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 r4773300 = 2.0;
        double r4773301 = x;
        double r4773302 = exp(r4773301);
        double r4773303 = -r4773301;
        double r4773304 = exp(r4773303);
        double r4773305 = r4773302 + r4773304;
        double r4773306 = r4773300 / r4773305;
        return r4773306;
}
↓
double f(double x) {
        double r4773307 = 2.0;
        double r4773308 = x;
        double r4773309 = exp(r4773308);
        double r4773310 = -r4773308;
        double r4773311 = exp(r4773310);
        double r4773312 = r4773309 + r4773311;
        double r4773313 = log(r4773312);
        double r4773314 = exp(r4773313);
        double r4773315 = r4773307 / r4773314;
        return r4773315;
}

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 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))