Average Error: 58.0 → 0.6
Time: 13.4s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{2 \cdot x + \left(\frac{1}{3} \cdot {x}^{3} + \frac{1}{60} \cdot {x}^{5}\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{2 \cdot x + \left(\frac{1}{3} \cdot {x}^{3} + \frac{1}{60} \cdot {x}^{5}\right)}{2}
double f(double x) {
        double r42818 = x;
        double r42819 = exp(r42818);
        double r42820 = -r42818;
        double r42821 = exp(r42820);
        double r42822 = r42819 - r42821;
        double r42823 = 2.0;
        double r42824 = r42822 / r42823;
        return r42824;
}
↓
double f(double x) {
        double r42825 = 2.0;
        double r42826 = x;
        double r42827 = r42825 * r42826;
        double r42828 = 0.3333333333333333;
        double r42829 = 3.0;
        double r42830 = pow(r42826, r42829);
        double r42831 = r42828 * r42830;
        double r42832 = 0.016666666666666666;
        double r42833 = 5.0;
        double r42834 = pow(r42826, r42833);
        double r42835 = r42832 * r42834;
        double r42836 = r42831 + r42835;
        double r42837 = r42827 + r42836;
        double r42838 = 2.0;
        double r42839 = r42837 / r42838;
        return r42839;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.0

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

  2. Taylor expanded around 0 0.6

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

  3. Final simplification0.6

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2.0))