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 r964527 = 2.0;
        double r964528 = x;
        double r964529 = exp(r964528);
        double r964530 = -r964528;
        double r964531 = exp(r964530);
        double r964532 = r964529 + r964531;
        double r964533 = r964527 / r964532;
        return r964533;
}
↓
double f(double x) {
        double r964534 = 2.0;
        double r964535 = x;
        double r964536 = exp(r964535);
        double r964537 = -r964535;
        double r964538 = exp(r964537);
        double r964539 = r964536 + r964538;
        double r964540 = r964534 / r964539;
        double r964541 = sqrt(r964540);
        double r964542 = r964541 * r964541;
        return r964542;
}

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 2019153 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))