Average Error: 57.9 → 0.7
Time: 10.2s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{\frac{1}{60} \cdot {x}^{5} + \left(x \cdot 2 + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{\frac{1}{60} \cdot {x}^{5} + \left(x \cdot 2 + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}
double f(double x) {
        double r1014915 = x;
        double r1014916 = exp(r1014915);
        double r1014917 = -r1014915;
        double r1014918 = exp(r1014917);
        double r1014919 = r1014916 - r1014918;
        double r1014920 = 2.0;
        double r1014921 = r1014919 / r1014920;
        return r1014921;
}
↓
double f(double x) {
        double r1014922 = 0.016666666666666666;
        double r1014923 = x;
        double r1014924 = 5.0;
        double r1014925 = pow(r1014923, r1014924);
        double r1014926 = r1014922 * r1014925;
        double r1014927 = 2.0;
        double r1014928 = r1014923 * r1014927;
        double r1014929 = 0.3333333333333333;
        double r1014930 = r1014923 * r1014923;
        double r1014931 = r1014929 * r1014930;
        double r1014932 = r1014931 * r1014923;
        double r1014933 = r1014928 + r1014932;
        double r1014934 = r1014926 + r1014933;
        double r1014935 = r1014934 / r1014927;
        return r1014935;
}

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 0.7

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

  3. Simplified0.7

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

  5. Applied distribute-lft-in0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2019151 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))