Average Error: 58.1 → 0.7
Time: 5.3s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{\frac{1}{3} \cdot {x}^{3} + \left(\frac{1}{60} \cdot {x}^{5} + 2 \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{\frac{1}{3} \cdot {x}^{3} + \left(\frac{1}{60} \cdot {x}^{5} + 2 \cdot x\right)}{2}
double f(double x) {
        double r64747 = x;
        double r64748 = exp(r64747);
        double r64749 = -r64747;
        double r64750 = exp(r64749);
        double r64751 = r64748 - r64750;
        double r64752 = 2.0;
        double r64753 = r64751 / r64752;
        return r64753;
}
↓
double f(double x) {
        double r64754 = 0.3333333333333333;
        double r64755 = x;
        double r64756 = 3.0;
        double r64757 = pow(r64755, r64756);
        double r64758 = r64754 * r64757;
        double r64759 = 0.016666666666666666;
        double r64760 = 5.0;
        double r64761 = pow(r64755, r64760);
        double r64762 = r64759 * r64761;
        double r64763 = 2.0;
        double r64764 = r64763 * r64755;
        double r64765 = r64762 + r64764;
        double r64766 = r64758 + r64765;
        double r64767 = 2.0;
        double r64768 = r64766 / r64767;
        return r64768;
}

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

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

  3. Final simplification0.7

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

Reproduce

herbie shell --seed 2020024 
(FPCore (x)
  :name "Hyperbolic sine"
  :precision binary64
  (/ (- (exp x) (exp (- x))) 2))