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

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

double f(double re, double im) {
        double r8851 = 0.5;
        double r8852 = 2.0;
        double r8853 = re;
        double r8854 = r8853 * r8853;
        double r8855 = im;
        double r8856 = r8855 * r8855;
        double r8857 = r8854 + r8856;
        double r8858 = sqrt(r8857);
        double r8859 = r8858 + r8853;
        double r8860 = r8852 * r8859;
        double r8861 = sqrt(r8860);
        double r8862 = r8851 * r8861;
        return r8862;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019191 +o rules:numerics
(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