Average Error: 0.0 → 0.0
Time: 1.9s
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 r59582 = 2.0;
        double r59583 = x;
        double r59584 = exp(r59583);
        double r59585 = -r59583;
        double r59586 = exp(r59585);
        double r59587 = r59584 + r59586;
        double r59588 = r59582 / r59587;
        return r59588;
}
↓
double f(double x) {
        double r59589 = 2.0;
        double r59590 = x;
        double r59591 = exp(r59590);
        double r59592 = -r59590;
        double r59593 = exp(r59592);
        double r59594 = r59591 + r59593;
        double r59595 = r59589 / r59594;
        double r59596 = log1p(r59595);
        double r59597 = expm1(r59596);
        return r59597;
}

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 2020018 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))