Average Error: 0.0 → 0.0
Time: 6.9s
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 r53567 = 2.0;
        double r53568 = x;
        double r53569 = exp(r53568);
        double r53570 = -r53568;
        double r53571 = exp(r53570);
        double r53572 = r53569 + r53571;
        double r53573 = r53567 / r53572;
        return r53573;
}
↓
double f(double x) {
        double r53574 = 2.0;
        double r53575 = x;
        double r53576 = exp(r53575);
        double r53577 = -r53575;
        double r53578 = exp(r53577);
        double r53579 = r53576 + r53578;
        double r53580 = r53574 / r53579;
        double r53581 = sqrt(r53580);
        double r53582 = r53581 * r53581;
        return r53582;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))