (x_46_re <= -1.75e-47)
		tmp = t_6;
	elseif (x_46_re <= -2e-115)
		tmp = t_7;
	elseif (x_46_re <= -4.5e-154)
		tmp = t_2 * exp(((y_46_re * log((x_46_im + (0.5 * ((x_46_re ^ 2.0) / x_46_im))))) - t_0));
	elseif (x_46_re <= -1.9e-204)
		tmp = t_7;
	elseif (x_46_re <= -2.35e-231)
		tmp = t_6;
	elseif (x_46_re <= -9e-260)
		tmp = t_7;
	elseif (x_46_re <= -5e-310)
		tmp = t_6;
	elseif (x_46_re <= 1.02e-306)
		tmp = t_5;
	elseif (x_46_re <= 3.8e-296)
		tmp = t_7;
	elseif (x_46_re <= 7.4e-267)
		tmp = t_4;
	elseif (x_46_re <= 2.7e-265)
		tmp = t_7;
	elseif (x_46_re <= 2e-245)
		tmp = t_5;
	elseif (x_46_re <= 1.02e-242)
		tmp = t_7;
	elseif (x_46_re <= 9e-192)
		tmp = t_4;
	elseif (x_46_re <= 1.3e-188)
		tmp = t_7;
	elseif (x_46_re <= 4.2e-188)
		tmp = t_5;
	elseif (x_46_re <= 3.1e-175)
		tmp = t_7;
	elseif (x_46_re <= 5.8e-171)
		tmp = t_5;
	elseif (x_46_re <= 3e-149)
		tmp = t_7;
	elseif (x_46_re <= 9.8e-65)
		tmp = t_4;
	elseif (x_46_re <= 5.5e+42)
		tmp = t_2 * t_7;
	elseif (x_46_re <= 5.2e+132)
		tmp = t_4;
	elseif (x_46_re <= 2.2e+133)
		tmp = t_7;
	elseif (x_46_re <= 2.6e+252)
		tmp = t_4;
	elseif (x_46_re <= 4e+253)
		tmp = t_7;
	elseif (x_46_re <= 2.4e+284)
		tmp = t_5;
	elseif ((x_46_re <= 2.5e+284) || ~((x_46_re <= 3.8e+293)))
		tmp = t_7;
	else
		tmp = t_4;
	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[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$1 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Cos[t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Exp[N[(N[(y$46$re * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * N[Cos[N[(t$95$1 + N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 * t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(N[Exp[N[(N[(y$46$re * N[Log[(-x$46$re)], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]], $MachinePrecision] * t$95$2), $MachinePrecision]}, Block[{t$95$7 = N[Exp[N[(N[(N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * y$46$re), $MachinePrecision] - t$95$0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x$46$re, -3e+121], t$95$6, If[LessEqual[x$46$re, -1.06e-38], t$95$7, If[LessEqual[x$46$re, -1.75e-47], t$95$6, If[LessEqual[x$46$re, -2e-115], t$95$7, If[LessEqual[x$46$re, -4.5e-154], N[(t$95$2 * N[Exp[N[(N[(y$46$re * N[Log[N[(x$46$im + N[(0.5 * N[(N[Power[x$46$re, 2.0], $MachinePrecision] / x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x$46$re, -1.9e-204], t$95$7, If[LessEqual[x$46$re, -2.35e-231], t$95$6, If[LessEqual[x$46$re, -9e-260], t$95$7, If[LessEqual[x$46$re, -5e-310], t$95$6, If[LessEqual[x$46$re, 1.02e-306], t$95$5, If[LessEqual[x$46$re, 3.8e-296], t$95$7, If[LessEqual[x$46$re, 7.4e-267], t$95$4, If[LessEqual[x$46$re, 2.7e-265], t$95$7, If[LessEqual[x$46$re, 2e-245], t$95$5, If[LessEqual[x$46$re, 1.02e-242], t$95$7, If[LessEqual[x$46$re, 9e-192], t$95$4, If[LessEqual[x$46$re, 1.3e-188], t$95$7, If[LessEqual[x$46$re, 4.2e-188], t$95$5, If[LessEqual[x$46$re, 3.1e-175], t$95$7, If[LessEqual[x$46$re, 5.8e-171], t$95$5, If[LessEqual[x$46$re, 3e-149], t$95$7, If[LessEqual[x$46$re, 9.8e-65], t$95$4, If[LessEqual[x$46$re, 5.5e+42], N[(t$95$2 * t$95$7), $MachinePrecision], If[LessEqual[x$46$re, 5.2e+132], t$95$4, If[LessEqual[x$46$re, 2.2e+133], t$95$7, If[LessEqual[x$46$re, 2.6e+252], t$95$4, If[LessEqual[x$46$re, 4e+253], t$95$7, If[LessEqual[x$46$re, 2.4e+284], t$95$5, If[Or[LessEqual[x$46$re, 2.5e+284], N[Not[LessEqual[x$46$re, 3.8e+293]], $MachinePrecision]], t$95$7, t$95$4]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x.re < -3.0000000000000002e121 or -1.06000000000000001e-38 < x.re < -1.7499999999999999e-47 or -1.89999999999999991e-204 < x.re < -2.3500000000000001e-231 or -8.9999999999999995e-260 < x.re < -4.999999999999985e-310

   1. Initial program 26.3%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 53.7%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around -inf 91.5%

      \[\leadsto e^{\log \color{blue}{\left(-1 \cdot x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 91.5%

         \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 91.5%

      \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -3.0000000000000002e121 < x.re < -1.06000000000000001e-38 or -1.7499999999999999e-47 < x.re < -2.0000000000000001e-115 or -4.4999999999999997e-154 < x.re < -1.89999999999999991e-204 or -2.3500000000000001e-231 < x.re < -8.9999999999999995e-260 or 1.02e-306 < x.re < 3.8000000000000002e-296 or 7.39999999999999971e-267 < x.re < 2.7000000000000002e-265 or 1.9999999999999999e-245 < x.re < 1.0199999999999999e-242 or 9.00000000000000048e-192 < x.re < 1.3e-188 or 4.1999999999999998e-188 < x.re < 3.09999999999999999e-175 or 5.7999999999999997e-171 < x.re < 3.0000000000000002e-149 or 5.2e132 < x.re < 2.2e133 or 2.60000000000000018e252 < x.re < 3.9999999999999997e253 or 2.4000000000000001e284 < x.re < 2.5e284 or 3.80000000000000014e293 < x.re

   1. Initial program 52.4%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 70.9%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in y.re around 0 83.1%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{1} \]

   if -2.0000000000000001e-115 < x.re < -4.4999999999999997e-154

   1. Initial program 66.7%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 67.0%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around 0 78.0%

      \[\leadsto e^{\log \color{blue}{\left(x.im + 0.5 \cdot \frac{{x.re}^{2}}{x.im}\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -4.999999999999985e-310 < x.re < 1.02e-306 or 2.7000000000000002e-265 < x.re < 1.9999999999999999e-245 or 1.3e-188 < x.re < 4.1999999999999998e-188 or 3.09999999999999999e-175 < x.re < 5.7999999999999997e-171 or 3.9999999999999997e253 < x.re < 2.4000000000000001e284

   1. Initial program 36.4%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 38.1%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around inf 90.9%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if 3.8000000000000002e-296 < x.re < 7.39999999999999971e-267 or 1.0199999999999999e-242 < x.re < 9.00000000000000048e-192 or 3.0000000000000002e-149 < x.re < 9.79999999999999929e-65 or 5.50000000000000001e42 < x.re < 5.2e132 or 2.2e133 < x.re < 2.60000000000000018e252 or 2.5e284 < x.re < 3.80000000000000014e293

   1. Initial program 39.5%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x.re around inf 65.3%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \color{blue}{x.re} \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

