Average Error: 17.1 → 0.4
Time: 21.8s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\ell \cdot 2 + \frac{1}{60} \cdot {\ell}^{5}\right)\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\ell \cdot 2 + \frac{1}{60} \cdot {\ell}^{5}\right)\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)
double f(double J, double l, double K, double U) {
        double r66826 = J;
        double r66827 = l;
        double r66828 = exp(r66827);
        double r66829 = -r66827;
        double r66830 = exp(r66829);
        double r66831 = r66828 - r66830;
        double r66832 = r66826 * r66831;
        double r66833 = K;
        double r66834 = 2.0;
        double r66835 = r66833 / r66834;
        double r66836 = cos(r66835);
        double r66837 = r66832 * r66836;
        double r66838 = U;
        double r66839 = r66837 + r66838;
        return r66839;
}
↓
double f(double J, double l, double K, double U) {
        double r66840 = U;
        double r66841 = 0.3333333333333333;
        double r66842 = l;
        double r66843 = 3.0;
        double r66844 = pow(r66842, r66843);
        double r66845 = r66841 * r66844;
        double r66846 = 2.0;
        double r66847 = r66842 * r66846;
        double r66848 = 0.016666666666666666;
        double r66849 = 5.0;
        double r66850 = pow(r66842, r66849);
        double r66851 = r66848 * r66850;
        double r66852 = r66847 + r66851;
        double r66853 = r66845 + r66852;
        double r66854 = J;
        double r66855 = r66853 * r66854;
        double r66856 = K;
        double r66857 = 2.0;
        double r66858 = r66856 / r66857;
        double r66859 = cos(r66858);
        double r66860 = r66855 * r66859;
        double r66861 = r66840 + r66860;
        return r66861;
}

Error

Bits error versus J

Bits error versus l

Bits error versus K

Bits error versus U

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 17.1

    \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  2. Taylor expanded around 0 0.4

    \[\leadsto \left(J \cdot \color{blue}{\left(2 \cdot \ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  3. Simplified0.4

    \[\leadsto \left(J \cdot \color{blue}{\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  4. Final simplification0.4

    \[\leadsto U + \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\ell \cdot 2 + \frac{1}{60} \cdot {\ell}^{5}\right)\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\]

Reproduce

herbie shell --seed 2019194 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))