Average Error: 0.0 → 0.0
Time: 4.0s
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 r924519 = 2.0;
        double r924520 = x;
        double r924521 = exp(r924520);
        double r924522 = -r924520;
        double r924523 = exp(r924522);
        double r924524 = r924521 + r924523;
        double r924525 = r924519 / r924524;
        return r924525;
}
↓
double f(double x) {
        double r924526 = 2.0;
        double r924527 = x;
        double r924528 = exp(r924527);
        double r924529 = -r924527;
        double r924530 = exp(r924529);
        double r924531 = r924528 + r924530;
        double r924532 = r924526 / r924531;
        double r924533 = log1p(r924532);
        double r924534 = expm1(r924533);
        return r924534;
}

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 2019156 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))