Average Error: 17.5 → 16.3
Time: 38.7s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;J \le -3.6033028488377203 \cdot 10^{-230}:\\ \;\;\;\;\sqrt{1 + \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} \cdot \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)}} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\\ \mathbf{elif}\;J \le 5.249148278725304 \cdot 10^{-150}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;\sqrt{1 + \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} \cdot \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)}} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\\ \end{array}\]
\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}
↓
\begin{array}{l}
\mathbf{if}\;J \le -3.6033028488377203 \cdot 10^{-230}:\\
\;\;\;\;\sqrt{1 + \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} \cdot \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)}} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\\

\mathbf{elif}\;J \le 5.249148278725304 \cdot 10^{-150}:\\
\;\;\;\;-U\\

\mathbf{else}:\\
\;\;\;\;\sqrt{1 + \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} \cdot \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)}} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\\

\end{array}
double f(double J, double K, double U) {
        double r4444880 = -2.0;
        double r4444881 = J;
        double r4444882 = r4444880 * r4444881;
        double r4444883 = K;
        double r4444884 = 2.0;
        double r4444885 = r4444883 / r4444884;
        double r4444886 = cos(r4444885);
        double r4444887 = r4444882 * r4444886;
        double r4444888 = 1.0;
        double r4444889 = U;
        double r4444890 = r4444884 * r4444881;
        double r4444891 = r4444890 * r4444886;
        double r4444892 = r4444889 / r4444891;
        double r4444893 = pow(r4444892, r4444884);
        double r4444894 = r4444888 + r4444893;
        double r4444895 = sqrt(r4444894);
        double r4444896 = r4444887 * r4444895;
        return r4444896;
}
↓
double f(double J, double K, double U) {
        double r4444897 = J;
        double r4444898 = -3.6033028488377203e-230;
        bool r4444899 = r4444897 <= r4444898;
        double r4444900 = 1.0;
        double r4444901 = U;
        double r4444902 = K;
        double r4444903 = 2.0;
        double r4444904 = r4444902 / r4444903;
        double r4444905 = cos(r4444904);
        double r4444906 = r4444903 * r4444897;
        double r4444907 = r4444905 * r4444906;
        double r4444908 = r4444901 / r4444907;
        double r4444909 = r4444908 * r4444908;
        double r4444910 = r4444900 + r4444909;
        double r4444911 = sqrt(r4444910);
        double r4444912 = -2.0;
        double r4444913 = r4444912 * r4444897;
        double r4444914 = r4444905 * r4444913;
        double r4444915 = r4444911 * r4444914;
        double r4444916 = 5.249148278725304e-150;
        bool r4444917 = r4444897 <= r4444916;
        double r4444918 = -r4444901;
        double r4444919 = r4444917 ? r4444918 : r4444915;
        double r4444920 = r4444899 ? r4444915 : r4444919;
        return r4444920;
}

Error

Bits error versus J

Bits error versus K

Bits error versus U

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if J < -3.6033028488377203e-230 or 5.249148278725304e-150 < J

    1. Initial program 12.0

      \[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]

    2. Simplified12.0

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

    if -3.6033028488377203e-230 < J < 5.249148278725304e-150

    1. Initial program 40.2

      \[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]

    2. Simplified40.2

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

    3. Taylor expanded around inf 34.1

      \[\leadsto \color{blue}{-1 \cdot U}\]

    4. Simplified34.1

      \[\leadsto \color{blue}{-U}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification16.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;J \le -3.6033028488377203 \cdot 10^{-230}:\\ \;\;\;\;\sqrt{1 + \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} \cdot \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)}} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\\ \mathbf{elif}\;J \le 5.249148278725304 \cdot 10^{-150}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;\sqrt{1 + \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} \cdot \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)}} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019146 
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))