Average Error: 0.0 → 0.0
Time: 2.6s
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 r64448 = 2.0;
        double r64449 = x;
        double r64450 = exp(r64449);
        double r64451 = -r64449;
        double r64452 = exp(r64451);
        double r64453 = r64450 + r64452;
        double r64454 = r64448 / r64453;
        return r64454;
}
↓
double f(double x) {
        double r64455 = 2.0;
        double r64456 = x;
        double r64457 = exp(r64456);
        double r64458 = -r64456;
        double r64459 = exp(r64458);
        double r64460 = r64457 + r64459;
        double r64461 = r64455 / r64460;
        double r64462 = sqrt(r64461);
        double r64463 = r64462 * r64462;
        return r64463;
}

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 2020039 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))