Average Error: 0.0 → 0.0
Time: 9.2s
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 r39414 = 2.0;
        double r39415 = x;
        double r39416 = exp(r39415);
        double r39417 = -r39415;
        double r39418 = exp(r39417);
        double r39419 = r39416 + r39418;
        double r39420 = r39414 / r39419;
        return r39420;
}
↓
double f(double x) {
        double r39421 = 2.0;
        double r39422 = x;
        double r39423 = exp(r39422);
        double r39424 = -r39422;
        double r39425 = exp(r39424);
        double r39426 = r39423 + r39425;
        double r39427 = r39421 / r39426;
        return r39427;
}

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 2020042 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))