Exception for invcot (example 3.9)

\[-0.026 < x \land x < 0.026\]

Math

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

FPCore

(FPCore (x) :precision binary64 (- (/ 1.0 x) (/ 1.0 (tan x))))

C

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

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / x) - (1.0d0 / tan(x))
end function

Java

public static double code(double x) {
	return (1.0 / x) - (1.0 / Math.tan(x));
}

Python

def code(x):
	return (1.0 / x) - (1.0 / math.tan(x))

Julia

function code(x)
	return Float64(Float64(1.0 / x) - Float64(1.0 / tan(x)))
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / x) - (1.0 / tan(x));
end

Wolfram

code[x_] := N[(N[(1.0 / x), $MachinePrecision] - N[(1.0 / N[Tan[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2023098 
(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

hash-ref: no value found for key key: 'false		L	C
(unnamed)	/home/nightlies/herbie/ruler-no-fast-forwarding/src/syntax/syntax.rkt	231	2
f336	.../match/compiler.rkt	548	40
expand-parametric	/home/nightlies/herbie/ruler-no-fast-forwarding/src/syntax/sugar.rkt	62	0
(unnamed)	/home/nightlies/herbie/ruler-no-fast-forwarding/src/core/egg-herbie.rkt	255	9
rule->egg-rules	/home/nightlies/herbie/ruler-no-fast-forwarding/src/core/egg-herbie.rkt	224	0
expand-rules	/home/nightlies/herbie/ruler-no-fast-forwarding/src/core/egg-herbie.rkt	488	0
egraph-run-rules	/home/nightlies/herbie/ruler-no-fast-forwarding/src/core/egg-herbie.rkt	509	0
(unnamed)	/home/nightlies/herbie/ruler-no-fast-forwarding/src/core/simplify.rkt	58	3
with-egraph	/home/nightlies/herbie/ruler-no-fast-forwarding/src/core/egg-herbie.rkt	333	0
simplify-batch	/home/nightlies/herbie/ruler-no-fast-forwarding/src/core/simplify.rkt	23	0
(unnamed)	/usr/share/racket/collects/racket/contract/private/arrow-higher-order.rkt	379	33
get-swaps	/home/nightlies/herbie/ruler-no-fast-forwarding/src/symmetry.rkt	6	0
connected-components	/home/nightlies/herbie/ruler-no-fast-forwarding/src/symmetry.rkt	18	0
run-improve!	/home/nightlies/herbie/ruler-no-fast-forwarding/src/mainloop.rkt	320	0
run-herbie	/home/nightlies/herbie/ruler-no-fast-forwarding/src/sandbox.rkt	57	0
(unnamed)	/home/nightlies/herbie/ruler-no-fast-forwarding/src/sandbox.rkt	133	6
(unnamed)	/usr/share/racket/pkgs/profile-lib/main.rkt	40	10
profile-thunk	/usr/share/racket/pkgs/profile-lib/main.rkt	9	0
(unnamed)	/usr/share/racket/collects/racket/engine.rkt	42	24