Average Error: 0.0 → 0.0
Time: 4.3s
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 r61603 = 2.0;
        double r61604 = x;
        double r61605 = exp(r61604);
        double r61606 = -r61604;
        double r61607 = exp(r61606);
        double r61608 = r61605 + r61607;
        double r61609 = r61603 / r61608;
        return r61609;
}
↓
double f(double x) {
        double r61610 = 2.0;
        double r61611 = x;
        double r61612 = exp(r61611);
        double r61613 = -r61611;
        double r61614 = exp(r61613);
        double r61615 = r61612 + r61614;
        double r61616 = r61610 / r61615;
        double r61617 = sqrt(r61616);
        double r61618 = r61617 * r61617;
        return r61618;
}

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)))))