Exception for 2tan (problem 3.3.2)

Specification

\[\left(\left(-10000 \leq x \land x \leq 10000\right) \land 10^{-16} \cdot \left|x\right| < \varepsilon\right) \land \varepsilon < \left|x\right|\]

Math

\[\begin{array}{l} \\ \tan \left(x + \varepsilon\right) - \tan x \end{array} \]

FPCore

(FPCore (x eps) :precision binary64 (- (tan (+ x eps)) (tan x)))

C

double code(double x, double eps) {
	return tan((x + eps)) - tan(x);
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = tan((x + eps)) - tan(x)
end function

Java

public static double code(double x, double eps) {
	return Math.tan((x + eps)) - Math.tan(x);
}

Python

def code(x, eps):
	return math.tan((x + eps)) - math.tan(x)

Julia

function code(x, eps)
	return Float64(tan(Float64(x + eps)) - tan(x))
end

MATLAB

function tmp = code(x, eps)
	tmp = tan((x + eps)) - tan(x);
end

Wolfram

code[x_, eps_] := N[(N[Tan[N[(x + eps), $MachinePrecision]], $MachinePrecision] - N[Tan[x], $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024261 
(FPCore (x eps)
  :name "2tan (problem 3.3.2)"
  :precision binary64
  :pre (and (and (and (<= -10000.0 x) (<= x 10000.0)) (< (* 1e-16 (fabs x)) eps)) (< eps (fabs x)))

  :alt
  (! :herbie-platform default (+ eps (* eps (tan x) (tan x))))

  (- (tan (+ x eps)) (tan x)))

Please file a bug report with this information.

Backtrace

run-egg: cannot find proof; start and end are not equal. start: #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 eps (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) end: (*.f64 #s(literal 17/45 binary64) eps)		L	C
add-soundiness	/home/nightlies/herbie/artem-batch-finish-rewrite/src/core/soundiness.rkt	140	0
extract!	/home/nightlies/herbie/artem-batch-finish-rewrite/src/core/mainloop.rkt	79	0
run-improve!	/home/nightlies/herbie/artem-batch-finish-rewrite/src/core/mainloop.rkt	45	0
get-alternatives/report	/home/nightlies/herbie/artem-batch-finish-rewrite/src/api/sandbox.rkt	186	0
(unnamed)	/home/nightlies/herbie/artem-batch-finish-rewrite/src/api/sandbox.rkt	282	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