\[0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} - re\right)}\]
0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} - re\right)}
double f(double re, double im) {
        double r8098 = 0.5;
        double r8099 = 2.0;
        double r8100 = re;
        double r8101 = r8100 * r8100;
        double r8102 = im;
        double r8103 = r8102 * r8102;
        double r8104 = r8101 + r8103;
        double r8105 = sqrt(r8104);
        double r8106 = r8105 - r8100;
        double r8107 = r8099 * r8106;
        double r8108 = sqrt(r8107);
        double r8109 = r8098 * r8108;
        return r8109;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019194 +o rules:numerics
(FPCore (re im)
  :name "math.sqrt on complex, imaginary part, im greater than 0 branch"
  (* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))))

Backtrace

result arity mismatch; expected number of values not received expected: 2 received: 1 in: local-binding form values...: 0LC
loop/data/pavpan/nightlies/herbie/various-cleanup/src/core/extraction.rkt252
(unnamed)/data/pavpan/nightlies/herbie/various-cleanup/src/core/simplify.rkt260
simplify!/data/pavpan/nightlies/herbie/various-cleanup/src/mainloop.rkt2200
run-improve47/data/pavpan/nightlies/herbie/various-cleanup/src/mainloop.rkt3420
(unnamed)/opt/racket-7.0/collects/racket/private/more-scheme.rkt26128
run/opt/racket-7.0/share/pkgs/profile-lib/main.rkt392
profile-thunk16/opt/racket-7.0/share/pkgs/profile-lib/main.rkt90
(unnamed)/opt/racket-7.0/collects/racket/private/more-scheme.rkt26128