\[1.000000000000000006295358232172963997211 \cdot 10^{-150} \lt \left|x\right| \lt 9.999999999999999808355961724373745905731 \cdot 10^{149}\]
\[\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{\left(4 \cdot p\right) \cdot p + x \cdot x}}\right)}\]
\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{\left(4 \cdot p\right) \cdot p + x \cdot x}}\right)}
double f(double p, double x) {
        double r13912278 = 0.5;
        double r13912279 = 1.0;
        double r13912280 = x;
        double r13912281 = 4.0;
        double r13912282 = p;
        double r13912283 = r13912281 * r13912282;
        double r13912284 = r13912283 * r13912282;
        double r13912285 = r13912280 * r13912280;
        double r13912286 = r13912284 + r13912285;
        double r13912287 = sqrt(r13912286);
        double r13912288 = r13912280 / r13912287;
        double r13912289 = r13912279 + r13912288;
        double r13912290 = r13912278 * r13912289;
        double r13912291 = sqrt(r13912290);
        return r13912291;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019173 
(FPCore (p x)
  :name "Given's Rotation SVD example"
  :pre (< 1e-150 (fabs x) 1e+150)

  :herbie-target
  (sqrt (+ 0.5 (/ (copysign 0.5 x) (hypot 1.0 (/ (* 2.0 p) x)))))

  (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))

Backtrace

hash-ref: no value found for key key: #<enode 255(255)>LC
for-loop/data/pavpan/nightlies/herbie/various-cleanup/src/core/simplify.rkt1972
extractor-extract/data/pavpan/nightlies/herbie/various-cleanup/src/core/simplify.rkt1960
for-loop/data/pavpan/nightlies/herbie/various-cleanup/src/core/simplify.rkt352
(unnamed)/data/pavpan/nightlies/herbie/various-cleanup/src/core/simplify.rkt260
simplify!/data/pavpan/nightlies/herbie/various-cleanup/src/mainloop.rkt2170
run-iter!/data/pavpan/nightlies/herbie/various-cleanup/src/mainloop.rkt3200
for-loop/data/pavpan/nightlies/herbie/various-cleanup/src/mainloop.rkt3544
run-improve43/data/pavpan/nightlies/herbie/various-cleanup/src/mainloop.rkt3390
(unnamed)/opt/racket-7.0/collects/racket/private/more-scheme.rkt26128
run/opt/racket-7.0/share/pkgs/profile-lib/main.rkt392
profile-thunk16/opt/racket-7.0/share/pkgs/profile-lib/main.rkt90
(unnamed)/opt/racket-7.0/collects/racket/private/more-scheme.rkt26128