Average Error: 58.1 → 0.6
Time: 14.7s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{\frac{1}{60} \cdot {x}^{5} + \left(2 + \left(x \cdot \frac{1}{3}\right) \cdot x\right) \cdot x}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{\frac{1}{60} \cdot {x}^{5} + \left(2 + \left(x \cdot \frac{1}{3}\right) \cdot x\right) \cdot x}{2}
double f(double x) {
        double r2874912 = x;
        double r2874913 = exp(r2874912);
        double r2874914 = -r2874912;
        double r2874915 = exp(r2874914);
        double r2874916 = r2874913 - r2874915;
        double r2874917 = 2.0;
        double r2874918 = r2874916 / r2874917;
        return r2874918;
}
↓
double f(double x) {
        double r2874919 = 0.016666666666666666;
        double r2874920 = x;
        double r2874921 = 5.0;
        double r2874922 = pow(r2874920, r2874921);
        double r2874923 = r2874919 * r2874922;
        double r2874924 = 2.0;
        double r2874925 = 0.3333333333333333;
        double r2874926 = r2874920 * r2874925;
        double r2874927 = r2874926 * r2874920;
        double r2874928 = r2874924 + r2874927;
        double r2874929 = r2874928 * r2874920;
        double r2874930 = r2874923 + r2874929;
        double r2874931 = 2.0;
        double r2874932 = r2874930 / r2874931;
        return r2874932;
}

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

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2.0))