   4. Taylor expanded in x.re around inf 92.7%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log x.re \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]

   if 9.79999999999999929e-65 < x.re < 5.50000000000000001e42

   1. Initial program 71.4%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 90.5%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq -3 \cdot 10^{+121}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -1.06 \cdot 10^{-38}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -1.75 \cdot 10^{-47}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -2 \cdot 10^{-115}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -4.5 \cdot 10^{-154}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log \left(x.im + 0.5 \cdot \frac{{x.re}^{2}}{x.im}\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -1.9 \cdot 10^{-204}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -2.35 \cdot 10^{-231}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -9 \cdot 10^{-260}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -5 \cdot 10^{-310}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq 1.02 \cdot 10^{-306}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 3.8 \cdot 10^{-296}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 7.4 \cdot 10^{-267}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 2.7 \cdot 10^{-265}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2 \cdot 10^{-245}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.02 \cdot 10^{-242}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 9 \cdot 10^{-192}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 1.3 \cdot 10^{-188}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 4.2 \cdot 10^{-188}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 3.1 \cdot 10^{-175}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 5.8 \cdot 10^{-171}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 3 \cdot 10^{-149}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 9.8 \cdot 10^{-65}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 5.5 \cdot 10^{+42}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 5.2 \cdot 10^{+132}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.6 \cdot 10^{+252}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \mathbf{elif}\;x.re \leq 4 \cdot 10^{+253}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{+284}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.5 \cdot 10^{+284} \lor \neg \left(x.re \leq 3.8 \cdot 10^{+293}\right):\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} + y.im \cdot \log x.re\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ t_1 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_2 := t\_0 \cdot e^{y.re \cdot \log x.re - t\_1}\\ t_3 := t\_0 \cdot e^{y.re \cdot \log x.im - t\_1}\\ t_4 := e^{y.re \cdot \log \left(-x.re\right) - t\_1} \cdot t\_0\\ t_5 := e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - t\_1}\\ \mathbf{if}\;x.re \leq -1.45 \cdot 10^{+122}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq -2.4 \cdot 10^{-47}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq -3.4 \cdot 10^{-51}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq -4.3 \cdot 10^{-94}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq -5.3 \cdot 10^{-121}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq -4.5 \cdot 10^{-154}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq -2.9 \cdot 10^{-205}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq -2.05 \cdot 10^{-231}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq -1.95 \cdot 10^{-259}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x.re \leq 3 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 2.15 \cdot 10^{-299}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 1.8 \cdot 10^{-266}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 3.1 \cdot 10^{-261}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 1.85 \cdot 10^{-245}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 5.5 \cdot 10^{-238}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 2.95 \cdot 10^{-213}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 6.2 \cdot 10^{-204}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 7 \cdot 10^{-193}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 1.35 \cdot 10^{-188}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 7.6 \cdot 10^{-188}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 9.2 \cdot 10^{-176}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 6 \cdot 10^{-171}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 7.1 \cdot 10^{-122}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 5 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 1.55 \cdot 10^{-61}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 0.00035:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 6.4 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 2.1 \cdot 10^{+43}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 2 \cdot 10^{+132}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 7.5 \cdot 10^{+132}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x.re \leq 1.2 \cdot 10^{+176}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 2.7 \cdot 10^{+177}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 3.1 \cdot 10^{+227} \lor \neg \left(x.re \leq 3.2 \cdot 10^{+227}\right) \land \left(x.re \leq 2.6 \cdot 10^{+252} \lor \neg \left(x.re \leq 4 \cdot 10^{+253}\right) \land \left(x.re \leq 2.4 \cdot 10^{+284} \lor \neg \left(x.re \leq 2.5 \cdot 10^{+284}\right) \land x.re \leq 3.8 \cdot 10^{+293}\right)\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (cos (* y.re (atan2 x.im x.re))))
        (t_1 (* (atan2 x.im x.re) y.im))
        (t_2 (* t_0 (exp (- (* y.re (log x.re)) t_1))))
        (t_3 (* t_0 (exp (- (* y.re (log x.im)) t_1))))
        (t_4 (* (exp (- (* y.re (log (- x.re))) t_1)) t_0))
        (t_5
         (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) t_1))))
   (if (<= x.re -1.45e+122)
     t_4
     (if (<= x.re -2.4e-47)
       t_5
       (if (<= x.re -3.4e-51)
         t_4
         (if (<= x.re -4.3e-94)
           t_5
           (if (<= x.re -5.3e-121)
             t_4
             (if (<= x.re -4.5e-154)
               t_3
               (if (<= x.re -2.9e-205)
                 t_5
                 (if (<= x.re -2.05e-231)
                   t_4
                   (if (<= x.re -1.95e-259)
                     t_5
                     (if (<= x.re -5e-310)
                       t_4
                       (if (<= x.re 3e-304)
                         t_2
                         (if (<= x.re 2.15e-299)
                           t_5
                           (if (<= x.re 1.8e-266)
                             t_2
                             (if (<= x.re 3.1e-261)
                               t_5
                               (if (<= x.re 1.85e-245)
                                 t_2
                                 (if (<= x.re 5.5e-238)
                                   t_5
                                   (if (<= x.re 2.95e-213)
                                     t_2
                                     (if (<= x.re 6.2e-204)
                                       t_5
                                       (if (<= x.re 7e-193)
                                         t_2
                                         (if (<= x.re 1.35e-188)
                                           t_5
                                           (if (<= x.re 7.6e-188)
                                             t_2
                                             (if (<= x.re 9.2e-176)
                                               t_5
                                               (if (<= x.re 6e-171)
                                                 t_2
                                                 (if (<= x.re 7.1e-122)
                                                   t_5
                                                   (if (<= x.re 5e-66)
                                                     t_2
                                                     (if (<= x.re 1.55e-61)
                                                       t_5
                                                       (if (<= x.re 1.2e-35)
                                                         t_2
                                                         (if (<= x.re 0.00035)
                                                           t_5
                                                           (if (<=
                                                                x.re
                                                                6.4e+42)
                                                             t_2
                                                             (if (<=
                                                                  x.re
                                                                  2.1e+43)
                                                               t_5
                                                               (if (<=
                                                                    x.re
                                                                    2e+132)
                                                                 t_2
                                                                 (if (<=
                                                                      x.re
                                                                      7.5e+132)
