Average Error: 0.0 → 0.0
Time: 19.8s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{\sqrt{2}}{\sqrt{e^{x} + e^{-x}}} \cdot \left(\sqrt{\frac{\sqrt{2}}{\sqrt{e^{x} + e^{-x}}}} \cdot \sqrt{\frac{\sqrt{2}}{\sqrt{e^{x} + e^{-x}}}}\right)\]
\frac{2}{e^{x} + e^{-x}}
↓
\frac{\sqrt{2}}{\sqrt{e^{x} + e^{-x}}} \cdot \left(\sqrt{\frac{\sqrt{2}}{\sqrt{e^{x} + e^{-x}}}} \cdot \sqrt{\frac{\sqrt{2}}{\sqrt{e^{x} + e^{-x}}}}\right)
double f(double x) {
        double r2322349 = 2.0;
        double r2322350 = x;
        double r2322351 = exp(r2322350);
        double r2322352 = -r2322350;
        double r2322353 = exp(r2322352);
        double r2322354 = r2322351 + r2322353;
        double r2322355 = r2322349 / r2322354;
        return r2322355;
}
↓
double f(double x) {
        double r2322356 = 2.0;
        double r2322357 = sqrt(r2322356);
        double r2322358 = x;
        double r2322359 = exp(r2322358);
        double r2322360 = -r2322358;
        double r2322361 = exp(r2322360);
        double r2322362 = r2322359 + r2322361;
        double r2322363 = sqrt(r2322362);
        double r2322364 = r2322357 / r2322363;
        double r2322365 = sqrt(r2322364);
        double r2322366 = r2322365 * r2322365;
        double r2322367 = r2322364 * r2322366;
        return r2322367;
}

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-sqrt0.8

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

  4. Applied add-sqr-sqrt0.0

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

  5. Applied times-frac0.0

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

  7. Applied add-sqr-sqrt0.0

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

  8. Final simplification0.0

    \[\leadsto \frac{\sqrt{2}}{\sqrt{e^{x} + e^{-x}}} \cdot \left(\sqrt{\frac{\sqrt{2}}{\sqrt{e^{x} + e^{-x}}}} \cdot \sqrt{\frac{\sqrt{2}}{\sqrt{e^{x} + e^{-x}}}}\right)\]

Reproduce

herbie shell --seed 2019151 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))