Average Error: 0.0 → 0.0
Time: 9.6s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{-2}{\left(-e^{x}\right) + \frac{-1}{e^{x}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\frac{-2}{\left(-e^{x}\right) + \frac{-1}{e^{x}}}
double f(double x) {
        double r882220 = 2.0;
        double r882221 = x;
        double r882222 = exp(r882221);
        double r882223 = -r882221;
        double r882224 = exp(r882223);
        double r882225 = r882222 + r882224;
        double r882226 = r882220 / r882225;
        return r882226;
}
↓
double f(double x) {
        double r882227 = -2.0;
        double r882228 = x;
        double r882229 = exp(r882228);
        double r882230 = -r882229;
        double r882231 = -1.0;
        double r882232 = r882231 / r882229;
        double r882233 = r882230 + r882232;
        double r882234 = r882227 / r882233;
        return r882234;
}

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

    \[\leadsto \frac{-2}{\color{blue}{\frac{-1}{e^{x}} + \left(-e^{x}\right)}}\]

  6. Final simplification0.0

    \[\leadsto \frac{-2}{\left(-e^{x}\right) + \frac{-1}{e^{x}}}\]

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))