Average Error: 0.0 → 0.0
Time: 26.4s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{\frac{\sqrt{2}}{\frac{\sqrt{e^{x} + e^{-x}}}{\sqrt{2}}}}{\sqrt{e^{x} + e^{-x}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\frac{\frac{\sqrt{2}}{\frac{\sqrt{e^{x} + e^{-x}}}{\sqrt{2}}}}{\sqrt{e^{x} + e^{-x}}}
double f(double x) {
        double r2656823 = 2.0;
        double r2656824 = x;
        double r2656825 = exp(r2656824);
        double r2656826 = -r2656824;
        double r2656827 = exp(r2656826);
        double r2656828 = r2656825 + r2656827;
        double r2656829 = r2656823 / r2656828;
        return r2656829;
}
↓
double f(double x) {
        double r2656830 = 2.0;
        double r2656831 = sqrt(r2656830);
        double r2656832 = x;
        double r2656833 = exp(r2656832);
        double r2656834 = -r2656832;
        double r2656835 = exp(r2656834);
        double r2656836 = r2656833 + r2656835;
        double r2656837 = sqrt(r2656836);
        double r2656838 = r2656837 / r2656831;
        double r2656839 = r2656831 / r2656838;
        double r2656840 = r2656839 / r2656837;
        return r2656840;
}

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-sqrt0.8

    \[\leadsto \frac{2}{\color{blue}{\sqrt{e^{x} + e^{-x}} \cdot \sqrt{e^{x} + e^{-x}}}}\]

  4. Applied associate-/r*0.5

    \[\leadsto \color{blue}{\frac{\frac{2}{\sqrt{e^{x} + e^{-x}}}}{\sqrt{e^{x} + e^{-x}}}}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.5

    \[\leadsto \frac{\frac{\color{blue}{\sqrt{2} \cdot \sqrt{2}}}{\sqrt{e^{x} + e^{-x}}}}{\sqrt{e^{x} + e^{-x}}}\]

  7. Applied associate-/l*0.0

    \[\leadsto \frac{\color{blue}{\frac{\sqrt{2}}{\frac{\sqrt{e^{x} + e^{-x}}}{\sqrt{2}}}}}{\sqrt{e^{x} + e^{-x}}}\]

  8. Final simplification0.0

    \[\leadsto \frac{\frac{\sqrt{2}}{\frac{\sqrt{e^{x} + e^{-x}}}{\sqrt{2}}}}{\sqrt{e^{x} + e^{-x}}}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2.0 (+ (exp x) (exp (- x)))))