Average Error: 17.6 → 0.4
Time: 41.2s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right)\right) + U
double f(double J, double l, double K, double U) {
        double r9775799 = J;
        double r9775800 = l;
        double r9775801 = exp(r9775800);
        double r9775802 = -r9775800;
        double r9775803 = exp(r9775802);
        double r9775804 = r9775801 - r9775803;
        double r9775805 = r9775799 * r9775804;
        double r9775806 = K;
        double r9775807 = 2.0;
        double r9775808 = r9775806 / r9775807;
        double r9775809 = cos(r9775808);
        double r9775810 = r9775805 * r9775809;
        double r9775811 = U;
        double r9775812 = r9775810 + r9775811;
        return r9775812;
}
↓
double f(double J, double l, double K, double U) {
        double r9775813 = J;
        double r9775814 = K;
        double r9775815 = 2.0;
        double r9775816 = r9775814 / r9775815;
        double r9775817 = cos(r9775816);
        double r9775818 = l;
        double r9775819 = 5.0;
        double r9775820 = pow(r9775818, r9775819);
        double r9775821 = 0.016666666666666666;
        double r9775822 = r9775820 * r9775821;
        double r9775823 = 0.3333333333333333;
        double r9775824 = r9775823 * r9775818;
        double r9775825 = r9775824 * r9775818;
        double r9775826 = r9775815 + r9775825;
        double r9775827 = r9775826 * r9775818;
        double r9775828 = r9775822 + r9775827;
        double r9775829 = r9775817 * r9775828;
        double r9775830 = r9775813 * r9775829;
        double r9775831 = U;
        double r9775832 = r9775830 + r9775831;
        return r9775832;
}

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 17.6

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

  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

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

  5. Applied associate-*l*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019120 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))