Average Error: 0.0 → 0.0
Time: 8.7s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{2}}{\sqrt{e^{x} + e^{-x}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\frac{\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{2}}{\sqrt{e^{x} + e^{-x}}}
double f(double x) {
        double r34728 = 2.0;
        double r34729 = x;
        double r34730 = exp(r34729);
        double r34731 = -r34729;
        double r34732 = exp(r34731);
        double r34733 = r34730 + r34732;
        double r34734 = r34728 / r34733;
        return r34734;
}
↓
double f(double x) {
        double r34735 = 2.0;
        double r34736 = x;
        double r34737 = exp(r34736);
        double r34738 = -r34736;
        double r34739 = exp(r34738);
        double r34740 = r34737 + r34739;
        double r34741 = r34735 / r34740;
        double r34742 = sqrt(r34741);
        double r34743 = sqrt(r34735);
        double r34744 = r34742 * r34743;
        double r34745 = sqrt(r34740);
        double r34746 = r34744 / r34745;
        return r34746;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  5. Applied sqrt-div0.0

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

  6. Applied associate-*r/0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))