Average Error: 0.0 → 0.0
Time: 7.1s
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 r56664 = 2.0;
        double r56665 = x;
        double r56666 = exp(r56665);
        double r56667 = -r56665;
        double r56668 = exp(r56667);
        double r56669 = r56666 + r56668;
        double r56670 = r56664 / r56669;
        return r56670;
}
↓
double f(double x) {
        double r56671 = 2.0;
        double r56672 = x;
        double r56673 = exp(r56672);
        double r56674 = -r56672;
        double r56675 = exp(r56674);
        double r56676 = r56673 + r56675;
        double r56677 = r56671 / r56676;
        double r56678 = sqrt(r56677);
        double r56679 = r56678 * r56678;
        return r56679;
}

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