Average Error: 17.2 → 0.4
Time: 1.3m
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r12217904 = J;
        double r12217905 = l;
        double r12217906 = exp(r12217905);
        double r12217907 = -r12217905;
        double r12217908 = exp(r12217907);
        double r12217909 = r12217906 - r12217908;
        double r12217910 = r12217904 * r12217909;
        double r12217911 = K;
        double r12217912 = 2.0;
        double r12217913 = r12217911 / r12217912;
        double r12217914 = cos(r12217913);
        double r12217915 = r12217910 * r12217914;
        double r12217916 = U;
        double r12217917 = r12217915 + r12217916;
        return r12217917;
}
↓
double f(double J, double l, double K, double U) {
        double r12217918 = l;
        double r12217919 = 5.0;
        double r12217920 = pow(r12217918, r12217919);
        double r12217921 = 0.016666666666666666;
        double r12217922 = r12217920 * r12217921;
        double r12217923 = 2.0;
        double r12217924 = 0.3333333333333333;
        double r12217925 = r12217924 * r12217918;
        double r12217926 = r12217925 * r12217918;
        double r12217927 = r12217923 + r12217926;
        double r12217928 = r12217927 * r12217918;
        double r12217929 = r12217922 + r12217928;
        double r12217930 = J;
        double r12217931 = r12217929 * r12217930;
        double r12217932 = K;
        double r12217933 = r12217932 / r12217923;
        double r12217934 = cos(r12217933);
        double r12217935 = r12217931 * r12217934;
        double r12217936 = U;
        double r12217937 = r12217935 + r12217936;
        return r12217937;
}

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 17.2

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

  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

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2019128 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))