Average Error: 0.0 → 0.0
Time: 13.4s
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 r4850706 = 2.0;
        double r4850707 = x;
        double r4850708 = exp(r4850707);
        double r4850709 = -r4850707;
        double r4850710 = exp(r4850709);
        double r4850711 = r4850708 + r4850710;
        double r4850712 = r4850706 / r4850711;
        return r4850712;
}
↓
double f(double x) {
        double r4850713 = 2.0;
        double r4850714 = x;
        double r4850715 = exp(r4850714);
        double r4850716 = -r4850714;
        double r4850717 = exp(r4850716);
        double r4850718 = r4850715 + r4850717;
        double r4850719 = r4850713 / r4850718;
        double r4850720 = log1p(r4850719);
        double r4850721 = expm1(r4850720);
        return r4850721;
}

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 2019173 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2.0 (+ (exp x) (exp (- x)))))