Average Error: 0.0 → 0.0
Time: 7.2s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{2}{e^{x} + e^{-x}}\]
double f(double x) {
        double r11358931 = 2.0;
        double r11358932 = x;
        double r11358933 = exp(r11358932);
        double r11358934 = -r11358932;
        double r11358935 = exp(r11358934);
        double r11358936 = r11358933 + r11358935;
        double r11358937 = r11358931 / r11358936;
        return r11358937;
}
↓
double f(double x) {
        double r11358938 = 2.0;
        double r11358939 = x;
        double r11358940 = exp(r11358939);
        double r11358941 = -r11358939;
        double r11358942 = exp(r11358941);
        double r11358943 = r11358940 + r11358942;
        double r11358944 = r11358938 / r11358943;
        return r11358944;
}


\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 2019102 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))