                                                                   t_5
                                                                   (if (<=
                                                                        x.re
                                                                        1.2e+176)
                                                                     t_2
                                                                     (if (<=
                                                                          x.re
                                                                          2.7e+177)
                                                                       t_3
                                                                       (if (or (<=
                                                                                x.re
                                                                                3.1e+227)
                                                                               (and (not
                                                                                     (<=
                                                                                      x.re
                                                                                      3.2e+227))
                                                                                    (or (<=
                                                                                         x.re
                                                                                         2.6e+252)
                                                                                        (and (not
                                                                                              (<=
                                                                                               x.re
                                                                                               4e+253))
                                                                                             (or (<=
                                                                                                  x.re
                                                                                                  2.4e+284)
                                                                                                 (and (not
                                                                                                       (<=
                                                                                                        x.re
                                                                                                        2.5e+284))
                                                                                                      (<=
                                                                                                       x.re
                                                                                                       3.8e+293)))))))
                                                                         t_2
                                                                         t_5)))))))))))))))))))))))))))))))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = cos((y_46_re * atan2(x_46_im, x_46_re)));
	double t_1 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_2 = t_0 * exp(((y_46_re * log(x_46_re)) - t_1));
	double t_3 = t_0 * exp(((y_46_re * log(x_46_im)) - t_1));
	double t_4 = exp(((y_46_re * log(-x_46_re)) - t_1)) * t_0;
	double t_5 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_1));
	double tmp;
	if (x_46_re <= -1.45e+122) {
		tmp = t_4;
	} else if (x_46_re <= -2.4e-47) {
		tmp = t_5;
	} else if (x_46_re <= -3.4e-51) {
		tmp = t_4;
	} else if (x_46_re <= -4.3e-94) {
		tmp = t_5;
	} else if (x_46_re <= -5.3e-121) {
		tmp = t_4;
	} else if (x_46_re <= -4.5e-154) {
		tmp = t_3;
	} else if (x_46_re <= -2.9e-205) {
		tmp = t_5;
	} else if (x_46_re <= -2.05e-231) {
		tmp = t_4;
	} else if (x_46_re <= -1.95e-259) {
		tmp = t_5;
	} else if (x_46_re <= -5e-310) {
		tmp = t_4;
	} else if (x_46_re <= 3e-304) {
		tmp = t_2;
	} else if (x_46_re <= 2.15e-299) {
		tmp = t_5;
	} else if (x_46_re <= 1.8e-266) {
		tmp = t_2;
	} else if (x_46_re <= 3.1e-261) {
		tmp = t_5;
	} else if (x_46_re <= 1.85e-245) {
		tmp = t_2;
	} else if (x_46_re <= 5.5e-238) {
		tmp = t_5;
	} else if (x_46_re <= 2.95e-213) {
		tmp = t_2;
	} else if (x_46_re <= 6.2e-204) {
		tmp = t_5;
	} else if (x_46_re <= 7e-193) {
		tmp = t_2;
	} else if (x_46_re <= 1.35e-188) {
		tmp = t_5;
	} else if (x_46_re <= 7.6e-188) {
		tmp = t_2;
	} else if (x_46_re <= 9.2e-176) {
		tmp = t_5;
	} else if (x_46_re <= 6e-171) {
		tmp = t_2;
	} else if (x_46_re <= 7.1e-122) {
		tmp = t_5;
	} else if (x_46_re <= 5e-66) {
		tmp = t_2;
	} else if (x_46_re <= 1.55e-61) {
		tmp = t_5;
	} else if (x_46_re <= 1.2e-35) {
		tmp = t_2;
	} else if (x_46_re <= 0.00035) {
		tmp = t_5;
	} else if (x_46_re <= 6.4e+42) {
		tmp = t_2;
	} else if (x_46_re <= 2.1e+43) {
		tmp = t_5;
	} else if (x_46_re <= 2e+132) {
		tmp = t_2;
	} else if (x_46_re <= 7.5e+132) {
		tmp = t_5;
	} else if (x_46_re <= 1.2e+176) {
		tmp = t_2;
	} else if (x_46_re <= 2.7e+177) {
		tmp = t_3;
	} else if ((x_46_re <= 3.1e+227) || (!(x_46_re <= 3.2e+227) && ((x_46_re <= 2.6e+252) || (!(x_46_re <= 4e+253) && ((x_46_re <= 2.4e+284) || (!(x_46_re <= 2.5e+284) && (x_46_re <= 3.8e+293))))))) {
		tmp = t_2;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = cos((y_46re * atan2(x_46im, x_46re)))
    t_1 = atan2(x_46im, x_46re) * y_46im
    t_2 = t_0 * exp(((y_46re * log(x_46re)) - t_1))
    t_3 = t_0 * exp(((y_46re * log(x_46im)) - t_1))
    t_4 = exp(((y_46re * log(-x_46re)) - t_1)) * t_0
    t_5 = exp(((log(sqrt(((x_46re * x_46re) + (x_46im * x_46im)))) * y_46re) - t_1))
    if (x_46re <= (-1.45d+122)) then
        tmp = t_4
    else if (x_46re <= (-2.4d-47)) then
        tmp = t_5
    else if (x_46re <= (-3.4d-51)) then
        tmp = t_4
    else if (x_46re <= (-4.3d-94)) then
        tmp = t_5
    else if (x_46re <= (-5.3d-121)) then
        tmp = t_4
    else if (x_46re <= (-4.5d-154)) then
        tmp = t_3
    else if (x_46re <= (-2.9d-205)) then
        tmp = t_5
    else if (x_46re <= (-2.05d-231)) then
        tmp = t_4
    else if (x_46re <= (-1.95d-259)) then
        tmp = t_5
    else if (x_46re <= (-5d-310)) then
        tmp = t_4
    else if (x_46re <= 3d-304) then
        tmp = t_2
    else if (x_46re <= 2.15d-299) then
        tmp = t_5
    else if (x_46re <= 1.8d-266) then
        tmp = t_2
    else if (x_46re <= 3.1d-261) then
        tmp = t_5
    else if (x_46re <= 1.85d-245) then
        tmp = t_2
    else if (x_46re <= 5.5d-238) then
        tmp = t_5
    else if (x_46re <= 2.95d-213) then
        tmp = t_2
    else if (x_46re <= 6.2d-204) then
        tmp = t_5
    else if (x_46re <= 7d-193) then
        tmp = t_2
    else if (x_46re <= 1.35d-188) then
        tmp = t_5
    else if (x_46re <= 7.6d-188) then
        tmp = t_2
    else if (x_46re <= 9.2d-176) then
        tmp = t_5
    else if (x_46re <= 6d-171) then
        tmp = t_2
    else if (x_46re <= 7.1d-122) then
        tmp = t_5
    else if (x_46re <= 5d-66) then
        tmp = t_2
    else if (x_46re <= 1.55d-61) then
        tmp = t_5
    else if (x_46re <= 1.2d-35) then
        tmp = t_2
    else if (x_46re <= 0.00035d0) then
        tmp = t_5
    else if (x_46re <= 6.4d+42) then
        tmp = t_2
    else if (x_46re <= 2.1d+43) then
        tmp = t_5
    else if (x_46re <= 2d+132) then
        tmp = t_2
    else if (x_46re <= 7.5d+132) then
        tmp = t_5
    else if (x_46re <= 1.2d+176) then
        tmp = t_2
    else if (x_46re <= 2.7d+177) then
        tmp = t_3
    else if ((x_46re <= 3.1d+227) .or. (.not. (x_46re <= 3.2d+227)) .and. (x_46re <= 2.6d+252) .or. (.not. (x_46re <= 4d+253)) .and. (x_46re <= 2.4d+284) .or. (.not. (x_46re <= 2.5d+284)) .and. (x_46re <= 3.8d+293)) then
        tmp = t_2
    else
        tmp = t_5
    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 = Math.cos((y_46_re * Math.atan2(x_46_im, x_46_re)));
	double t_1 = Math.atan2(x_46_im, x_46_re) * y_46_im;
	double t_2 = t_0 * Math.exp(((y_46_re * Math.log(x_46_re)) - t_1));
	double t_3 = t_0 * Math.exp(((y_46_re * Math.log(x_46_im)) - t_1));
	double t_4 = Math.exp(((y_46_re * Math.log(-x_46_re)) - t_1)) * t_0;
	double t_5 = Math.exp(((Math.log(Math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_1));
	double tmp;
	if (x_46_re <= -1.45e+122) {
		tmp = t_4;
	} else if (x_46_re <= -2.4e-47) {
		tmp = t_5;
	} else if (x_46_re <= -3.4e-51) {
		tmp = t_4;
	} else if (x_46_re <= -4.3e-94) {
		tmp = t_5;
	} else if (x_46_re <= -5.3e-121) {
		tmp = t_4;
	} else if (x_46_re <= -4.5e-154) {
		tmp = t_3;
	} else if (x_46_re <= -2.9e-205) {
		tmp = t_5;
	} else if (x_46_re <= -2.05e-231) {
		tmp = t_4;
	} else if (x_46_re <= -1.95e-259) {
		tmp = t_5;
	} else if (x_46_re <= -5e-310) {
		tmp = t_4;
	} else if (x_46_re <= 3e-304) {
		tmp = t_2;
	} else if (x_46_re <= 2.15e-299) {
		tmp = t_5;
	} else if (x_46_re <= 1.8e-266) {
		tmp = t_2;
	} else if (x_46_re <= 3.1e-261) {
		tmp = t_5;
	} else if (x_46_re <= 1.85e-245) {
		tmp = t_2;
	} else if (x_46_re <= 5.5e-238) {
		tmp = t_5;
	} else if (x_46_re <= 2.95e-213) {
		tmp = t_2;
	} else if (x_46_re <= 6.2e-204) {
		tmp = t_5;
	} else if (x_46_re <= 7e-193) {
		tmp = t_2;
	} else if (x_46_re <= 1.35e-188) {
		tmp = t_5;
	} else if (x_46_re <= 7.6e-188) {
		tmp = t_2;
