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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 r56470873 = 1.0;
        double r56470874 = x;
        double r56470875 = tan(r56470874);
        double r56470876 = r56470875 * r56470875;
        double r56470877 = r56470873 - r56470876;
        double r56470878 = r56470873 + r56470876;
        double r56470879 = r56470877 / r56470878;
        return r56470879;
}

Reproduce

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