Average Error: 0.0 → 0.0
Time: 1.7s
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 r71408 = 2.0;
        double r71409 = x;
        double r71410 = exp(r71409);
        double r71411 = -r71409;
        double r71412 = exp(r71411);
        double r71413 = r71410 + r71412;
        double r71414 = r71408 / r71413;
        return r71414;
}
↓
double f(double x) {
        double r71415 = 2.0;
        double r71416 = x;
        double r71417 = exp(r71416);
        double r71418 = -r71416;
        double r71419 = exp(r71418);
        double r71420 = r71417 + r71419;
        double r71421 = r71415 / r71420;
        double r71422 = sqrt(r71421);
        double r71423 = r71422 * r71422;
        return r71423;
}

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)))))