	} else if (x_46_re <= 9.2e-176) {
		tmp = t_5;
	} else if (x_46_re <= 6e-171) {
		tmp = t_2;
	} else if (x_46_re <= 7.1e-122) {
		tmp = t_5;
	} else if (x_46_re <= 5e-66) {
		tmp = t_2;
	} else if (x_46_re <= 1.55e-61) {
		tmp = t_5;
	} else if (x_46_re <= 1.2e-35) {
		tmp = t_2;
	} else if (x_46_re <= 0.00035) {
		tmp = t_5;
	} else if (x_46_re <= 6.4e+42) {
		tmp = t_2;
	} else if (x_46_re <= 2.1e+43) {
		tmp = t_5;
	} else if (x_46_re <= 2e+132) {
		tmp = t_2;
	} else if (x_46_re <= 7.5e+132) {
		tmp = t_5;
	} else if (x_46_re <= 1.2e+176) {
		tmp = t_2;
	} else if (x_46_re <= 2.7e+177) {
		tmp = t_3;
	} else if ((x_46_re <= 3.1e+227) || (!(x_46_re <= 3.2e+227) && ((x_46_re <= 2.6e+252) || (!(x_46_re <= 4e+253) && ((x_46_re <= 2.4e+284) || (!(x_46_re <= 2.5e+284) && (x_46_re <= 3.8e+293))))))) {
		tmp = t_2;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = math.cos((y_46_re * math.atan2(x_46_im, x_46_re)))
	t_1 = math.atan2(x_46_im, x_46_re) * y_46_im
	t_2 = t_0 * math.exp(((y_46_re * math.log(x_46_re)) - t_1))
	t_3 = t_0 * math.exp(((y_46_re * math.log(x_46_im)) - t_1))
	t_4 = math.exp(((y_46_re * math.log(-x_46_re)) - t_1)) * t_0
	t_5 = math.exp(((math.log(math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_1))
	tmp = 0
	if x_46_re <= -1.45e+122:
		tmp = t_4
	elif x_46_re <= -2.4e-47:
		tmp = t_5
	elif x_46_re <= -3.4e-51:
		tmp = t_4
	elif x_46_re <= -4.3e-94:
		tmp = t_5
	elif x_46_re <= -5.3e-121:
		tmp = t_4
	elif x_46_re <= -4.5e-154:
		tmp = t_3
	elif x_46_re <= -2.9e-205:
		tmp = t_5
	elif x_46_re <= -2.05e-231:
		tmp = t_4
	elif x_46_re <= -1.95e-259:
		tmp = t_5
	elif x_46_re <= -5e-310:
		tmp = t_4
	elif x_46_re <= 3e-304:
		tmp = t_2
	elif x_46_re <= 2.15e-299:
		tmp = t_5
	elif x_46_re <= 1.8e-266:
		tmp = t_2
	elif x_46_re <= 3.1e-261:
		tmp = t_5
	elif x_46_re <= 1.85e-245:
		tmp = t_2
	elif x_46_re <= 5.5e-238:
		tmp = t_5
	elif x_46_re <= 2.95e-213:
		tmp = t_2
	elif x_46_re <= 6.2e-204:
		tmp = t_5
	elif x_46_re <= 7e-193:
		tmp = t_2
	elif x_46_re <= 1.35e-188:
		tmp = t_5
	elif x_46_re <= 7.6e-188:
		tmp = t_2
	elif x_46_re <= 9.2e-176:
		tmp = t_5
	elif x_46_re <= 6e-171:
		tmp = t_2
	elif x_46_re <= 7.1e-122:
		tmp = t_5
	elif x_46_re <= 5e-66:
		tmp = t_2
	elif x_46_re <= 1.55e-61:
		tmp = t_5
	elif x_46_re <= 1.2e-35:
		tmp = t_2
	elif x_46_re <= 0.00035:
		tmp = t_5
	elif x_46_re <= 6.4e+42:
		tmp = t_2
	elif x_46_re <= 2.1e+43:
		tmp = t_5
	elif x_46_re <= 2e+132:
		tmp = t_2
	elif x_46_re <= 7.5e+132:
		tmp = t_5
	elif x_46_re <= 1.2e+176:
		tmp = t_2
	elif x_46_re <= 2.7e+177:
		tmp = t_3
	elif (x_46_re <= 3.1e+227) or (not (x_46_re <= 3.2e+227) and ((x_46_re <= 2.6e+252) or (not (x_46_re <= 4e+253) and ((x_46_re <= 2.4e+284) or (not (x_46_re <= 2.5e+284) and (x_46_re <= 3.8e+293)))))):
		tmp = t_2
	else:
		tmp = t_5
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = cos(Float64(y_46_re * atan(x_46_im, x_46_re)))
	t_1 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_2 = Float64(t_0 * exp(Float64(Float64(y_46_re * log(x_46_re)) - t_1)))
	t_3 = Float64(t_0 * exp(Float64(Float64(y_46_re * log(x_46_im)) - t_1)))
	t_4 = Float64(exp(Float64(Float64(y_46_re * log(Float64(-x_46_re))) - t_1)) * t_0)
	t_5 = exp(Float64(Float64(log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im)))) * y_46_re) - t_1))
	tmp = 0.0
	if (x_46_re <= -1.45e+122)
		tmp = t_4;
	elseif (x_46_re <= -2.4e-47)
		tmp = t_5;
	elseif (x_46_re <= -3.4e-51)
		tmp = t_4;
	elseif (x_46_re <= -4.3e-94)
		tmp = t_5;
	elseif (x_46_re <= -5.3e-121)
		tmp = t_4;
	elseif (x_46_re <= -4.5e-154)
		tmp = t_3;
	elseif (x_46_re <= -2.9e-205)
		tmp = t_5;
	elseif (x_46_re <= -2.05e-231)
		tmp = t_4;
	elseif (x_46_re <= -1.95e-259)
		tmp = t_5;
	elseif (x_46_re <= -5e-310)
		tmp = t_4;
	elseif (x_46_re <= 3e-304)
		tmp = t_2;
	elseif (x_46_re <= 2.15e-299)
		tmp = t_5;
	elseif (x_46_re <= 1.8e-266)
		tmp = t_2;
	elseif (x_46_re <= 3.1e-261)
		tmp = t_5;
	elseif (x_46_re <= 1.85e-245)
		tmp = t_2;
	elseif (x_46_re <= 5.5e-238)
		tmp = t_5;
	elseif (x_46_re <= 2.95e-213)
		tmp = t_2;
	elseif (x_46_re <= 6.2e-204)
		tmp = t_5;
	elseif (x_46_re <= 7e-193)
		tmp = t_2;
	elseif (x_46_re <= 1.35e-188)
		tmp = t_5;
	elseif (x_46_re <= 7.6e-188)
		tmp = t_2;
	elseif (x_46_re <= 9.2e-176)
		tmp = t_5;
	elseif (x_46_re <= 6e-171)
		tmp = t_2;
	elseif (x_46_re <= 7.1e-122)
		tmp = t_5;
	elseif (x_46_re <= 5e-66)
		tmp = t_2;
	elseif (x_46_re <= 1.55e-61)
		tmp = t_5;
	elseif (x_46_re <= 1.2e-35)
		tmp = t_2;
	elseif (x_46_re <= 0.00035)
		tmp = t_5;
	elseif (x_46_re <= 6.4e+42)
		tmp = t_2;
	elseif (x_46_re <= 2.1e+43)
		tmp = t_5;
	elseif (x_46_re <= 2e+132)
		tmp = t_2;
	elseif (x_46_re <= 7.5e+132)
		tmp = t_5;
	elseif (x_46_re <= 1.2e+176)
		tmp = t_2;
	elseif (x_46_re <= 2.7e+177)
		tmp = t_3;
	elseif ((x_46_re <= 3.1e+227) || (!(x_46_re <= 3.2e+227) && ((x_46_re <= 2.6e+252) || (!(x_46_re <= 4e+253) && ((x_46_re <= 2.4e+284) || (!(x_46_re <= 2.5e+284) && (x_46_re <= 3.8e+293)))))))
		tmp = t_2;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = cos((y_46_re * atan2(x_46_im, x_46_re)));
	t_1 = atan2(x_46_im, x_46_re) * y_46_im;
	t_2 = t_0 * exp(((y_46_re * log(x_46_re)) - t_1));
	t_3 = t_0 * exp(((y_46_re * log(x_46_im)) - t_1));
	t_4 = exp(((y_46_re * log(-x_46_re)) - t_1)) * t_0;
	t_5 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_1));
	tmp = 0.0;
	if (x_46_re <= -1.45e+122)
		tmp = t_4;
	elseif (x_46_re <= -2.4e-47)
		tmp = t_5;
	elseif (x_46_re <= -3.4e-51)
		tmp = t_4;
	elseif (x_46_re <= -4.3e-94)
		tmp = t_5;
	elseif (x_46_re <= -5.3e-121)
		tmp = t_4;
	elseif (x_46_re <= -4.5e-154)
		tmp = t_3;
	elseif (x_46_re <= -2.9e-205)
		tmp = t_5;
	elseif (x_46_re <= -2.05e-231)
		tmp = t_4;
	elseif (x_46_re <= -1.95e-259)
		tmp = t_5;
	elseif (x_46_re <= -5e-310)
		tmp = t_4;
	elseif (x_46_re <= 3e-304)
		tmp = t_2;
	elseif (x_46_re <= 2.15e-299)
		tmp = t_5;
	elseif (x_46_re <= 1.8e-266)
		tmp = t_2;
	elseif (x_46_re <= 3.1e-261)
		tmp = t_5;
	elseif (x_46_re <= 1.85e-245)
		tmp = t_2;
	elseif (x_46_re <= 5.5e-238)
		tmp = t_5;
	elseif (x_46_re <= 2.95e-213)
		tmp = t_2;
	elseif (x_46_re <= 6.2e-204)
		tmp = t_5;
	elseif (x_46_re <= 7e-193)
		tmp = t_2;
	elseif (x_46_re <= 1.35e-188)
		tmp = t_5;
	elseif (x_46_re <= 7.6e-188)
		tmp = t_2;
	elseif (x_46_re <= 9.2e-176)
		tmp = t_5;
	elseif (x_46_re <= 6e-171)
		tmp = t_2;
	elseif (x_46_re <= 7.1e-122)
		tmp = t_5;
	elseif (x_46_re <= 5e-66)
		tmp = t_2;
	elseif (x_46_re <= 1.55e-61)
		tmp = t_5;
	elseif (x_46_re <= 1.2e-35)
		tmp = t_2;
	elseif (x_46_re <= 0.00035)
		tmp = t_5;
	elseif (x_46_re <= 6.4e+42)
		tmp = t_2;
	elseif (x_46_re <= 2.1e+43)
		tmp = t_5;
	elseif (x_46_re <= 2e+132)
		tmp = t_2;
	elseif (x_46_re <= 7.5e+132)
		tmp = t_5;
	elseif (x_46_re <= 1.2e+176)
		tmp = t_2;
	elseif (x_46_re <= 2.7e+177)
		tmp = t_3;
	elseif ((x_46_re <= 3.1e+227) || (~((x_46_re <= 3.2e+227)) && ((x_46_re <= 2.6e+252) || (~((x_46_re <= 4e+253)) && ((x_46_re <= 2.4e+284) || (~((x_46_re <= 2.5e+284)) && (x_46_re <= 3.8e+293)))))))
		tmp = t_2;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[Cos[N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * N[Exp[N[(N[(y$46$re * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 * N[Exp[N[(N[(y$46$re * N[Log[x$46$im], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[Exp[N[(N[(y$46$re * N[Log[(-x$46$re)], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[Exp[N[(N[(N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * y$46$re), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x$46$re, -1.45e+122], t$95$4, If[LessEqual[x$46$re, -2.4e-47], t$95$5, If[LessEqual[x$46$re, -3.4e-51], t$95$4, If[LessEqual[x$46$re, -4.3e-94], t$95$5, If[LessEqual[x$46$re, -5.3e-121], t$95$4, If[LessEqual[x$46$re, -4.5e-154], t$95$3, If[LessEqual[x$46$re, -2.9e-205], t$95$5, If[LessEqual[x$46$re, -2.05e-231], t$95$4, If[LessEqual[x$46$re, -1.95e-259], t$95$5, If[LessEqual[x$46$re, -5e-310], t$95$4, If[LessEqual[x$46$re, 3e-304], t$95$2, If[LessEqual[x$46$re, 2.15e-299], t$95$5, If[LessEqual[x$46$re, 1.8e-266], t$95$2, If[LessEqual[x$46$re, 3.1e-261], t$95$5, If[LessEqual[x$46$re, 1.85e-245], t$95$2, If[LessEqual[x$46$re, 5.5e-238], t$95$5, If[LessEqual[x$46$re, 2.95e-213], t$95$2, If[LessEqual[x$46$re, 6.2e-204], t$95$5, If[LessEqual[x$46$re, 7e-193], t$95$2, If[LessEqual[x$46$re, 1.35e-188], t$95$5, If[LessEqual[x$46$re, 7.6e-188], t$95$2, If[LessEqual[x$46$re, 9.2e-176], t$95$5, If[LessEqual[x$46$re, 6e-171], t$95$2, If[LessEqual[x$46$re, 7.1e-122], t$95$5, If[LessEqual[x$46$re, 5e-66], t$95$2, If[LessEqual[x$46$re, 1.55e-61], t$95$5, If[LessEqual[x$46$re, 1.2e-35], t$95$2, If[LessEqual[x$46$re, 0.00035], t$95$5, If[LessEqual[x$46$re, 6.4e+42], t$95$2, If[LessEqual[x$46$re, 2.1e+43], t$95$5, If[LessEqual[x$46$re, 2e+132], t$95$2, If[LessEqual[x$46$re, 7.5e+132], t$95$5, If[LessEqual[x$46$re, 1.2e+176], t$95$2, If[LessEqual[x$46$re, 2.7e+177], t$95$3, If[Or[LessEqual[x$46$re, 3.1e+227], And[N[Not[LessEqual[x$46$re, 3.2e+227]], $MachinePrecision], Or[LessEqual[x$46$re, 2.6e+252], And[N[Not[LessEqual[x$46$re, 4e+253]], $MachinePrecision], Or[LessEqual[x$46$re, 2.4e+284], And[N[Not[LessEqual[x$46$re, 2.5e+284]], $MachinePrecision], LessEqual[x$46$re, 3.8e+293]]]]]]], t$95$2, t$95$5]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x.re < -1.45e122 or -2.3999999999999999e-47 < x.re < -3.40000000000000003e-51 or -4.2999999999999998e-94 < x.re < -5.2999999999999996e-121 or -2.90000000000000018e-205 < x.re < -2.0500000000000001e-231 or -1.95000000000000008e-259 < x.re < -4.999999999999985e-310

