Average Error: 17.5 → 0.4
Time: 35.1s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \cos \left(\frac{K}{2}\right) \cdot \left(\left(\left(\frac{1}{60} \cdot \left(\ell \cdot \ell\right) + \frac{1}{3}\right) \cdot \left(\ell \cdot \left(\ell \cdot \ell\right)\right) + 2 \cdot \ell\right) \cdot J\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \cos \left(\frac{K}{2}\right) \cdot \left(\left(\left(\frac{1}{60} \cdot \left(\ell \cdot \ell\right) + \frac{1}{3}\right) \cdot \left(\ell \cdot \left(\ell \cdot \ell\right)\right) + 2 \cdot \ell\right) \cdot J\right)
double f(double J, double l, double K, double U) {
        double r2915865 = J;
        double r2915866 = l;
        double r2915867 = exp(r2915866);
        double r2915868 = -r2915866;
        double r2915869 = exp(r2915868);
        double r2915870 = r2915867 - r2915869;
        double r2915871 = r2915865 * r2915870;
        double r2915872 = K;
        double r2915873 = 2.0;
        double r2915874 = r2915872 / r2915873;
        double r2915875 = cos(r2915874);
        double r2915876 = r2915871 * r2915875;
        double r2915877 = U;
        double r2915878 = r2915876 + r2915877;
        return r2915878;
}
↓
double f(double J, double l, double K, double U) {
        double r2915879 = U;
        double r2915880 = K;
        double r2915881 = 2.0;
        double r2915882 = r2915880 / r2915881;
        double r2915883 = cos(r2915882);
        double r2915884 = 0.016666666666666666;
        double r2915885 = l;
        double r2915886 = r2915885 * r2915885;
        double r2915887 = r2915884 * r2915886;
        double r2915888 = 0.3333333333333333;
        double r2915889 = r2915887 + r2915888;
        double r2915890 = r2915885 * r2915886;
        double r2915891 = r2915889 * r2915890;
        double r2915892 = r2915881 * r2915885;
        double r2915893 = r2915891 + r2915892;
        double r2915894 = J;
        double r2915895 = r2915893 * r2915894;
        double r2915896 = r2915883 * r2915895;
        double r2915897 = r2915879 + r2915896;
        return r2915897;
}

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 17.5

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

  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. Using strategy rm

  5. Applied associate-*l*0.4

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

  6. Simplified0.4

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

  8. Applied associate-*r*0.4

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

  9. Simplified0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019141 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))