Average Error: 58.4 → 1.6
Time: 36.3s
Precision: 64
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
↓
\[{x}^{5} \cdot \frac{2}{15} + \left(x + \frac{-1}{3} \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)\]
\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}
↓
{x}^{5} \cdot \frac{2}{15} + \left(x + \frac{-1}{3} \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)
double f(double x) {
        double r2424442 = x;
        double r2424443 = exp(r2424442);
        double r2424444 = -r2424442;
        double r2424445 = exp(r2424444);
        double r2424446 = r2424443 - r2424445;
        double r2424447 = r2424443 + r2424445;
        double r2424448 = r2424446 / r2424447;
        return r2424448;
}
↓
double f(double x) {
        double r2424449 = x;
        double r2424450 = 5.0;
        double r2424451 = pow(r2424449, r2424450);
        double r2424452 = 0.13333333333333333;
        double r2424453 = r2424451 * r2424452;
        double r2424454 = -0.3333333333333333;
        double r2424455 = r2424449 * r2424449;
        double r2424456 = r2424455 * r2424449;
        double r2424457 = r2424454 * r2424456;
        double r2424458 = r2424449 + r2424457;
        double r2424459 = r2424453 + r2424458;
        return r2424459;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.4

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]

  2. Taylor expanded around 0 1.6

    \[\leadsto \color{blue}{\left(x + \frac{2}{15} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}}\]

  3. Simplified1.6

    \[\leadsto \color{blue}{{x}^{5} \cdot \frac{2}{15} + \left(x + \left(\left(x \cdot x\right) \cdot x\right) \cdot \frac{-1}{3}\right)}\]

  4. Final simplification1.6

    \[\leadsto {x}^{5} \cdot \frac{2}{15} + \left(x + \frac{-1}{3} \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)\]

Reproduce

herbie shell --seed 2019149 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))