Timeout in 10.0m

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\[e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \sin \left(\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right)\]
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 \sin \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)
double f(double x_re, double x_im, double y_re, double y_im) {
        double r21530 = x_re;
        double r21531 = r21530 * r21530;
        double r21532 = x_im;
        double r21533 = r21532 * r21532;
        double r21534 = r21531 + r21533;
        double r21535 = sqrt(r21534);
        double r21536 = log(r21535);
        double r21537 = y_re;
        double r21538 = r21536 * r21537;
        double r21539 = atan2(r21532, r21530);
        double r21540 = y_im;
        double r21541 = r21539 * r21540;
        double r21542 = r21538 - r21541;
        double r21543 = exp(r21542);
        double r21544 = r21536 * r21540;
        double r21545 = r21539 * r21537;
        double r21546 = r21544 + r21545;
        double r21547 = sin(r21546);
        double r21548 = r21543 * r21547;
        return r21548;
}

Reproduce

herbie shell --seed 2020045 
(FPCore (x.re x.im y.re y.im)
  :name "powComplex, imaginary part"
  :precision binary64
  (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))))