Average Error: 0.0 → 0.0
Time: 9.3s
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 r1584831 = 2.0;
        double r1584832 = x;
        double r1584833 = exp(r1584832);
        double r1584834 = -r1584832;
        double r1584835 = exp(r1584834);
        double r1584836 = r1584833 + r1584835;
        double r1584837 = r1584831 / r1584836;
        return r1584837;
}
↓
double f(double x) {
        double r1584838 = 2.0;
        double r1584839 = x;
        double r1584840 = exp(r1584839);
        double r1584841 = -r1584839;
        double r1584842 = exp(r1584841);
        double r1584843 = r1584840 + r1584842;
        double r1584844 = r1584838 / r1584843;
        double r1584845 = log1p(r1584844);
        double r1584846 = expm1(r1584845);
        return r1584846;
}

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 2019134 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))