\[0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]
0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}
double f(double re, double im) {
        double r8135 = 0.5;
        double r8136 = 2.0;
        double r8137 = re;
        double r8138 = r8137 * r8137;
        double r8139 = im;
        double r8140 = r8139 * r8139;
        double r8141 = r8138 + r8140;
        double r8142 = sqrt(r8141);
        double r8143 = r8142 + r8137;
        double r8144 = r8136 * r8143;
        double r8145 = sqrt(r8144);
        double r8146 = r8135 * r8145;
        return r8146;
}

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, real part"

  :herbie-target
  (if (< re 0.0) (* 0.5 (* (sqrt 2.0) (sqrt (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))) (* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))

  (* 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