Average Error: 17.2 → 0.4
Time: 32.1s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(\left(\ell \cdot \ell\right) \cdot \frac{1}{3} + 2\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(\left(\ell \cdot \ell\right) \cdot \frac{1}{3} + 2\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r2463898 = J;
        double r2463899 = l;
        double r2463900 = exp(r2463899);
        double r2463901 = -r2463899;
        double r2463902 = exp(r2463901);
        double r2463903 = r2463900 - r2463902;
        double r2463904 = r2463898 * r2463903;
        double r2463905 = K;
        double r2463906 = 2.0;
        double r2463907 = r2463905 / r2463906;
        double r2463908 = cos(r2463907);
        double r2463909 = r2463904 * r2463908;
        double r2463910 = U;
        double r2463911 = r2463909 + r2463910;
        return r2463911;
}
↓
double f(double J, double l, double K, double U) {
        double r2463912 = l;
        double r2463913 = 5.0;
        double r2463914 = pow(r2463912, r2463913);
        double r2463915 = 0.016666666666666666;
        double r2463916 = r2463914 * r2463915;
        double r2463917 = r2463912 * r2463912;
        double r2463918 = 0.3333333333333333;
        double r2463919 = r2463917 * r2463918;
        double r2463920 = 2.0;
        double r2463921 = r2463919 + r2463920;
        double r2463922 = r2463921 * r2463912;
        double r2463923 = r2463916 + r2463922;
        double r2463924 = J;
        double r2463925 = r2463923 * r2463924;
        double r2463926 = K;
        double r2463927 = r2463926 / r2463920;
        double r2463928 = cos(r2463927);
        double r2463929 = r2463925 * r2463928;
        double r2463930 = U;
        double r2463931 = r2463929 + r2463930;
        return r2463931;
}

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 17.2

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

  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

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2019132 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))