Average Error: 0.0 → 0.0
Time: 7.0s
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 r38004 = 2.0;
        double r38005 = x;
        double r38006 = exp(r38005);
        double r38007 = -r38005;
        double r38008 = exp(r38007);
        double r38009 = r38006 + r38008;
        double r38010 = r38004 / r38009;
        return r38010;
}
↓
double f(double x) {
        double r38011 = 2.0;
        double r38012 = x;
        double r38013 = exp(r38012);
        double r38014 = -r38012;
        double r38015 = exp(r38014);
        double r38016 = r38013 + r38015;
        double r38017 = r38011 / r38016;
        double r38018 = log1p(r38017);
        double r38019 = expm1(r38018);
        return r38019;
}

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 2019305 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))