Average Error: 57.9 → 0.6
Time: 29.1s
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 r9298910 = x;
        double r9298911 = exp(r9298910);
        double r9298912 = -r9298910;
        double r9298913 = exp(r9298912);
        double r9298914 = r9298911 - r9298913;
        double r9298915 = 2.0;
        double r9298916 = r9298914 / r9298915;
        return r9298916;
}
↓
double f(double x) {
        double r9298917 = x;
        double r9298918 = 5.0;
        double r9298919 = pow(r9298917, r9298918);
        double r9298920 = 0.016666666666666666;
        double r9298921 = r9298919 * r9298920;
        double r9298922 = 2.0;
        double r9298923 = r9298922 * r9298917;
        double r9298924 = 0.3333333333333333;
        double r9298925 = r9298917 * r9298924;
        double r9298926 = r9298917 * r9298925;
        double r9298927 = r9298926 * r9298917;
        double r9298928 = r9298923 + r9298927;
        double r9298929 = r9298921 + r9298928;
        double r9298930 = r9298929 / r9298922;
        return r9298930;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 57.9

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

  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 2019125 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))