Average Error: 0.0 → 0.0
Time: 33.9s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{2}{e^{x} + e^{-x}}\right)\right)\]
\frac{2}{e^{x} + e^{-x}}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{2}{e^{x} + e^{-x}}\right)\right)
double f(double x) {
        double r64166 = 2.0;
        double r64167 = x;
        double r64168 = exp(r64167);
        double r64169 = -r64167;
        double r64170 = exp(r64169);
        double r64171 = r64168 + r64170;
        double r64172 = r64166 / r64171;
        return r64172;
}
↓
double f(double x) {
        double r64173 = 2.0;
        double r64174 = x;
        double r64175 = exp(r64174);
        double r64176 = -r64174;
        double r64177 = exp(r64176);
        double r64178 = r64175 + r64177;
        double r64179 = r64173 / r64178;
        double r64180 = log1p(r64179);
        double r64181 = expm1(r64180);
        return r64181;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{2}{e^{x} + e^{-x}}\]
  2. Using strategy rm

  3. Applied expm1-log1p-u0.0

    \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{2}{e^{x} + e^{-x}}\right)\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{2}{e^{x} + e^{-x}}\right)\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))