Average Error: 0.0 → 0.0
Time: 34.9s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}
double f(double x) {
        double r71976 = 2.0;
        double r71977 = x;
        double r71978 = exp(r71977);
        double r71979 = -r71977;
        double r71980 = exp(r71979);
        double r71981 = r71978 + r71980;
        double r71982 = r71976 / r71981;
        return r71982;
}
↓
double f(double x) {
        double r71983 = 2.0;
        double r71984 = x;
        double r71985 = exp(r71984);
        double r71986 = -r71984;
        double r71987 = exp(r71986);
        double r71988 = r71985 + r71987;
        double r71989 = r71983 / r71988;
        double r71990 = sqrt(r71989);
        double r71991 = r71990 * r71990;
        return r71991;
}

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-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))