Average Error: 0.0 → 0.0
Time: 23.7s
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 r1477296 = 2.0;
        double r1477297 = x;
        double r1477298 = exp(r1477297);
        double r1477299 = -r1477297;
        double r1477300 = exp(r1477299);
        double r1477301 = r1477298 + r1477300;
        double r1477302 = r1477296 / r1477301;
        return r1477302;
}
↓
double f(double x) {
        double r1477303 = -2.0;
        double r1477304 = -1.0;
        double r1477305 = x;
        double r1477306 = exp(r1477305);
        double r1477307 = r1477304 / r1477306;
        double r1477308 = r1477307 - r1477306;
        double r1477309 = r1477303 / r1477308;
        return r1477309;
}

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 frac-2neg0.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019146 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))