Exception for 2tan (problem 3.3.2)

Specification

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

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

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

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

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

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

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

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

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

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

\begin{array}{l}

\\
\tan \left(x + \varepsilon\right) - \tan x
\end{array}