Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{2}{e^{x} + e^{-x}}\right)\right)\]
\frac{2}{e^{x} + e^{-x}}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{2}{e^{x} + e^{-x}}\right)\right)
double f(double x) {
        double r83924 = 2.0;
        double r83925 = x;
        double r83926 = exp(r83925);
        double r83927 = -r83925;
        double r83928 = exp(r83927);
        double r83929 = r83926 + r83928;
        double r83930 = r83924 / r83929;
        return r83930;
}
↓
double f(double x) {
        double r83931 = 2.0;
        double r83932 = x;
        double r83933 = exp(r83932);
        double r83934 = -r83932;
        double r83935 = exp(r83934);
        double r83936 = r83933 + r83935;
        double r83937 = r83931 / r83936;
        double r83938 = expm1(r83937);
        double r83939 = log1p(r83938);
        return r83939;
}

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 log1p-expm1-u0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))