Average Error: 58.0 → 0.7
Time: 23.2s
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 r6835907 = x;
        double r6835908 = exp(r6835907);
        double r6835909 = -r6835907;
        double r6835910 = exp(r6835909);
        double r6835911 = r6835908 - r6835910;
        double r6835912 = 2.0;
        double r6835913 = r6835911 / r6835912;
        return r6835913;
}
↓
double f(double x) {
        double r6835914 = x;
        double r6835915 = 5.0;
        double r6835916 = pow(r6835914, r6835915);
        double r6835917 = 0.016666666666666666;
        double r6835918 = r6835916 * r6835917;
        double r6835919 = 2.0;
        double r6835920 = r6835919 * r6835914;
        double r6835921 = 0.3333333333333333;
        double r6835922 = r6835914 * r6835921;
        double r6835923 = r6835914 * r6835922;
        double r6835924 = r6835923 * r6835914;
        double r6835925 = r6835920 + r6835924;
        double r6835926 = r6835918 + r6835925;
        double r6835927 = r6835926 / r6835919;
        return r6835927;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.0

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

  2. Taylor expanded around 0 0.7

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

  3. Simplified0.7

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

  5. Applied distribute-rgt-in0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2019112 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))