   1. Initial program 29.7%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 57.2%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around -inf 90.9%

      \[\leadsto e^{\log \color{blue}{\left(-1 \cdot x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 90.9%

         \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 90.9%

      \[\leadsto e^{\log \color{blue}{\left(-x.re\right)} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -1.45e122 < x.re < -2.3999999999999999e-47 or -3.40000000000000003e-51 < x.re < -4.2999999999999998e-94 or -4.4999999999999997e-154 < x.re < -2.90000000000000018e-205 or -2.0500000000000001e-231 < x.re < -1.95000000000000008e-259 or 3.0000000000000001e-304 < x.re < 2.1499999999999999e-299 or 1.8e-266 < x.re < 3.0999999999999998e-261 or 1.8500000000000001e-245 < x.re < 5.49999999999999995e-238 or 2.9499999999999999e-213 < x.re < 6.1999999999999998e-204 or 7.00000000000000009e-193 < x.re < 1.35e-188 or 7.599999999999999e-188 < x.re < 9.2000000000000005e-176 or 5.9999999999999999e-171 < x.re < 7.09999999999999955e-122 or 4.99999999999999962e-66 < x.re < 1.54999999999999997e-61 or 1.2000000000000001e-35 < x.re < 3.49999999999999996e-4 or 6.40000000000000004e42 < x.re < 2.10000000000000002e43 or 1.99999999999999998e132 < x.re < 7.50000000000000017e132 or 3.0999999999999999e227 < x.re < 3.19999999999999988e227 or 2.60000000000000018e252 < x.re < 3.9999999999999997e253 or 2.4000000000000001e284 < x.re < 2.5e284 or 3.80000000000000014e293 < x.re

   1. Initial program 51.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 68.9%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in y.re around 0 79.3%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{1} \]

   if -5.2999999999999996e-121 < x.re < -4.4999999999999997e-154 or 1.2000000000000001e176 < x.re < 2.69999999999999991e177

   1. Initial program 60.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 70.6%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around 0 82.0%

      \[\leadsto e^{\color{blue}{y.re \cdot \log x.im} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. *-commutative 82.0%

         \[\leadsto e^{\color{blue}{\log x.im \cdot y.re} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 82.0%

      \[\leadsto e^{\color{blue}{\log x.im \cdot y.re} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if -4.999999999999985e-310 < x.re < 3.0000000000000001e-304 or 2.1499999999999999e-299 < x.re < 1.8e-266 or 3.0999999999999998e-261 < x.re < 1.8500000000000001e-245 or 5.49999999999999995e-238 < x.re < 2.9499999999999999e-213 or 6.1999999999999998e-204 < x.re < 7.00000000000000009e-193 or 1.35e-188 < x.re < 7.599999999999999e-188 or 9.2000000000000005e-176 < x.re < 5.9999999999999999e-171 or 7.09999999999999955e-122 < x.re < 4.99999999999999962e-66 or 1.54999999999999997e-61 < x.re < 1.2000000000000001e-35 or 3.49999999999999996e-4 < x.re < 6.40000000000000004e42 or 2.10000000000000002e43 < x.re < 1.99999999999999998e132 or 7.50000000000000017e132 < x.re < 1.2000000000000001e176 or 2.69999999999999991e177 < x.re < 3.0999999999999999e227 or 3.19999999999999988e227 < x.re < 2.60000000000000018e252 or 3.9999999999999997e253 < x.re < 2.4000000000000001e284 or 2.5e284 < x.re < 3.80000000000000014e293

