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

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

double f(double re, double im) {
        double r8601 = 0.5;
        double r8602 = 2.0;
        double r8603 = re;
        double r8604 = r8603 * r8603;
        double r8605 = im;
        double r8606 = r8605 * r8605;
        double r8607 = r8604 + r8606;
        double r8608 = sqrt(r8607);
        double r8609 = r8608 + r8603;
        double r8610 = r8602 * r8609;
        double r8611 = sqrt(r8610);
        double r8612 = r8601 * r8611;
        return r8612;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019305 
(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: 1.0		L	C
for-loop	/data/pavpan/nightlies/herbie/eggmath-testversion/src/core/eggmath.rkt	70	6
egg-parsed->expr	/data/pavpan/nightlies/herbie/eggmath-testversion/src/core/eggmath.rkt	65	0
for-loop	/data/pavpan/nightlies/herbie/eggmath-testversion/src/core/eggmath.rkt	70	6
egg-parsed->expr	/data/pavpan/nightlies/herbie/eggmath-testversion/src/core/eggmath.rkt	65	0
(unnamed)	/data/pavpan/nightlies/herbie/eggmath-testversion/src/core/simplify.rkt	49	8
egraph-add-exprs	/data/pavpan/nightlies/herbie/eggmath-testversion/src/core/eggmath.rkt	122	0
egraph-run	/data/pavpan/nightlies/herbie/eggmath-testversion/src/core/eggmath.rkt	55	0
(unnamed)	/data/pavpan/nightlies/herbie/eggmath-testversion/src/core/simplify.rkt	38	0
simplify!	/data/pavpan/nightlies/herbie/eggmath-testversion/src/mainloop.rkt	223	0
run-improve47	/data/pavpan/nightlies/herbie/eggmath-testversion/src/mainloop.rkt	345	0
(unnamed)	/opt/racket-7.2/collects/racket/private/more-scheme.rkt	261	28
run	/opt/racket-7.2/share/pkgs/profile-lib/main.rkt	39	2
profile-thunk16	/opt/racket-7.2/share/pkgs/profile-lib/main.rkt	9	0
(unnamed)	/opt/racket-7.2/collects/racket/private/more-scheme.rkt	261	28