\[0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} - re\right)}\]
0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} - re\right)}
double f(double re, double im) {
        double r3114 = 0.5;
        double r3115 = 2.0;
        double r3116 = re;
        double r3117 = r3116 * r3116;
        double r3118 = im;
        double r3119 = r3118 * r3118;
        double r3120 = r3117 + r3119;
        double r3121 = sqrt(r3120);
        double r3122 = r3121 - r3116;
        double r3123 = r3115 * r3122;
        double r3124 = sqrt(r3123);
        double r3125 = r3114 * r3124;
        return r3125;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2020045 
(FPCore (re im)
  :name "math.sqrt on complex, imaginary part, im greater than 0 branch"
  :precision binary64
  (* 0.5 (sqrt (* 2 (- (sqrt (+ (* re re) (* im im))) re)))))

Backtrace

hash-ref: no value found for key key: '(* #<enode 85(85)> #<enode 2(200)>)LC
for-loop/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding/regraph/egraph.rkt2706
update-leader!/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding/regraph/egraph.rkt2650
for-loop/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding/regraph/main.rkt772
prune-phase/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding/regraph/main.rkt740
for-loop/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding-2/src/core/simplify.rkt804
for-loop/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding-2/src/core/simplify.rkt762
(unnamed)/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding-2/src/core/simplify.rkt560
(unnamed)/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding-2/src/core/simplify.rkt380
simplify!/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding-2/src/mainloop.rkt2240
run-iter!/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding-2/src/mainloop.rkt3270
for-loop/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding-2/src/mainloop.rkt3654
run-improve47/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding-2/src/mainloop.rkt3460
.../more-scheme.rkt:261:28unknown
run/opt/racket-7.5/share/pkgs/profile-lib/main.rkt392
profile-thunk16/opt/racket-7.5/share/pkgs/profile-lib/main.rkt90
(unnamed)/opt/racket-7.5/collects/racket/private/more-scheme.rkt26128