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

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)

double f(double x_re, double x_im, double y_re, double y_im) {
        double r23791 = x_re;
        double r23792 = r23791 * r23791;
        double r23793 = x_im;
        double r23794 = r23793 * r23793;
        double r23795 = r23792 + r23794;
        double r23796 = sqrt(r23795);
        double r23797 = log(r23796);
        double r23798 = y_re;
        double r23799 = r23797 * r23798;
        double r23800 = atan2(r23793, r23791);
        double r23801 = y_im;
        double r23802 = r23800 * r23801;
        double r23803 = r23799 - r23802;
        double r23804 = exp(r23803);
        double r23805 = r23797 * r23801;
        double r23806 = r23800 * r23798;
        double r23807 = r23805 + r23806;
        double r23808 = cos(r23807);
        double r23809 = r23804 * r23808;
        return r23809;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019323 +o rules:numerics
(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)))))

Backtrace

get-representation: Unknown representation real		L	C
(unnamed)	/data/pavpan/nightlies/herbie/fix-interface-bugs/src/core/regimes.rkt	65	3
filter	/opt/racket-7.2/collects/racket/private/list.rkt	256	2
infer-splitpoints	/data/pavpan/nightlies/herbie/fix-interface-bugs/src/core/regimes.rkt	34	0
get-final-combination	/data/pavpan/nightlies/herbie/fix-interface-bugs/src/mainloop.rkt	369	0
(unnamed)	/opt/racket-7.2/collects/racket/private/more-scheme.rkt	261	28
run	/opt/racket-7.2/share/pkgs/profile-lib/main.rkt	39	2
profile-thunk16	/opt/racket-7.2/share/pkgs/profile-lib/main.rkt	9	0
(unnamed)	/opt/racket-7.2/collects/racket/private/more-scheme.rkt	261	28