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\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
double f(double x, double __attribute__((unused)) y) {
        double r56678224 = 2.0;
        double r56678225 = 1.0;
        double r56678226 = -2.0;
        double r56678227 = x;
        double r56678228 = r56678226 * r56678227;
        double r56678229 = exp(r56678228);
        double r56678230 = r56678225 + r56678229;
        double r56678231 = r56678224 / r56678230;
        double r56678232 = r56678231 - r56678225;
        return r56678232;
}

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))