Average Error: 58.1 → 0.5
Time: 20.6s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{{x}^{5} \cdot \frac{1}{60} + x \cdot \left(2 + \left(x \cdot x\right) \cdot \frac{1}{3}\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{{x}^{5} \cdot \frac{1}{60} + x \cdot \left(2 + \left(x \cdot x\right) \cdot \frac{1}{3}\right)}{2}
double f(double x) {
        double r2202738 = x;
        double r2202739 = exp(r2202738);
        double r2202740 = -r2202738;
        double r2202741 = exp(r2202740);
        double r2202742 = r2202739 - r2202741;
        double r2202743 = 2.0;
        double r2202744 = r2202742 / r2202743;
        return r2202744;
}
↓
double f(double x) {
        double r2202745 = x;
        double r2202746 = 5.0;
        double r2202747 = pow(r2202745, r2202746);
        double r2202748 = 0.016666666666666666;
        double r2202749 = r2202747 * r2202748;
        double r2202750 = 2.0;
        double r2202751 = r2202745 * r2202745;
        double r2202752 = 0.3333333333333333;
        double r2202753 = r2202751 * r2202752;
        double r2202754 = r2202750 + r2202753;
        double r2202755 = r2202745 * r2202754;
        double r2202756 = r2202749 + r2202755;
        double r2202757 = r2202756 / r2202750;
        return r2202757;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.1

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

  2. Taylor expanded around 0 0.5

    \[\leadsto \frac{\color{blue}{2 \cdot x + \left(\frac{1}{3} \cdot {x}^{3} + \frac{1}{60} \cdot {x}^{5}\right)}}{2}\]

  3. Simplified0.5

    \[\leadsto \frac{\color{blue}{\left(2 + \frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x + \frac{1}{60} \cdot {x}^{5}}}{2}\]

  4. Final simplification0.5

    \[\leadsto \frac{{x}^{5} \cdot \frac{1}{60} + x \cdot \left(2 + \left(x \cdot x\right) \cdot \frac{1}{3}\right)}{2}\]

Reproduce

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