Average Error: 17.4 → 0.5
Time: 6.9s
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 r151962 = J;
        double r151963 = l;
        double r151964 = exp(r151963);
        double r151965 = -r151963;
        double r151966 = exp(r151965);
        double r151967 = r151964 - r151966;
        double r151968 = r151962 * r151967;
        double r151969 = K;
        double r151970 = 2.0;
        double r151971 = r151969 / r151970;
        double r151972 = cos(r151971);
        double r151973 = r151968 * r151972;
        double r151974 = U;
        double r151975 = r151973 + r151974;
        return r151975;
}
↓
double f(double J, double l, double K, double U) {
        double r151976 = J;
        double r151977 = 0.3333333333333333;
        double r151978 = l;
        double r151979 = 3.0;
        double r151980 = pow(r151978, r151979);
        double r151981 = r151977 * r151980;
        double r151982 = 0.016666666666666666;
        double r151983 = 5.0;
        double r151984 = pow(r151978, r151983);
        double r151985 = r151982 * r151984;
        double r151986 = 2.0;
        double r151987 = r151986 * r151978;
        double r151988 = r151985 + r151987;
        double r151989 = r151981 + r151988;
        double r151990 = K;
        double r151991 = 2.0;
        double r151992 = r151990 / r151991;
        double r151993 = cos(r151992);
        double r151994 = r151989 * r151993;
        double r151995 = r151976 * r151994;
        double r151996 = U;
        double r151997 = r151995 + r151996;
        return r151997;
}

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 17.4

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

  2. Taylor expanded around 0 0.5

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

  4. Applied associate-*l*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2020021 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))