   1. Initial program 45.3%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 63.7%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around inf 89.7%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq -1.45 \cdot 10^{+122}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -2.4 \cdot 10^{-47}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -3.4 \cdot 10^{-51}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -4.3 \cdot 10^{-94}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -5.3 \cdot 10^{-121}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -4.5 \cdot 10^{-154}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.im - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -2.9 \cdot 10^{-205}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -2.05 \cdot 10^{-231}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq -1.95 \cdot 10^{-259}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq -5 \cdot 10^{-310}:\\ \;\;\;\;e^{y.re \cdot \log \left(-x.re\right) - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{elif}\;x.re \leq 3 \cdot 10^{-304}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.15 \cdot 10^{-299}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.8 \cdot 10^{-266}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 3.1 \cdot 10^{-261}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.85 \cdot 10^{-245}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 5.5 \cdot 10^{-238}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.95 \cdot 10^{-213}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 6.2 \cdot 10^{-204}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 7 \cdot 10^{-193}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.35 \cdot 10^{-188}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 7.6 \cdot 10^{-188}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 9.2 \cdot 10^{-176}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 6 \cdot 10^{-171}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 7.1 \cdot 10^{-122}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 5 \cdot 10^{-66}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.55 \cdot 10^{-61}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 0.00035:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 6.4 \cdot 10^{+42}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.1 \cdot 10^{+43}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2 \cdot 10^{+132}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 7.5 \cdot 10^{+132}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.2 \cdot 10^{+176}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.7 \cdot 10^{+177}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.im - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 3.1 \cdot 10^{+227} \lor \neg \left(x.re \leq 3.2 \cdot 10^{+227}\right) \land \left(x.re \leq 2.6 \cdot 10^{+252} \lor \neg \left(x.re \leq 4 \cdot 10^{+253}\right) \land \left(x.re \leq 2.4 \cdot 10^{+284} \lor \neg \left(x.re \leq 2.5 \cdot 10^{+284}\right) \land x.re \leq 3.8 \cdot 10^{+293}\right)\right):\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_1 := \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ t_2 := e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - t\_0}\\ t_3 := t\_1 \cdot e^{y.re \cdot \log x.re - t\_0}\\ \mathbf{if}\;x.re \leq 6.5 \cdot 10^{-294}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 2.15 \cdot 10^{-246}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 7.5 \cdot 10^{-239}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 2.95 \cdot 10^{-213}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 5.4 \cdot 10^{-201}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 2.1 \cdot 10^{-195}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 1.4 \cdot 10^{-188}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 2 \cdot 10^{-188}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 9.6 \cdot 10^{-175}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 5 \cdot 10^{-171}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 9.5 \cdot 10^{-122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 2.9 \cdot 10^{-65}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 1.6 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 8 \cdot 10^{-38}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 0.1:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 6.4 \cdot 10^{+42}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 1.92 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 7 \cdot 10^{+132}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 7.5 \cdot 10^{+132}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x.re \leq 1.2 \cdot 10^{+176}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x.re \leq 2.7 \cdot 10^{+177}:\\ \;\;\;\;t\_1 \cdot e^{y.re \cdot \log x.im - t\_0}\\ \mathbf{elif}\;x.re \leq 3.1 \cdot 10^{+227} \lor \neg \left(x.re \leq 3.2 \cdot 10^{+227}\right) \land \left(x.re \leq 2.6 \cdot 10^{+252} \lor \neg \left(x.re \leq 4 \cdot 10^{+253}\right) \land \left(x.re \leq 2.4 \cdot 10^{+284} \lor \neg \left(x.re \leq 2.5 \cdot 10^{+284}\right) \land x.re \leq 3.8 \cdot 10^{+293}\right)\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* (atan2 x.im x.re) y.im))
        (t_1 (cos (* y.re (atan2 x.im x.re))))
        (t_2
         (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) t_0)))
        (t_3 (* t_1 (exp (- (* y.re (log x.re)) t_0)))))
   (if (<= x.re 6.5e-294)
     t_2
     (if (<= x.re 2.15e-246)
       t_3
       (if (<= x.re 7.5e-239)
         t_2
         (if (<= x.re 2.95e-213)
           t_3
           (if (<= x.re 5.4e-201)
             t_2
             (if (<= x.re 2.1e-195)
               t_3
               (if (<= x.re 1.4e-188)
                 t_2
                 (if (<= x.re 2e-188)
                   t_3
                   (if (<= x.re 9.6e-175)
                     t_2
                     (if (<= x.re 5e-171)
                       t_3
                       (if (<= x.re 9.5e-122)
                         t_2
                         (if (<= x.re 2.9e-65)
                           t_3
                           (if (<= x.re 1.6e-59)
                             t_2
                             (if (<= x.re 8e-38)
                               t_3
                               (if (<= x.re 0.1)
                                 t_2
                                 (if (<= x.re 6.4e+42)
                                   t_3
                                   (if (<= x.re 1.92e+43)
                                     t_2
                                     (if (<= x.re 7e+132)
                                       t_3
                                       (if (<= x.re 7.5e+132)
                                         t_2
                                         (if (<= x.re 1.2e+176)
                                           t_3
                                           (if (<= x.re 2.7e+177)
                                             (*
                                              t_1
                                              (exp
                                               (- (* y.re (log x.im)) t_0)))
                                             (if (or (<= x.re 3.1e+227)
                                                     (and (not
                                                           (<= x.re 3.2e+227))
                                                          (or (<=
                                                               x.re
                                                               2.6e+252)
                                                              (and (not
                                                                    (<=
                                                                     x.re
                                                                     4e+253))
                                                                   (or (<=
                                                                        x.re
                                                                        2.4e+284)
                                                                       (and (not
                                                                             (<=
                                                                              x.re
                                                                              2.5e+284))
                                                                            (<=
                                                                             x.re
                                                                             3.8e+293)))))))
                                               t_3
                                               t_2))))))))))))))))))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_1 = cos((y_46_re * atan2(x_46_im, x_46_re)));
	double t_2 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_0));
	double t_3 = t_1 * exp(((y_46_re * log(x_46_re)) - t_0));
	double tmp;
	if (x_46_re <= 6.5e-294) {
		tmp = t_2;
	} else if (x_46_re <= 2.15e-246) {
		tmp = t_3;
	} else if (x_46_re <= 7.5e-239) {
		tmp = t_2;
	} else if (x_46_re <= 2.95e-213) {
		tmp = t_3;
	} else if (x_46_re <= 5.4e-201) {
		tmp = t_2;
	} else if (x_46_re <= 2.1e-195) {
		tmp = t_3;
	} else if (x_46_re <= 1.4e-188) {
		tmp = t_2;
	} else if (x_46_re <= 2e-188) {
		tmp = t_3;
	} else if (x_46_re <= 9.6e-175) {
		tmp = t_2;
	} else if (x_46_re <= 5e-171) {
		tmp = t_3;
	} else if (x_46_re <= 9.5e-122) {
		tmp = t_2;
	} else if (x_46_re <= 2.9e-65) {
		tmp = t_3;
	} else if (x_46_re <= 1.6e-59) {
		tmp = t_2;
	} else if (x_46_re <= 8e-38) {
		tmp = t_3;
	} else if (x_46_re <= 0.1) {
		tmp = t_2;
	} else if (x_46_re <= 6.4e+42) {
		tmp = t_3;
	} else if (x_46_re <= 1.92e+43) {
		tmp = t_2;
	} else if (x_46_re <= 7e+132) {
		tmp = t_3;
	} else if (x_46_re <= 7.5e+132) {
		tmp = t_2;
	} else if (x_46_re <= 1.2e+176) {
		tmp = t_3;
	} else if (x_46_re <= 2.7e+177) {
