\[0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} - re\right)}\]
0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} - re\right)}
double f(double re, double im) {
        double r24294 = 0.5;
        double r24295 = 2.0;
        double r24296 = re;
        double r24297 = r24296 * r24296;
        double r24298 = im;
        double r24299 = r24298 * r24298;
        double r24300 = r24297 + r24299;
        double r24301 = sqrt(r24300);
        double r24302 = r24301 - r24296;
        double r24303 = r24295 * r24302;
        double r24304 = sqrt(r24303);
        double r24305 = r24294 * r24304;
        return r24305;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019323 
(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

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