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

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

double f(double x) {
        double r69771 = 1.0;
        double r69772 = 0.5;
        double r69773 = x;
        double r69774 = hypot(r69771, r69773);
        double r69775 = r69771 / r69774;
        double r69776 = r69771 + r69775;
        double r69777 = r69772 * r69776;
        double r69778 = sqrt(r69777);
        double r69779 = r69771 - r69778;
        return r69779;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2020045 +o rules:numerics
(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: '(* #<enode 62(62)> #<enode 0(130)>)		L	C
for-loop	/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding/regraph/egraph.rkt	270	6
update-leader!	/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding/regraph/egraph.rkt	265	0
for-loop	/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding/regraph/main.rkt	77	2
prune-phase	/data/pavpan/nightlies/herbie/simplify-regraph-rebuilding/regraph/main.rkt	74	0
for-loop	/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/core/simplify.rkt	80	4
for-loop	/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/core/simplify.rkt	76	2
(unnamed)	/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/core/simplify.rkt	56	0
(unnamed)	/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/core/simplify.rkt	38	0
simplify!	/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/mainloop.rkt	224	0
run-iter!	/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/mainloop.rkt	327	0
for-loop	/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/mainloop.rkt	365	4
run-improve47	/data/pavpan/nightlies/herbie/simplify-upwards-no-duplicates/src/mainloop.rkt	346	0
.../more-scheme.rkt:261:28	unknown
run	/opt/racket-7.5/share/pkgs/profile-lib/main.rkt	39	2
profile-thunk16	/opt/racket-7.5/share/pkgs/profile-lib/main.rkt	9	0
(unnamed)	/opt/racket-7.5/collects/racket/private/more-scheme.rkt	261	28

Falling back on racket egraph because egg-herbie package not installed (more)

Reproduce

Backtrace