Average Error: 58.1 → 0.6
Time: 15.6s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{x \cdot 2 + \left({x}^{5} \cdot \frac{1}{60} + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{x \cdot 2 + \left({x}^{5} \cdot \frac{1}{60} + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}
double f(double x) {
        double r868829 = x;
        double r868830 = exp(r868829);
        double r868831 = -r868829;
        double r868832 = exp(r868831);
        double r868833 = r868830 - r868832;
        double r868834 = 2.0;
        double r868835 = r868833 / r868834;
        return r868835;
}
↓
double f(double x) {
        double r868836 = x;
        double r868837 = 2.0;
        double r868838 = r868836 * r868837;
        double r868839 = 5.0;
        double r868840 = pow(r868836, r868839);
        double r868841 = 0.016666666666666666;
        double r868842 = r868840 * r868841;
        double r868843 = 0.3333333333333333;
        double r868844 = r868836 * r868836;
        double r868845 = r868843 * r868844;
        double r868846 = r868845 * r868836;
        double r868847 = r868842 + r868846;
        double r868848 = r868838 + r868847;
        double r868849 = r868848 / r868837;
        return r868849;
}

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 0.6

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

  3. Simplified0.6

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

  5. Applied distribute-lft-in0.6

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

  6. Applied associate-+l+0.6

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

  7. Final simplification0.6

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

Reproduce

herbie shell --seed 2019153 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))