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\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
double f(double x) {
        double r21572059 = 1.0;
        double r21572060 = x;
        double r21572061 = tan(r21572060);
        double r21572062 = r21572061 * r21572061;
        double r21572063 = r21572059 - r21572062;
        double r21572064 = r21572059 + r21572062;
        double r21572065 = r21572063 / r21572064;
        return r21572065;
}

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))