Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{2}{e^{\log \left(e^{x} + e^{-x}\right)}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\frac{2}{e^{\log \left(e^{x} + e^{-x}\right)}}
double f(double x) {
        double r10105340 = 2.0;
        double r10105341 = x;
        double r10105342 = exp(r10105341);
        double r10105343 = -r10105341;
        double r10105344 = exp(r10105343);
        double r10105345 = r10105342 + r10105344;
        double r10105346 = r10105340 / r10105345;
        return r10105346;
}
↓
double f(double x) {
        double r10105347 = 2.0;
        double r10105348 = x;
        double r10105349 = exp(r10105348);
        double r10105350 = -r10105348;
        double r10105351 = exp(r10105350);
        double r10105352 = r10105349 + r10105351;
        double r10105353 = log(r10105352);
        double r10105354 = exp(r10105353);
        double r10105355 = r10105347 / r10105354;
        return r10105355;
}

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 add-exp-log0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))