Average Error: 0.0 → 0.0
Time: 6.3s
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 r1770554 = 2.0;
        double r1770555 = x;
        double r1770556 = exp(r1770555);
        double r1770557 = -r1770555;
        double r1770558 = exp(r1770557);
        double r1770559 = r1770556 + r1770558;
        double r1770560 = r1770554 / r1770559;
        return r1770560;
}
↓
double f(double x) {
        double r1770561 = 2.0;
        double r1770562 = x;
        double r1770563 = exp(r1770562);
        double r1770564 = -r1770562;
        double r1770565 = exp(r1770564);
        double r1770566 = r1770563 + r1770565;
        double r1770567 = r1770561 / r1770566;
        double r1770568 = sqrt(r1770567);
        double r1770569 = r1770568 * r1770568;
        return r1770569;
}

Error

Bits error versus x

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