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 2023243 
(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

arb-<: arity mismatch; the expected number of arguments does not match the given number expected: 0 given: 2		L	C
f	/home/nightlies/herbie/arb-support/src/programs.rkt	187	2
(unnamed)	/home/nightlies/herbie/arb-support/src/ground-truth.rkt	23	2
search-step	/home/nightlies/herbie/arb-support/src/searchreals.rkt	37	0
find-intervals	/home/nightlies/herbie/arb-support/src/searchreals.rkt	87	0
make-sampler	/home/nightlies/herbie/arb-support/src/sampling.rkt	94	0
sample-points	/home/nightlies/herbie/arb-support/src/ground-truth.rkt	64	0
setup-context!	/home/nightlies/herbie/arb-support/src/mainloop.rkt	293	0
get-alternatives/report	/home/nightlies/herbie/arb-support/src/sandbox.rkt	148	0
(unnamed)	/home/nightlies/herbie/arb-support/src/sandbox.rkt	247	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