Average Error: 0.0 → 0.0
Time: 14.9s
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 r2466446 = 2.0;
        double r2466447 = x;
        double r2466448 = exp(r2466447);
        double r2466449 = -r2466447;
        double r2466450 = exp(r2466449);
        double r2466451 = r2466448 + r2466450;
        double r2466452 = r2466446 / r2466451;
        return r2466452;
}
↓
double f(double x) {
        double r2466453 = 2.0;
        double r2466454 = x;
        double r2466455 = exp(r2466454);
        double r2466456 = -r2466454;
        double r2466457 = exp(r2466456);
        double r2466458 = r2466455 + r2466457;
        double r2466459 = r2466453 / r2466458;
        double r2466460 = sqrt(r2466459);
        double r2466461 = r2466460 * r2466460;
        return r2466461;
}

Error

Bits error versus x

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Results

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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 2019149 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))