\[0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]
0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}
double f(double re, double im) {
        double r89283 = 0.5;
        double r89284 = 2.0;
        double r89285 = re;
        double r89286 = r89285 * r89285;
        double r89287 = im;
        double r89288 = r89287 * r89287;
        double r89289 = r89286 + r89288;
        double r89290 = sqrt(r89289);
        double r89291 = r89290 + r89285;
        double r89292 = r89284 * r89291;
        double r89293 = sqrt(r89292);
        double r89294 = r89283 * r89293;
        return r89294;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019323 
(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

get-representation: Unknown representation realLC
(unnamed)/data/pavpan/nightlies/herbie/fix-interface-bugs/src/core/regimes.rkt653
filter/opt/racket-7.2/collects/racket/private/list.rkt2562
infer-splitpoints/data/pavpan/nightlies/herbie/fix-interface-bugs/src/core/regimes.rkt340
get-final-combination/data/pavpan/nightlies/herbie/fix-interface-bugs/src/mainloop.rkt3690
(unnamed)/opt/racket-7.2/collects/racket/private/more-scheme.rkt26128
run/opt/racket-7.2/share/pkgs/profile-lib/main.rkt392
profile-thunk16/opt/racket-7.2/share/pkgs/profile-lib/main.rkt90
(unnamed)/opt/racket-7.2/collects/racket/private/more-scheme.rkt26128