Exception for invcot (example 3.9)

\[-0.0259999999999999988 \lt x \land x \lt 0.0259999999999999988\]

Math

\[\frac{1}{x} - \frac{1}{\tan x}\]

C

double code(double x) {
	return ((double) (((double) (1.0 / x)) - ((double) (1.0 / ((double) tan(x))))));
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2020155 
(FPCore (x)
  :name "invcot (example 3.9)"
  :precision binary64
  :pre (and (< -0.026 x) (< x 0.026))

  :herbie-target
  (if (< (fabs x) 0.026) (* (/ x 3.0) (+ 1.0 (/ (* x x) 15.0))) (- (/ 1.0 x) (/ 1.0 (tan x))))

  (- (/ 1.0 x) (/ 1.0 (tan x))))

Backtrace

not inclusive intervals		L	C
fpbench-ival->ival	/data/pavpan/nightlies/herbie/ival-find-range/src/findroot.rkt	63	0
loop	unknown
range-table->hyperrects	/data/pavpan/nightlies/herbie/ival-find-range/src/findroot.rkt	58	0
make-sampler	/data/pavpan/nightlies/herbie/ival-find-range/src/points.rkt	124	0
prepare-points-intervals	/data/pavpan/nightlies/herbie/ival-find-range/src/points.rkt	155	0
run-improve47	/data/pavpan/nightlies/herbie/ival-find-range/src/mainloop.rkt	365	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

Reproduce

herbie shell --seed 2020155 
(FPCore (x)
  :name "invcot (example 3.9)"
  :precision binary64
  :pre (and (< -0.026 x) (< x 0.026))

  :herbie-target
  (if (< (fabs x) 0.026) (* (/ x 3.0) (+ 1.0 (/ (* x x) 15.0))) (- (/ 1.0 x) (/ 1.0 (tan x))))

  (- (/ 1.0 x) (/ 1.0 (tan x))))