Average Error: 17.1 → 7.6
Time: 29.7s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;U \le 2.7876448164590437 \cdot 10^{+249}:\\ \;\;\;\;\left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \left(\frac{U}{J \cdot \left(2 \cdot \cos \left(\frac{K}{2}\right)\right)}\right)\right)\\ \mathbf{elif}\;U \le 1.579279709035961 \cdot 10^{+282}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;\left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \left(\frac{U}{J \cdot \left(2 \cdot \cos \left(\frac{K}{2}\right)\right)}\right)\right)\\ \end{array}\]
\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}\;U \le 2.7876448164590437 \cdot 10^{+249}:\\
\;\;\;\;\left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \left(\frac{U}{J \cdot \left(2 \cdot \cos \left(\frac{K}{2}\right)\right)}\right)\right)\\

\mathbf{elif}\;U \le 1.579279709035961 \cdot 10^{+282}:\\
\;\;\;\;-U\\

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

\end{array}
double f(double J, double K, double U) {
        double r3290825 = -2.0;
        double r3290826 = J;
        double r3290827 = r3290825 * r3290826;
        double r3290828 = K;
        double r3290829 = 2.0;
        double r3290830 = r3290828 / r3290829;
        double r3290831 = cos(r3290830);
        double r3290832 = r3290827 * r3290831;
        double r3290833 = 1.0;
        double r3290834 = U;
        double r3290835 = r3290829 * r3290826;
        double r3290836 = r3290835 * r3290831;
        double r3290837 = r3290834 / r3290836;
        double r3290838 = pow(r3290837, r3290829);
        double r3290839 = r3290833 + r3290838;
        double r3290840 = sqrt(r3290839);
        double r3290841 = r3290832 * r3290840;
        return r3290841;
}
↓
double f(double J, double K, double U) {
        double r3290842 = U;
        double r3290843 = 2.7876448164590437e+249;
        bool r3290844 = r3290842 <= r3290843;
        double r3290845 = J;
        double r3290846 = -2.0;
        double r3290847 = r3290845 * r3290846;
        double r3290848 = K;
        double r3290849 = 2.0;
        double r3290850 = r3290848 / r3290849;
        double r3290851 = cos(r3290850);
        double r3290852 = r3290847 * r3290851;
        double r3290853 = 1.0;
        double r3290854 = r3290849 * r3290851;
        double r3290855 = r3290845 * r3290854;
        double r3290856 = r3290842 / r3290855;
        double r3290857 = hypot(r3290853, r3290856);
        double r3290858 = r3290852 * r3290857;
        double r3290859 = 1.579279709035961e+282;
        bool r3290860 = r3290842 <= r3290859;
        double r3290861 = -r3290842;
        double r3290862 = r3290860 ? r3290861 : r3290858;
        double r3290863 = r3290844 ? r3290858 : r3290862;
        return r3290863;
}

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 U < 2.7876448164590437e+249 or 1.579279709035961e+282 < U

    1. Initial program 16.4

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

    2. Simplified6.9

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

    if 2.7876448164590437e+249 < U < 1.579279709035961e+282

    1. Initial program 40.4

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

    2. Simplified28.1

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

    3. Taylor expanded around -inf 33.3

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

    4. Simplified33.3

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

  4. Final simplification7.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;U \le 2.7876448164590437 \cdot 10^{+249}:\\ \;\;\;\;\left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \left(\frac{U}{J \cdot \left(2 \cdot \cos \left(\frac{K}{2}\right)\right)}\right)\right)\\ \mathbf{elif}\;U \le 1.579279709035961 \cdot 10^{+282}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;\left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(1, \left(\frac{U}{J \cdot \left(2 \cdot \cos \left(\frac{K}{2}\right)\right)}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(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)))))