Average Error: 0.0 → 0.0
Time: 6.1s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{2}{e^{x} + e^{-x}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\frac{2}{e^{x} + e^{-x}}
double f(double x) {
        double r51096 = 2.0;
        double r51097 = x;
        double r51098 = exp(r51097);
        double r51099 = -r51097;
        double r51100 = exp(r51099);
        double r51101 = r51098 + r51100;
        double r51102 = r51096 / r51101;
        return r51102;
}
↓
double f(double x) {
        double r51103 = 2.0;
        double r51104 = x;
        double r51105 = exp(r51104);
        double r51106 = -r51104;
        double r51107 = exp(r51106);
        double r51108 = r51105 + r51107;
        double r51109 = r51103 / r51108;
        return r51109;
}

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. Final simplification0.0

    \[\leadsto \frac{2}{e^{x} + e^{-x}}\]

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))