Average Error: 17.6 → 17.8
Time: 23.0s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;J \le -5.409574867481547 \cdot 10^{-290}:\\ \;\;\;\;J \cdot \left(\left(-2 \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} \cdot \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} + 1}\right)\\ \mathbf{elif}\;J \le 9.21309517046108 \cdot 10^{-234}:\\ \;\;\;\;\left(\frac{U}{J \cdot \cos \left(K \cdot \frac{1}{2}\right)} \cdot \frac{1}{2}\right) \cdot \left(J \cdot \left(-2 \cdot \cos \left(\frac{K}{2}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(\left(-2 \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} \cdot \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} + 1}\right)\\ \end{array}\]
\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 -5.409574867481547 \cdot 10^{-290}:\\
\;\;\;\;J \cdot \left(\left(-2 \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\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)} + 1}\right)\\

\mathbf{elif}\;J \le 9.21309517046108 \cdot 10^{-234}:\\
\;\;\;\;\left(\frac{U}{J \cdot \cos \left(K \cdot \frac{1}{2}\right)} \cdot \frac{1}{2}\right) \cdot \left(J \cdot \left(-2 \cdot \cos \left(\frac{K}{2}\right)\right)\right)\\

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

\end{array}
double f(double J, double K, double U) {
        double r2693490 = -2.0;
        double r2693491 = J;
        double r2693492 = r2693490 * r2693491;
        double r2693493 = K;
        double r2693494 = 2.0;
        double r2693495 = r2693493 / r2693494;
        double r2693496 = cos(r2693495);
        double r2693497 = r2693492 * r2693496;
        double r2693498 = 1.0;
        double r2693499 = U;
        double r2693500 = r2693494 * r2693491;
        double r2693501 = r2693500 * r2693496;
        double r2693502 = r2693499 / r2693501;
        double r2693503 = pow(r2693502, r2693494);
        double r2693504 = r2693498 + r2693503;
        double r2693505 = sqrt(r2693504);
        double r2693506 = r2693497 * r2693505;
        return r2693506;
}
↓
double f(double J, double K, double U) {
        double r2693507 = J;
        double r2693508 = -5.409574867481547e-290;
        bool r2693509 = r2693507 <= r2693508;
        double r2693510 = -2.0;
        double r2693511 = K;
        double r2693512 = 2.0;
        double r2693513 = r2693511 / r2693512;
        double r2693514 = cos(r2693513);
        double r2693515 = r2693510 * r2693514;
        double r2693516 = U;
        double r2693517 = r2693512 * r2693507;
        double r2693518 = r2693514 * r2693517;
        double r2693519 = r2693516 / r2693518;
        double r2693520 = r2693519 * r2693519;
        double r2693521 = 1.0;
        double r2693522 = r2693520 + r2693521;
        double r2693523 = sqrt(r2693522);
        double r2693524 = r2693515 * r2693523;
        double r2693525 = r2693507 * r2693524;
        double r2693526 = 9.21309517046108e-234;
        bool r2693527 = r2693507 <= r2693526;
        double r2693528 = 0.5;
        double r2693529 = r2693511 * r2693528;
        double r2693530 = cos(r2693529);
        double r2693531 = r2693507 * r2693530;
        double r2693532 = r2693516 / r2693531;
        double r2693533 = r2693532 * r2693528;
        double r2693534 = r2693507 * r2693515;
        double r2693535 = r2693533 * r2693534;
        double r2693536 = r2693527 ? r2693535 : r2693525;
        double r2693537 = r2693509 ? r2693525 : r2693536;
        return r2693537;
}

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 < -5.409574867481547e-290 or 9.21309517046108e-234 < J

    1. Initial program 15.4

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

    2. Simplified15.4

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

    4. Applied associate-*l*15.4

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

    if -5.409574867481547e-290 < J < 9.21309517046108e-234

    1. Initial program 43.9

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

    2. Simplified43.9

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

    3. Taylor expanded around inf 47.0

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

  4. Final simplification17.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;J \le -5.409574867481547 \cdot 10^{-290}:\\ \;\;\;\;J \cdot \left(\left(-2 \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} \cdot \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} + 1}\right)\\ \mathbf{elif}\;J \le 9.21309517046108 \cdot 10^{-234}:\\ \;\;\;\;\left(\frac{U}{J \cdot \cos \left(K \cdot \frac{1}{2}\right)} \cdot \frac{1}{2}\right) \cdot \left(J \cdot \left(-2 \cdot \cos \left(\frac{K}{2}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;J \cdot \left(\left(-2 \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} \cdot \frac{U}{\cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot J\right)} + 1}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019154 
(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)))))