		tmp = t_1 * exp(((y_46_re * log(x_46_im)) - t_0));
	} else if ((x_46_re <= 3.1e+227) || (!(x_46_re <= 3.2e+227) && ((x_46_re <= 2.6e+252) || (!(x_46_re <= 4e+253) && ((x_46_re <= 2.4e+284) || (!(x_46_re <= 2.5e+284) && (x_46_re <= 3.8e+293))))))) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = atan2(x_46im, x_46re) * y_46im
    t_1 = cos((y_46re * atan2(x_46im, x_46re)))
    t_2 = exp(((log(sqrt(((x_46re * x_46re) + (x_46im * x_46im)))) * y_46re) - t_0))
    t_3 = t_1 * exp(((y_46re * log(x_46re)) - t_0))
    if (x_46re <= 6.5d-294) then
        tmp = t_2
    else if (x_46re <= 2.15d-246) then
        tmp = t_3
    else if (x_46re <= 7.5d-239) then
        tmp = t_2
    else if (x_46re <= 2.95d-213) then
        tmp = t_3
    else if (x_46re <= 5.4d-201) then
        tmp = t_2
    else if (x_46re <= 2.1d-195) then
        tmp = t_3
    else if (x_46re <= 1.4d-188) then
        tmp = t_2
    else if (x_46re <= 2d-188) then
        tmp = t_3
    else if (x_46re <= 9.6d-175) then
        tmp = t_2
    else if (x_46re <= 5d-171) then
        tmp = t_3
    else if (x_46re <= 9.5d-122) then
        tmp = t_2
    else if (x_46re <= 2.9d-65) then
        tmp = t_3
    else if (x_46re <= 1.6d-59) then
        tmp = t_2
    else if (x_46re <= 8d-38) then
        tmp = t_3
    else if (x_46re <= 0.1d0) then
        tmp = t_2
    else if (x_46re <= 6.4d+42) then
        tmp = t_3
    else if (x_46re <= 1.92d+43) then
        tmp = t_2
    else if (x_46re <= 7d+132) then
        tmp = t_3
    else if (x_46re <= 7.5d+132) then
        tmp = t_2
    else if (x_46re <= 1.2d+176) then
        tmp = t_3
    else if (x_46re <= 2.7d+177) then
        tmp = t_1 * exp(((y_46re * log(x_46im)) - t_0))
    else if ((x_46re <= 3.1d+227) .or. (.not. (x_46re <= 3.2d+227)) .and. (x_46re <= 2.6d+252) .or. (.not. (x_46re <= 4d+253)) .and. (x_46re <= 2.4d+284) .or. (.not. (x_46re <= 2.5d+284)) .and. (x_46re <= 3.8d+293)) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = Math.atan2(x_46_im, x_46_re) * y_46_im;
	double t_1 = Math.cos((y_46_re * Math.atan2(x_46_im, x_46_re)));
	double t_2 = Math.exp(((Math.log(Math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_0));
	double t_3 = t_1 * Math.exp(((y_46_re * Math.log(x_46_re)) - t_0));
	double tmp;
	if (x_46_re <= 6.5e-294) {
		tmp = t_2;
	} else if (x_46_re <= 2.15e-246) {
		tmp = t_3;
	} else if (x_46_re <= 7.5e-239) {
		tmp = t_2;
	} else if (x_46_re <= 2.95e-213) {
		tmp = t_3;
	} else if (x_46_re <= 5.4e-201) {
		tmp = t_2;
	} else if (x_46_re <= 2.1e-195) {
		tmp = t_3;
	} else if (x_46_re <= 1.4e-188) {
		tmp = t_2;
	} else if (x_46_re <= 2e-188) {
		tmp = t_3;
	} else if (x_46_re <= 9.6e-175) {
		tmp = t_2;
	} else if (x_46_re <= 5e-171) {
		tmp = t_3;
	} else if (x_46_re <= 9.5e-122) {
		tmp = t_2;
	} else if (x_46_re <= 2.9e-65) {
		tmp = t_3;
	} else if (x_46_re <= 1.6e-59) {
		tmp = t_2;
	} else if (x_46_re <= 8e-38) {
		tmp = t_3;
	} else if (x_46_re <= 0.1) {
		tmp = t_2;
	} else if (x_46_re <= 6.4e+42) {
		tmp = t_3;
	} else if (x_46_re <= 1.92e+43) {
		tmp = t_2;
	} else if (x_46_re <= 7e+132) {
		tmp = t_3;
	} else if (x_46_re <= 7.5e+132) {
		tmp = t_2;
	} else if (x_46_re <= 1.2e+176) {
		tmp = t_3;
	} else if (x_46_re <= 2.7e+177) {
		tmp = t_1 * Math.exp(((y_46_re * Math.log(x_46_im)) - t_0));
	} else if ((x_46_re <= 3.1e+227) || (!(x_46_re <= 3.2e+227) && ((x_46_re <= 2.6e+252) || (!(x_46_re <= 4e+253) && ((x_46_re <= 2.4e+284) || (!(x_46_re <= 2.5e+284) && (x_46_re <= 3.8e+293))))))) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = math.atan2(x_46_im, x_46_re) * y_46_im
	t_1 = math.cos((y_46_re * math.atan2(x_46_im, x_46_re)))
	t_2 = math.exp(((math.log(math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_0))
	t_3 = t_1 * math.exp(((y_46_re * math.log(x_46_re)) - t_0))
	tmp = 0
	if x_46_re <= 6.5e-294:
		tmp = t_2
	elif x_46_re <= 2.15e-246:
		tmp = t_3
	elif x_46_re <= 7.5e-239:
		tmp = t_2
	elif x_46_re <= 2.95e-213:
		tmp = t_3
	elif x_46_re <= 5.4e-201:
		tmp = t_2
	elif x_46_re <= 2.1e-195:
		tmp = t_3
	elif x_46_re <= 1.4e-188:
		tmp = t_2
	elif x_46_re <= 2e-188:
		tmp = t_3
	elif x_46_re <= 9.6e-175:
		tmp = t_2
	elif x_46_re <= 5e-171:
		tmp = t_3
	elif x_46_re <= 9.5e-122:
		tmp = t_2
	elif x_46_re <= 2.9e-65:
		tmp = t_3
	elif x_46_re <= 1.6e-59:
		tmp = t_2
	elif x_46_re <= 8e-38:
		tmp = t_3
	elif x_46_re <= 0.1:
		tmp = t_2
	elif x_46_re <= 6.4e+42:
		tmp = t_3
	elif x_46_re <= 1.92e+43:
		tmp = t_2
	elif x_46_re <= 7e+132:
		tmp = t_3
	elif x_46_re <= 7.5e+132:
		tmp = t_2
	elif x_46_re <= 1.2e+176:
		tmp = t_3
	elif x_46_re <= 2.7e+177:
		tmp = t_1 * math.exp(((y_46_re * math.log(x_46_im)) - t_0))
	elif (x_46_re <= 3.1e+227) or (not (x_46_re <= 3.2e+227) and ((x_46_re <= 2.6e+252) or (not (x_46_re <= 4e+253) and ((x_46_re <= 2.4e+284) or (not (x_46_re <= 2.5e+284) and (x_46_re <= 3.8e+293)))))):
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_1 = cos(Float64(y_46_re * atan(x_46_im, x_46_re)))
	t_2 = exp(Float64(Float64(log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im)))) * y_46_re) - t_0))
	t_3 = Float64(t_1 * exp(Float64(Float64(y_46_re * log(x_46_re)) - t_0)))
	tmp = 0.0
	if (x_46_re <= 6.5e-294)
		tmp = t_2;
	elseif (x_46_re <= 2.15e-246)
		tmp = t_3;
	elseif (x_46_re <= 7.5e-239)
		tmp = t_2;
	elseif (x_46_re <= 2.95e-213)
		tmp = t_3;
	elseif (x_46_re <= 5.4e-201)
		tmp = t_2;
	elseif (x_46_re <= 2.1e-195)
		tmp = t_3;
	elseif (x_46_re <= 1.4e-188)
		tmp = t_2;
	elseif (x_46_re <= 2e-188)
		tmp = t_3;
	elseif (x_46_re <= 9.6e-175)
		tmp = t_2;
	elseif (x_46_re <= 5e-171)
		tmp = t_3;
	elseif (x_46_re <= 9.5e-122)
		tmp = t_2;
	elseif (x_46_re <= 2.9e-65)
		tmp = t_3;
	elseif (x_46_re <= 1.6e-59)
		tmp = t_2;
	elseif (x_46_re <= 8e-38)
		tmp = t_3;
	elseif (x_46_re <= 0.1)
		tmp = t_2;
	elseif (x_46_re <= 6.4e+42)
		tmp = t_3;
	elseif (x_46_re <= 1.92e+43)
		tmp = t_2;
	elseif (x_46_re <= 7e+132)
		tmp = t_3;
	elseif (x_46_re <= 7.5e+132)
		tmp = t_2;
	elseif (x_46_re <= 1.2e+176)
		tmp = t_3;
	elseif (x_46_re <= 2.7e+177)
		tmp = Float64(t_1 * exp(Float64(Float64(y_46_re * log(x_46_im)) - t_0)));
	elseif ((x_46_re <= 3.1e+227) || (!(x_46_re <= 3.2e+227) && ((x_46_re <= 2.6e+252) || (!(x_46_re <= 4e+253) && ((x_46_re <= 2.4e+284) || (!(x_46_re <= 2.5e+284) && (x_46_re <= 3.8e+293)))))))
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = atan2(x_46_im, x_46_re) * y_46_im;
	t_1 = cos((y_46_re * atan2(x_46_im, x_46_re)));
	t_2 = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_0));
	t_3 = t_1 * exp(((y_46_re * log(x_46_re)) - t_0));
	tmp = 0.0;
	if (x_46_re <= 6.5e-294)
		tmp = t_2;
	elseif (x_46_re <= 2.15e-246)
		tmp = t_3;
	elseif (x_46_re <= 7.5e-239)
		tmp = t_2;
	elseif (x_46_re <= 2.95e-213)
		tmp = t_3;
	elseif (x_46_re <= 5.4e-201)
		tmp = t_2;
	elseif (x_46_re <= 2.1e-195)
		tmp = t_3;
	elseif (x_46_re <= 1.4e-188)
		tmp = t_2;
	elseif (x_46_re <= 2e-188)
		tmp = t_3;
	elseif (x_46_re <= 9.6e-175)
		tmp = t_2;
	elseif (x_46_re <= 5e-171)
		tmp = t_3;
	elseif (x_46_re <= 9.5e-122)
		tmp = t_2;
	elseif (x_46_re <= 2.9e-65)
		tmp = t_3;
	elseif (x_46_re <= 1.6e-59)
		tmp = t_2;
	elseif (x_46_re <= 8e-38)
		tmp = t_3;
	elseif (x_46_re <= 0.1)
		tmp = t_2;
	elseif (x_46_re <= 6.4e+42)
		tmp = t_3;
	elseif (x_46_re <= 1.92e+43)
		tmp = t_2;
	elseif (x_46_re <= 7e+132)
		tmp = t_3;
	elseif (x_46_re <= 7.5e+132)
		tmp = t_2;
	elseif (x_46_re <= 1.2e+176)
		tmp = t_3;
	elseif (x_46_re <= 2.7e+177)
		tmp = t_1 * exp(((y_46_re * log(x_46_im)) - t_0));
	elseif ((x_46_re <= 3.1e+227) || (~((x_46_re <= 3.2e+227)) && ((x_46_re <= 2.6e+252) || (~((x_46_re <= 4e+253)) && ((x_46_re <= 2.4e+284) || (~((x_46_re <= 2.5e+284)) && (x_46_re <= 3.8e+293)))))))
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$1 = N[Cos[N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(N[(N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * y$46$re), $MachinePrecision] - t$95$0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 * N[Exp[N[(N[(y$46$re * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x$46$re, 6.5e-294], t$95$2, If[LessEqual[x$46$re, 2.15e-246], t$95$3, If[LessEqual[x$46$re, 7.5e-239], t$95$2, If[LessEqual[x$46$re, 2.95e-213], t$95$3, If[LessEqual[x$46$re, 5.4e-201], t$95$2, If[LessEqual[x$46$re, 2.1e-195], t$95$3, If[LessEqual[x$46$re, 1.4e-188], t$95$2, If[LessEqual[x$46$re, 2e-188], t$95$3, If[LessEqual[x$46$re, 9.6e-175], t$95$2, If[LessEqual[x$46$re, 5e-171], t$95$3, If[LessEqual[x$46$re, 9.5e-122], t$95$2, If[LessEqual[x$46$re, 2.9e-65], t$95$3, If[LessEqual[x$46$re, 1.6e-59], t$95$2, If[LessEqual[x$46$re, 8e-38], t$95$3, If[LessEqual[x$46$re, 0.1], t$95$2, If[LessEqual[x$46$re, 6.4e+42], t$95$3, If[LessEqual[x$46$re, 1.92e+43], t$95$2, If[LessEqual[x$46$re, 7e+132], t$95$3, If[LessEqual[x$46$re, 7.5e+132], t$95$2, If[LessEqual[x$46$re, 1.2e+176], t$95$3, If[LessEqual[x$46$re, 2.7e+177], N[(t$95$1 * N[Exp[N[(N[(y$46$re * N[Log[x$46$im], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x$46$re, 3.1e+227], And[N[Not[LessEqual[x$46$re, 3.2e+227]], $MachinePrecision], Or[LessEqual[x$46$re, 2.6e+252], And[N[Not[LessEqual[x$46$re, 4e+253]], $MachinePrecision], Or[LessEqual[x$46$re, 2.4e+284], And[N[Not[LessEqual[x$46$re, 2.5e+284]], $MachinePrecision], LessEqual[x$46$re, 3.8e+293]]]]]]], t$95$3, t$95$2]]]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x.re < 6.4999999999999995e-294 or 2.14999999999999996e-246 < x.re < 7.4999999999999999e-239 or 2.9499999999999999e-213 < x.re < 5.40000000000000011e-201 or 2.1e-195 < x.re < 1.4000000000000001e-188 or 1.9999999999999999e-188 < x.re < 9.6e-175 or 4.99999999999999992e-171 < x.re < 9.5000000000000002e-122 or 2.8999999999999998e-65 < x.re < 1.6e-59 or 7.9999999999999997e-38 < x.re < 0.10000000000000001 or 6.40000000000000004e42 < x.re < 1.9199999999999999e43 or 7.00000000000000041e132 < x.re < 7.50000000000000017e132 or 3.0999999999999999e227 < x.re < 3.19999999999999988e227 or 2.60000000000000018e252 < x.re < 3.9999999999999997e253 or 2.4000000000000001e284 < x.re < 2.5e284 or 3.80000000000000014e293 < x.re

