Average Error: 0.0 → 0.0
Time: 3.0s
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 r73463 = 2.0;
        double r73464 = x;
        double r73465 = exp(r73464);
        double r73466 = -r73464;
        double r73467 = exp(r73466);
        double r73468 = r73465 + r73467;
        double r73469 = r73463 / r73468;
        return r73469;
}
↓
double f(double x) {
        double r73470 = 2.0;
        double r73471 = x;
        double r73472 = exp(r73471);
        double r73473 = -r73471;
        double r73474 = exp(r73473);
        double r73475 = r73472 + r73474;
        double r73476 = r73470 / r73475;
        double r73477 = sqrt(r73476);
        double r73478 = r73477 * r73477;
        return r73478;
}

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