Average Error: 17.6 → 0.4
Time: 42.7s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U
double f(double J, double l, double K, double U) {
        double r79894 = J;
        double r79895 = l;
        double r79896 = exp(r79895);
        double r79897 = -r79895;
        double r79898 = exp(r79897);
        double r79899 = r79896 - r79898;
        double r79900 = r79894 * r79899;
        double r79901 = K;
        double r79902 = 2.0;
        double r79903 = r79901 / r79902;
        double r79904 = cos(r79903);
        double r79905 = r79900 * r79904;
        double r79906 = U;
        double r79907 = r79905 + r79906;
        return r79907;
}
↓
double f(double J, double l, double K, double U) {
        double r79908 = J;
        double r79909 = 0.3333333333333333;
        double r79910 = l;
        double r79911 = 3.0;
        double r79912 = pow(r79910, r79911);
        double r79913 = r79909 * r79912;
        double r79914 = 0.016666666666666666;
        double r79915 = 5.0;
        double r79916 = pow(r79910, r79915);
        double r79917 = r79914 * r79916;
        double r79918 = 2.0;
        double r79919 = r79918 * r79910;
        double r79920 = r79917 + r79919;
        double r79921 = r79913 + r79920;
        double r79922 = K;
        double r79923 = 2.0;
        double r79924 = r79922 / r79923;
        double r79925 = cos(r79924);
        double r79926 = r79921 * r79925;
        double r79927 = r79908 * r79926;
        double r79928 = U;
        double r79929 = r79927 + r79928;
        return r79929;
}

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

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

  4. Applied associate-*l*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019303 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))