Average Error: 16.9 → 16.3
Time: 1.8m
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;U \le -1.6416870737127194 \cdot 10^{+260}:\\ \;\;\;\;-U\\ \mathbf{elif}\;U \le 1.8384104522567525 \cdot 10^{+175}:\\ \;\;\;\;\left(-2 \cdot \sqrt{\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2} \cdot \frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2} + 1}\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\\ \mathbf{else}:\\ \;\;\;\;-U\\ \end{array}\]
\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 -1.6416870737127194 \cdot 10^{+260}:\\
\;\;\;\;-U\\

\mathbf{elif}\;U \le 1.8384104522567525 \cdot 10^{+175}:\\
\;\;\;\;\left(-2 \cdot \sqrt{\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2} \cdot \frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2} + 1}\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\\

\mathbf{else}:\\
\;\;\;\;-U\\

\end{array}
double f(double J, double K, double U) {
        double r19069505 = -2.0;
        double r19069506 = J;
        double r19069507 = r19069505 * r19069506;
        double r19069508 = K;
        double r19069509 = 2.0;
        double r19069510 = r19069508 / r19069509;
        double r19069511 = cos(r19069510);
        double r19069512 = r19069507 * r19069511;
        double r19069513 = 1.0;
        double r19069514 = U;
        double r19069515 = r19069509 * r19069506;
        double r19069516 = r19069515 * r19069511;
        double r19069517 = r19069514 / r19069516;
        double r19069518 = pow(r19069517, r19069509);
        double r19069519 = r19069513 + r19069518;
        double r19069520 = sqrt(r19069519);
        double r19069521 = r19069512 * r19069520;
        return r19069521;
}
↓
double f(double J, double K, double U) {
        double r19069522 = U;
        double r19069523 = -1.6416870737127194e+260;
        bool r19069524 = r19069522 <= r19069523;
        double r19069525 = -r19069522;
        double r19069526 = 1.8384104522567525e+175;
        bool r19069527 = r19069522 <= r19069526;
        double r19069528 = -2.0;
        double r19069529 = K;
        double r19069530 = 2.0;
        double r19069531 = r19069529 / r19069530;
        double r19069532 = cos(r19069531);
        double r19069533 = J;
        double r19069534 = r19069532 * r19069533;
        double r19069535 = r19069534 * r19069530;
        double r19069536 = r19069522 / r19069535;
        double r19069537 = r19069536 * r19069536;
        double r19069538 = 1.0;
        double r19069539 = r19069537 + r19069538;
        double r19069540 = sqrt(r19069539);
        double r19069541 = r19069528 * r19069540;
        double r19069542 = r19069541 * r19069534;
        double r19069543 = r19069527 ? r19069542 : r19069525;
        double r19069544 = r19069524 ? r19069525 : r19069543;
        return r19069544;
}

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 < -1.6416870737127194e+260 or 1.8384104522567525e+175 < U

    1. Initial program 38.6

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

    2. Simplified38.6

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

    4. Applied add-cube-cbrt38.8

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

    5. Applied associate-*l*38.8

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

    6. Taylor expanded around -inf 34.9

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

    7. Simplified34.9

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

    if -1.6416870737127194e+260 < U < 1.8384104522567525e+175

    1. Initial program 13.0

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

    2. Simplified13.0

      \[\leadsto \color{blue}{\left(\sqrt{\frac{U}{2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)} \cdot \frac{U}{2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)} + 1} \cdot -2\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification16.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;U \le -1.6416870737127194 \cdot 10^{+260}:\\ \;\;\;\;-U\\ \mathbf{elif}\;U \le 1.8384104522567525 \cdot 10^{+175}:\\ \;\;\;\;\left(-2 \cdot \sqrt{\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2} \cdot \frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2} + 1}\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\\ \mathbf{else}:\\ \;\;\;\;-U\\ \end{array}\]

Reproduce

herbie shell --seed 2019120 
(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)))))