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

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

double f(double re, double im) {
        double r173391 = 0.5;
        double r173392 = 2.0;
        double r173393 = re;
        double r173394 = r173393 * r173393;
        double r173395 = im;
        double r173396 = r173395 * r173395;
        double r173397 = r173394 + r173396;
        double r173398 = sqrt(r173397);
        double r173399 = r173398 + r173393;
        double r173400 = r173392 * r173399;
        double r173401 = sqrt(r173400);
        double r173402 = r173391 * r173401;
        return r173402;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019304 
(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: +inf.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
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
(unnamed)	/data/pavpan/nightlies/herbie/eggmath-testversion/src/core/simplify.rkt	25	0
get-final-combination	/data/pavpan/nightlies/herbie/eggmath-testversion/src/mainloop.rkt	370	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