Average Error: 0.0 → 0.0
Time: 22.2s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{-2}{\frac{-1}{e^{x}} - e^{x}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\frac{-2}{\frac{-1}{e^{x}} - e^{x}}
double f(double x) {
        double r2600346 = 2.0;
        double r2600347 = x;
        double r2600348 = exp(r2600347);
        double r2600349 = -r2600347;
        double r2600350 = exp(r2600349);
        double r2600351 = r2600348 + r2600350;
        double r2600352 = r2600346 / r2600351;
        return r2600352;
}
↓
double f(double x) {
        double r2600353 = 2.0;
        double r2600354 = -r2600353;
        double r2600355 = -1.0;
        double r2600356 = x;
        double r2600357 = exp(r2600356);
        double r2600358 = r2600355 / r2600357;
        double r2600359 = r2600358 - r2600357;
        double r2600360 = r2600354 / r2600359;
        return r2600360;
}

Error

Bits error versus x

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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 frac-2neg0.0

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

  4. Simplified0.0

    \[\leadsto \frac{-2}{\color{blue}{\frac{-1}{e^{x}} - e^{x}}}\]

  5. Final simplification0.0

    \[\leadsto \frac{-2}{\frac{-1}{e^{x}} - e^{x}}\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2.0 (+ (exp x) (exp (- x)))))