Average Error: 0.0 → 0.0
Time: 7.8s
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 r4431869 = 2.0;
        double r4431870 = x;
        double r4431871 = exp(r4431870);
        double r4431872 = -r4431870;
        double r4431873 = exp(r4431872);
        double r4431874 = r4431871 + r4431873;
        double r4431875 = r4431869 / r4431874;
        return r4431875;
}
↓
double f(double x) {
        double r4431876 = 2.0;
        double r4431877 = x;
        double r4431878 = exp(r4431877);
        double r4431879 = -r4431877;
        double r4431880 = exp(r4431879);
        double r4431881 = r4431878 + r4431880;
        double r4431882 = r4431876 / r4431881;
        double r4431883 = sqrt(r4431882);
        double r4431884 = r4431883 * r4431883;
        return r4431884;
}

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 2019107 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))