Average Error: 58.2 → 0.6
Time: 25.9s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{{x}^{5} \cdot \frac{1}{60} + \left(2 \cdot x + \left(x \cdot \left(x \cdot \frac{1}{3}\right)\right) \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{{x}^{5} \cdot \frac{1}{60} + \left(2 \cdot x + \left(x \cdot \left(x \cdot \frac{1}{3}\right)\right) \cdot x\right)}{2}
double f(double x) {
        double r3703842 = x;
        double r3703843 = exp(r3703842);
        double r3703844 = -r3703842;
        double r3703845 = exp(r3703844);
        double r3703846 = r3703843 - r3703845;
        double r3703847 = 2.0;
        double r3703848 = r3703846 / r3703847;
        return r3703848;
}
↓
double f(double x) {
        double r3703849 = x;
        double r3703850 = 5.0;
        double r3703851 = pow(r3703849, r3703850);
        double r3703852 = 0.016666666666666666;
        double r3703853 = r3703851 * r3703852;
        double r3703854 = 2.0;
        double r3703855 = r3703854 * r3703849;
        double r3703856 = 0.3333333333333333;
        double r3703857 = r3703849 * r3703856;
        double r3703858 = r3703849 * r3703857;
        double r3703859 = r3703858 * r3703849;
        double r3703860 = r3703855 + r3703859;
        double r3703861 = r3703853 + r3703860;
        double r3703862 = r3703861 / r3703854;
        return r3703862;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.2

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

  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. Simplified0.6

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

  5. Applied distribute-rgt-in0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2019128 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))