\[0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]

0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}

double f(double re, double im) {
        double r8750 = 0.5;
        double r8751 = 2.0;
        double r8752 = re;
        double r8753 = r8752 * r8752;
        double r8754 = im;
        double r8755 = r8754 * r8754;
        double r8756 = r8753 + r8755;
        double r8757 = sqrt(r8756);
        double r8758 = r8757 + r8752;
        double r8759 = r8751 * r8758;
        double r8760 = sqrt(r8759);
        double r8761 = r8750 * r8760;
        return r8761;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019191 
(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

get-representation: Unknown representation #f		L	C
loop	/data/pavpan/nightlies/herbie/interface2/src/points.rkt	122	4
prepare-points	/data/pavpan/nightlies/herbie/interface2/src/points.rkt	146	0
setup-prog!34	/data/pavpan/nightlies/herbie/interface2/src/mainloop.rkt	67	0
run-improve43	/data/pavpan/nightlies/herbie/interface2/src/mainloop.rkt	339	0
(unnamed)	/opt/racket-7.0/collects/racket/private/more-scheme.rkt	261	28
run	/opt/racket-7.0/share/pkgs/profile-lib/main.rkt	39	2
profile-thunk16	/opt/racket-7.0/share/pkgs/profile-lib/main.rkt	9	0
(unnamed)	/opt/racket-7.0/collects/racket/private/more-scheme.rkt	261	28