Average Error: 0.0 → 0.0
Time: 2.9s
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 r75868 = 2.0;
        double r75869 = x;
        double r75870 = exp(r75869);
        double r75871 = -r75869;
        double r75872 = exp(r75871);
        double r75873 = r75870 + r75872;
        double r75874 = r75868 / r75873;
        return r75874;
}
↓
double f(double x) {
        double r75875 = 2.0;
        double r75876 = x;
        double r75877 = exp(r75876);
        double r75878 = -r75876;
        double r75879 = exp(r75878);
        double r75880 = r75877 + r75879;
        double r75881 = r75875 / r75880;
        double r75882 = sqrt(r75881);
        double r75883 = r75882 * r75882;
        return r75883;
}

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 2019346 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))