Average Error: 0.0 → 0.0
Time: 7.9s
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 r2000033 = 2.0;
        double r2000034 = x;
        double r2000035 = exp(r2000034);
        double r2000036 = -r2000034;
        double r2000037 = exp(r2000036);
        double r2000038 = r2000035 + r2000037;
        double r2000039 = r2000033 / r2000038;
        return r2000039;
}
↓
double f(double x) {
        double r2000040 = 2.0;
        double r2000041 = x;
        double r2000042 = exp(r2000041);
        double r2000043 = -r2000041;
        double r2000044 = exp(r2000043);
        double r2000045 = r2000042 + r2000044;
        double r2000046 = r2000040 / r2000045;
        double r2000047 = sqrt(r2000046);
        double r2000048 = r2000047 * r2000047;
        return r2000048;
}

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