Average Error: 16.9 → 0.4
Time: 9.5s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \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
double f(double J, double l, double K, double U) {
        double r140866 = J;
        double r140867 = l;
        double r140868 = exp(r140867);
        double r140869 = -r140867;
        double r140870 = exp(r140869);
        double r140871 = r140868 - r140870;
        double r140872 = r140866 * r140871;
        double r140873 = K;
        double r140874 = 2.0;
        double r140875 = r140873 / r140874;
        double r140876 = cos(r140875);
        double r140877 = r140872 * r140876;
        double r140878 = U;
        double r140879 = r140877 + r140878;
        return r140879;
}
↓
double f(double J, double l, double K, double U) {
        double r140880 = J;
        double r140881 = 0.3333333333333333;
        double r140882 = l;
        double r140883 = 3.0;
        double r140884 = pow(r140882, r140883);
        double r140885 = r140881 * r140884;
        double r140886 = 0.016666666666666666;
        double r140887 = 5.0;
        double r140888 = pow(r140882, r140887);
        double r140889 = r140886 * r140888;
        double r140890 = 2.0;
        double r140891 = r140890 * r140882;
        double r140892 = r140889 + r140891;
        double r140893 = r140885 + r140892;
        double r140894 = r140880 * r140893;
        double r140895 = K;
        double r140896 = 2.0;
        double r140897 = r140895 / r140896;
        double r140898 = cos(r140897);
        double r140899 = r140894 * r140898;
        double r140900 = U;
        double r140901 = r140899 + r140900;
        return r140901;
}

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 16.9

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

  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. Final simplification0.4

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

Reproduce

herbie shell --seed 2020100 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))