Average Error: 17.6 → 0.4
Time: 24.4s
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 r74866 = J;
        double r74867 = l;
        double r74868 = exp(r74867);
        double r74869 = -r74867;
        double r74870 = exp(r74869);
        double r74871 = r74868 - r74870;
        double r74872 = r74866 * r74871;
        double r74873 = K;
        double r74874 = 2.0;
        double r74875 = r74873 / r74874;
        double r74876 = cos(r74875);
        double r74877 = r74872 * r74876;
        double r74878 = U;
        double r74879 = r74877 + r74878;
        return r74879;
}
↓
double f(double J, double l, double K, double U) {
        double r74880 = J;
        double r74881 = 0.3333333333333333;
        double r74882 = l;
        double r74883 = 3.0;
        double r74884 = pow(r74882, r74883);
        double r74885 = r74881 * r74884;
        double r74886 = 0.016666666666666666;
        double r74887 = 5.0;
        double r74888 = pow(r74882, r74887);
        double r74889 = r74886 * r74888;
        double r74890 = 2.0;
        double r74891 = r74890 * r74882;
        double r74892 = r74889 + r74891;
        double r74893 = r74885 + r74892;
        double r74894 = r74880 * r74893;
        double r74895 = K;
        double r74896 = 2.0;
        double r74897 = r74895 / r74896;
        double r74898 = cos(r74897);
        double r74899 = r74894 * r74898;
        double r74900 = U;
        double r74901 = r74899 + r74900;
        return r74901;
}

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. 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 2019235 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))