Average Error: 58.1 → 0.7
Time: 16.1s
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 r1771559 = x;
        double r1771560 = exp(r1771559);
        double r1771561 = -r1771559;
        double r1771562 = exp(r1771561);
        double r1771563 = r1771560 - r1771562;
        double r1771564 = 2.0;
        double r1771565 = r1771563 / r1771564;
        return r1771565;
}
↓
double f(double x) {
        double r1771566 = x;
        double r1771567 = 5.0;
        double r1771568 = pow(r1771566, r1771567);
        double r1771569 = 0.016666666666666666;
        double r1771570 = r1771568 * r1771569;
        double r1771571 = 2.0;
        double r1771572 = r1771566 * r1771566;
        double r1771573 = 0.3333333333333333;
        double r1771574 = r1771572 * r1771573;
        double r1771575 = r1771571 + r1771574;
        double r1771576 = r1771566 * r1771575;
        double r1771577 = r1771570 + r1771576;
        double r1771578 = r1771577 / r1771571;
        return r1771578;
}

Error

Bits error versus x

Try it out

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 0.7

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

  3. Simplified0.7

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

  4. Final simplification0.7

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

Reproduce

herbie shell --seed 2019144 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))