\[1 - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\]

1 - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}

double f(double x) {
        double r8512 = 1.0;
        double r8513 = 0.5;
        double r8514 = x;
        double r8515 = hypot(r8512, r8514);
        double r8516 = r8512 / r8515;
        double r8517 = r8512 + r8516;
        double r8518 = r8513 * r8517;
        double r8519 = sqrt(r8518);
        double r8520 = r8512 - r8519;
        return r8520;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019305 
(FPCore (x)
  :name "Given's Rotation SVD example, simplified"
  :precision binary64
  (- 1 (sqrt (* 0.5 (+ 1 (/ 1 (hypot 1 x)))))))

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
(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