Average Error: 0.0 → 0.0
Time: 11.6s
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 r1408179 = 2.0;
        double r1408180 = x;
        double r1408181 = exp(r1408180);
        double r1408182 = -r1408180;
        double r1408183 = exp(r1408182);
        double r1408184 = r1408181 + r1408183;
        double r1408185 = r1408179 / r1408184;
        return r1408185;
}
↓
double f(double x) {
        double r1408186 = 2.0;
        double r1408187 = x;
        double r1408188 = exp(r1408187);
        double r1408189 = -r1408187;
        double r1408190 = exp(r1408189);
        double r1408191 = r1408188 + r1408190;
        double r1408192 = r1408186 / r1408191;
        double r1408193 = sqrt(r1408192);
        double r1408194 = r1408193 * r1408193;
        return r1408194;
}

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 2019128 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))