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\[\tan \left(x + \varepsilon\right) - \tan x\]
\tan \left(x + \varepsilon\right) - \tan x
double code(double x, double eps) {
	return (tan((x + eps)) - tan(x));
}

Reproduce

herbie shell --seed 2020078 
(FPCore (x eps)
  :name "2tan (problem 3.3.2)"
  :precision binary64

  :herbie-target
  (/ (sin eps) (* (cos x) (cos (+ x eps))))

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