Average Error: 0.0 → 0.0
Time: 18.4s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{2}{e^{x} + e^{-x}}\]
double f(double x) {
        double r12585549 = 2.0;
        double r12585550 = x;
        double r12585551 = exp(r12585550);
        double r12585552 = -r12585550;
        double r12585553 = exp(r12585552);
        double r12585554 = r12585551 + r12585553;
        double r12585555 = r12585549 / r12585554;
        return r12585555;
}
↓
double f(double x) {
        double r12585556 = 2.0;
        double r12585557 = x;
        double r12585558 = exp(r12585557);
        double r12585559 = -r12585557;
        double r12585560 = exp(r12585559);
        double r12585561 = r12585558 + r12585560;
        double r12585562 = r12585556 / r12585561;
        return r12585562;
}


\frac{2}{e^{x} + e^{-x}}
↓
\frac{2}{e^{x} + e^{-x}}

Error

Bits error versus x

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 2019101 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))