   1. Initial program 43.8%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 64.4%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in y.re around 0 69.7%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{1} \]

   if 6.4999999999999995e-294 < x.re < 2.14999999999999996e-246 or 7.4999999999999999e-239 < x.re < 2.9499999999999999e-213 or 5.40000000000000011e-201 < x.re < 2.1e-195 or 1.4000000000000001e-188 < x.re < 1.9999999999999999e-188 or 9.6e-175 < x.re < 4.99999999999999992e-171 or 9.5000000000000002e-122 < x.re < 2.8999999999999998e-65 or 1.6e-59 < x.re < 7.9999999999999997e-38 or 0.10000000000000001 < x.re < 6.40000000000000004e42 or 1.9199999999999999e43 < x.re < 7.00000000000000041e132 or 7.50000000000000017e132 < x.re < 1.2000000000000001e176 or 2.69999999999999991e177 < x.re < 3.0999999999999999e227 or 3.19999999999999988e227 < x.re < 2.60000000000000018e252 or 3.9999999999999997e253 < x.re < 2.4000000000000001e284 or 2.5e284 < x.re < 3.80000000000000014e293

   1. Initial program 45.9%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 64.4%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around inf 88.4%

      \[\leadsto e^{\log \color{blue}{x.re} \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   if 1.2000000000000001e176 < x.re < 2.69999999999999991e177

   1. Initial program 0.0%

      \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y.im around 0 51.6%

      \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

   4. Taylor expanded in x.re around 0 60.0%

      \[\leadsto e^{\color{blue}{y.re \cdot \log x.im} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
   5. Step-by-step derivation

      1. *-commutative 60.0%

         \[\leadsto e^{\color{blue}{\log x.im \cdot y.re} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]

   6. Simplified 60.0%

      \[\leadsto e^{\color{blue}{\log x.im \cdot y.re} - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq 6.5 \cdot 10^{-294}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.15 \cdot 10^{-246}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 7.5 \cdot 10^{-239}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.95 \cdot 10^{-213}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 5.4 \cdot 10^{-201}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.1 \cdot 10^{-195}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.4 \cdot 10^{-188}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2 \cdot 10^{-188}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 9.6 \cdot 10^{-175}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 5 \cdot 10^{-171}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 9.5 \cdot 10^{-122}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.9 \cdot 10^{-65}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.6 \cdot 10^{-59}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 8 \cdot 10^{-38}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 0.1:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 6.4 \cdot 10^{+42}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.92 \cdot 10^{+43}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 7 \cdot 10^{+132}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 7.5 \cdot 10^{+132}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 1.2 \cdot 10^{+176}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 2.7 \cdot 10^{+177}:\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.im - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{elif}\;x.re \leq 3.1 \cdot 10^{+227} \lor \neg \left(x.re \leq 3.2 \cdot 10^{+227}\right) \land \left(x.re \leq 2.6 \cdot 10^{+252} \lor \neg \left(x.re \leq 4 \cdot 10^{+253}\right) \land \left(x.re \leq 2.4 \cdot 10^{+284} \lor \neg \left(x.re \leq 2.5 \cdot 10^{+284}\right) \land x.re \leq 3.8 \cdot 10^{+293}\right)\right):\\ \;\;\;\;\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right) \cdot e^{y.re \cdot \log x.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \mathbf{else}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (exp
  (-
   (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
   (* (atan2 x.im x.re) y.im))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - (atan2(x_46_im, x_46_re) * 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 = exp(((log(sqrt(((x_46re * x_46re) + (x_46im * x_46im)))) * y_46re) - (atan2(x_46im, x_46re) * 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 Math.exp(((Math.log(Math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - (Math.atan2(x_46_im, x_46_re) * y_46_im)));
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	return math.exp(((math.log(math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - (math.atan2(x_46_im, x_46_re) * y_46_im)))

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return exp(Float64(Float64(log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im)))) * y_46_re) - Float64(atan(x_46_im, x_46_re) * y_46_im)))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im)));
end

Wolfram

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

Derivation

1. Initial program 44.1%

   \[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \cos \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \]
2. Add Preprocessing

3. Taylor expanded in y.im around 0 64.3%

   \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{\cos \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)} \]

4. Taylor expanded in y.re around 0 65.5%

   \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \color{blue}{1} \]

5. Final simplification 65.5%

   \[\leadsto e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(FPCore (x.re x.im y.re y.im)
  :name "powComplex, real part"
  :precision binary64
  (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))))