Average Error: 58.1 → 0.6
Time: 13.3s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{\frac{1}{60} \cdot {x}^{5} + \left(2 \cdot x + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{\frac{1}{60} \cdot {x}^{5} + \left(2 \cdot x + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}
double f(double x) {
        double r2825827 = x;
        double r2825828 = exp(r2825827);
        double r2825829 = -r2825827;
        double r2825830 = exp(r2825829);
        double r2825831 = r2825828 - r2825830;
        double r2825832 = 2.0;
        double r2825833 = r2825831 / r2825832;
        return r2825833;
}
↓
double f(double x) {
        double r2825834 = 0.016666666666666666;
        double r2825835 = x;
        double r2825836 = 5.0;
        double r2825837 = pow(r2825835, r2825836);
        double r2825838 = r2825834 * r2825837;
        double r2825839 = 2.0;
        double r2825840 = r2825839 * r2825835;
        double r2825841 = 0.3333333333333333;
        double r2825842 = r2825835 * r2825835;
        double r2825843 = r2825841 * r2825842;
        double r2825844 = r2825843 * r2825835;
        double r2825845 = r2825840 + r2825844;
        double r2825846 = r2825838 + r2825845;
        double r2825847 = r2825846 / r2825839;
        return r2825847;
}

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 0.6

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

  3. Simplified0.7

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

  5. Applied distribute-rgt-in0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))