Average Error: 0.0 → 0.0
Time: 6.5s
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 r2536539 = 2.0;
        double r2536540 = x;
        double r2536541 = exp(r2536540);
        double r2536542 = -r2536540;
        double r2536543 = exp(r2536542);
        double r2536544 = r2536541 + r2536543;
        double r2536545 = r2536539 / r2536544;
        return r2536545;
}
↓
double f(double x) {
        double r2536546 = 2.0;
        double r2536547 = x;
        double r2536548 = exp(r2536547);
        double r2536549 = -r2536547;
        double r2536550 = exp(r2536549);
        double r2536551 = r2536548 + r2536550;
        double r2536552 = r2536546 / r2536551;
        double r2536553 = sqrt(r2536552);
        double r2536554 = r2536553 * r2536553;
        return r2536554;
}

Error

Bits error versus x

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Your Program's Arguments

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 2019165 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))