Average Error: 0.0 → 0.0
Time: 10.6s
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 r2900102 = 2.0;
        double r2900103 = x;
        double r2900104 = exp(r2900103);
        double r2900105 = -r2900103;
        double r2900106 = exp(r2900105);
        double r2900107 = r2900104 + r2900106;
        double r2900108 = r2900102 / r2900107;
        return r2900108;
}
↓
double f(double x) {
        double r2900109 = 2.0;
        double r2900110 = x;
        double r2900111 = exp(r2900110);
        double r2900112 = -r2900110;
        double r2900113 = exp(r2900112);
        double r2900114 = r2900111 + r2900113;
        double r2900115 = r2900109 / r2900114;
        double r2900116 = expm1(r2900115);
        double r2900117 = log1p(r2900116);
        return r2900117;
}

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 2019162 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))