\[1.000000000000000006295358232172963997211 \cdot 10^{-150} \lt \left|x\right| \lt 9.999999999999999808355961724373745905731 \cdot 10^{149}\]

\[\sqrt{0.5 \cdot \left(1 + \frac{x}{\sqrt{\left(4 \cdot p\right) \cdot p + x \cdot x}}\right)}\]

\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 r8833 = 0.5;
        double r8834 = 1.0;
        double r8835 = x;
        double r8836 = 4.0;
        double r8837 = p;
        double r8838 = r8836 * r8837;
        double r8839 = r8838 * r8837;
        double r8840 = r8835 * r8835;
        double r8841 = r8839 + r8840;
        double r8842 = sqrt(r8841);
        double r8843 = r8835 / r8842;
        double r8844 = r8834 + r8843;
        double r8845 = r8833 * r8844;
        double r8846 = sqrt(r8845);
        return r8846;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019191 
(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

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