Average Error: 18.7 → 19.6
Time: 22.6s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;J \le -1.454940457745922809601389624522144446421 \cdot 10^{-191} \lor \neg \left(J \le 2.839632097914101075502916192452293789493 \cdot 10^{-234}\right):\\ \;\;\;\;\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{{\left(\frac{\frac{U}{2}}{J \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{U \cdot \frac{\sqrt{0.25}}{\cos \left(0.5 \cdot K\right)}}{J} \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \left(-2 \cdot J\right)\\ \end{array}\]
\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 -1.454940457745922809601389624522144446421 \cdot 10^{-191} \lor \neg \left(J \le 2.839632097914101075502916192452293789493 \cdot 10^{-234}\right):\\
\;\;\;\;\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{{\left(\frac{\frac{U}{2}}{J \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1}\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{U \cdot \frac{\sqrt{0.25}}{\cos \left(0.5 \cdot K\right)}}{J} \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \left(-2 \cdot J\right)\\

\end{array}
double f(double J, double K, double U) {
        double r97500 = -2.0;
        double r97501 = J;
        double r97502 = r97500 * r97501;
        double r97503 = K;
        double r97504 = 2.0;
        double r97505 = r97503 / r97504;
        double r97506 = cos(r97505);
        double r97507 = r97502 * r97506;
        double r97508 = 1.0;
        double r97509 = U;
        double r97510 = r97504 * r97501;
        double r97511 = r97510 * r97506;
        double r97512 = r97509 / r97511;
        double r97513 = pow(r97512, r97504);
        double r97514 = r97508 + r97513;
        double r97515 = sqrt(r97514);
        double r97516 = r97507 * r97515;
        return r97516;
}
↓
double f(double J, double K, double U) {
        double r97517 = J;
        double r97518 = -1.4549404577459228e-191;
        bool r97519 = r97517 <= r97518;
        double r97520 = 2.839632097914101e-234;
        bool r97521 = r97517 <= r97520;
        double r97522 = !r97521;
        bool r97523 = r97519 || r97522;
        double r97524 = -2.0;
        double r97525 = r97524 * r97517;
        double r97526 = K;
        double r97527 = 2.0;
        double r97528 = r97526 / r97527;
        double r97529 = cos(r97528);
        double r97530 = U;
        double r97531 = r97530 / r97527;
        double r97532 = r97517 * r97529;
        double r97533 = r97531 / r97532;
        double r97534 = pow(r97533, r97527);
        double r97535 = 1.0;
        double r97536 = r97534 + r97535;
        double r97537 = sqrt(r97536);
        double r97538 = r97529 * r97537;
        double r97539 = r97525 * r97538;
        double r97540 = 0.25;
        double r97541 = sqrt(r97540);
        double r97542 = 0.5;
        double r97543 = r97542 * r97526;
        double r97544 = cos(r97543);
        double r97545 = r97541 / r97544;
        double r97546 = r97530 * r97545;
        double r97547 = r97546 / r97517;
        double r97548 = r97547 * r97529;
        double r97549 = r97548 * r97525;
        double r97550 = r97523 ? r97539 : r97549;
        return r97550;
}

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 < -1.4549404577459228e-191 or 2.839632097914101e-234 < J

    1. Initial program 14.2

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

    3. Applied associate-*l*14.2

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

    4. Simplified14.2

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

    if -1.4549404577459228e-191 < J < 2.839632097914101e-234

    1. Initial program 42.6

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

    3. Applied associate-*l*42.7

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

    4. Simplified42.7

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

    5. Taylor expanded around inf 48.2

      \[\leadsto \left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \color{blue}{\frac{\sqrt{0.25} \cdot U}{\cos \left(0.5 \cdot K\right) \cdot J}}\right)\]

    6. Simplified48.2

      \[\leadsto \left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \color{blue}{\frac{\frac{\sqrt{0.25}}{\cos \left(0.5 \cdot K\right)} \cdot U}{J}}\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification19.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;J \le -1.454940457745922809601389624522144446421 \cdot 10^{-191} \lor \neg \left(J \le 2.839632097914101075502916192452293789493 \cdot 10^{-234}\right):\\ \;\;\;\;\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{{\left(\frac{\frac{U}{2}}{J \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{U \cdot \frac{\sqrt{0.25}}{\cos \left(0.5 \cdot K\right)}}{J} \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \left(-2 \cdot J\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))