Average Error: 58.3 → 0.6
Time: 13.3s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{{x}^{5} \cdot \frac{1}{60} + \left(x \cdot 2 + \left(\left(\frac{1}{3} \cdot x\right) \cdot x\right) \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{{x}^{5} \cdot \frac{1}{60} + \left(x \cdot 2 + \left(\left(\frac{1}{3} \cdot x\right) \cdot x\right) \cdot x\right)}{2}
double f(double x) {
        double r2817818 = x;
        double r2817819 = exp(r2817818);
        double r2817820 = -r2817818;
        double r2817821 = exp(r2817820);
        double r2817822 = r2817819 - r2817821;
        double r2817823 = 2.0;
        double r2817824 = r2817822 / r2817823;
        return r2817824;
}
↓
double f(double x) {
        double r2817825 = x;
        double r2817826 = 5.0;
        double r2817827 = pow(r2817825, r2817826);
        double r2817828 = 0.016666666666666666;
        double r2817829 = r2817827 * r2817828;
        double r2817830 = 2.0;
        double r2817831 = r2817825 * r2817830;
        double r2817832 = 0.3333333333333333;
        double r2817833 = r2817832 * r2817825;
        double r2817834 = r2817833 * r2817825;
        double r2817835 = r2817834 * r2817825;
        double r2817836 = r2817831 + r2817835;
        double r2817837 = r2817829 + r2817836;
        double r2817838 = 2.0;
        double r2817839 = r2817837 / r2817838;
        return r2817839;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.3

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

  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

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

  5. Applied distribute-lft-in0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2.0))