\[0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]
0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}
double f(double re, double im) {
        double r245130 = 0.5;
        double r245131 = 2.0;
        double r245132 = re;
        double r245133 = r245132 * r245132;
        double r245134 = im;
        double r245135 = r245134 * r245134;
        double r245136 = r245133 + r245135;
        double r245137 = sqrt(r245136);
        double r245138 = r245137 + r245132;
        double r245139 = r245131 * r245138;
        double r245140 = sqrt(r245139);
        double r245141 = r245130 * r245140;
        return r245141;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2020045 +o rules:numerics
(FPCore (re im)
  :name "math.sqrt on complex, real part"
  :precision binary64

  :herbie-target
  (if (< re 0.0) (* 0.5 (* (sqrt 2) (sqrt (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))) (* 0.5 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))))

  (* 0.5 (sqrt (* 2 (+ (sqrt (+ (* re re) (* im im))) re)))))

Backtrace

hash-ref: no value found for key key: '(* #<enode 0(168)> #<enode 386(386)>)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-upwards-no-duplicates/src/core/simplify.rkt804
for-loop/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/core/simplify.rkt762
(unnamed)/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/core/simplify.rkt560
(unnamed)/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/core/simplify.rkt380
simplify!/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/mainloop.rkt2240
run-iter!/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/mainloop.rkt3270
for-loop/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/mainloop.rkt3654
run-improve47/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/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