Average Error: 0.0 → 0.0
Time: 8.4s
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 r947298 = 2.0;
        double r947299 = x;
        double r947300 = exp(r947299);
        double r947301 = -r947299;
        double r947302 = exp(r947301);
        double r947303 = r947300 + r947302;
        double r947304 = r947298 / r947303;
        return r947304;
}
↓
double f(double x) {
        double r947305 = -2.0;
        double r947306 = -1.0;
        double r947307 = x;
        double r947308 = exp(r947307);
        double r947309 = r947306 / r947308;
        double r947310 = r947309 - r947308;
        double r947311 = r947305 / r947310;
        return r947311;
}

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

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

  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 2019139 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))