Average Error: 18.0 → 13.0
Time: 32.2s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} = -\infty \lor \neg \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \le 2.060066890954713680905695378128061767254 \cdot 10^{306}\right):\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \frac{\sqrt{0.25} \cdot U}{J \cdot \cos \left(0.5 \cdot K\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\\ \end{array}\]
\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}\;\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}} = -\infty \lor \neg \left(\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}} \le 2.060066890954713680905695378128061767254 \cdot 10^{306}\right):\\
\;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \frac{\sqrt{0.25} \cdot U}{J \cdot \cos \left(0.5 \cdot K\right)}\\

\mathbf{else}:\\
\;\;\;\;\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}}\\

\end{array}
double f(double J, double K, double U) {
        double r104431 = -2.0;
        double r104432 = J;
        double r104433 = r104431 * r104432;
        double r104434 = K;
        double r104435 = 2.0;
        double r104436 = r104434 / r104435;
        double r104437 = cos(r104436);
        double r104438 = r104433 * r104437;
        double r104439 = 1.0;
        double r104440 = U;
        double r104441 = r104435 * r104432;
        double r104442 = r104441 * r104437;
        double r104443 = r104440 / r104442;
        double r104444 = pow(r104443, r104435);
        double r104445 = r104439 + r104444;
        double r104446 = sqrt(r104445);
        double r104447 = r104438 * r104446;
        return r104447;
}
↓
double f(double J, double K, double U) {
        double r104448 = -2.0;
        double r104449 = J;
        double r104450 = r104448 * r104449;
        double r104451 = K;
        double r104452 = 2.0;
        double r104453 = r104451 / r104452;
        double r104454 = cos(r104453);
        double r104455 = r104450 * r104454;
        double r104456 = 1.0;
        double r104457 = U;
        double r104458 = r104452 * r104449;
        double r104459 = r104458 * r104454;
        double r104460 = r104457 / r104459;
        double r104461 = pow(r104460, r104452);
        double r104462 = r104456 + r104461;
        double r104463 = sqrt(r104462);
        double r104464 = r104455 * r104463;
        double r104465 = -inf.0;
        bool r104466 = r104464 <= r104465;
        double r104467 = 2.0600668909547137e+306;
        bool r104468 = r104464 <= r104467;
        double r104469 = !r104468;
        bool r104470 = r104466 || r104469;
        double r104471 = 0.25;
        double r104472 = sqrt(r104471);
        double r104473 = r104472 * r104457;
        double r104474 = 0.5;
        double r104475 = r104474 * r104451;
        double r104476 = cos(r104475);
        double r104477 = r104449 * r104476;
        double r104478 = r104473 / r104477;
        double r104479 = r104455 * r104478;
        double r104480 = r104470 ? r104479 : r104464;
        return r104480;
}

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 (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) < -inf.0 or 2.0600668909547137e+306 < (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

    1. Initial program 63.6

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

    2. Taylor expanded around inf 45.8

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

    if -inf.0 < (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) < 2.0600668909547137e+306

    1. Initial program 0.1

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

  4. Final simplification13.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} = -\infty \lor \neg \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \le 2.060066890954713680905695378128061767254 \cdot 10^{306}\right):\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \frac{\sqrt{0.25} \cdot U}{J \cdot \cos \left(0.5 \cdot K\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  :precision binary64
  (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))