Average Error: 17.7 → 13.4
Time: 23.8s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) = -\infty \lor \neg \left(\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) \le 2.046657204468815031699915225739490531069 \cdot 10^{296}\right):\\ \;\;\;\;\left(\sqrt[3]{\cos \left(\frac{K}{2}\right)} \cdot \left(\left(-2 \cdot \left(\sqrt[3]{\cos \left(\frac{K}{2}\right)} \cdot J\right)\right) \cdot \sqrt[3]{\cos \left(\frac{K}{2}\right)}\right)\right) \cdot \frac{\frac{\sqrt{0.25} \cdot U}{J}}{\cos \left(0.5 \cdot K\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\\ \end{array}\]
\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}\;\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) = -\infty \lor \neg \left(\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) \le 2.046657204468815031699915225739490531069 \cdot 10^{296}\right):\\
\;\;\;\;\left(\sqrt[3]{\cos \left(\frac{K}{2}\right)} \cdot \left(\left(-2 \cdot \left(\sqrt[3]{\cos \left(\frac{K}{2}\right)} \cdot J\right)\right) \cdot \sqrt[3]{\cos \left(\frac{K}{2}\right)}\right)\right) \cdot \frac{\frac{\sqrt{0.25} \cdot U}{J}}{\cos \left(0.5 \cdot K\right)}\\

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

\end{array}
double f(double J, double K, double U) {
        double r105967 = -2.0;
        double r105968 = J;
        double r105969 = r105967 * r105968;
        double r105970 = K;
        double r105971 = 2.0;
        double r105972 = r105970 / r105971;
        double r105973 = cos(r105972);
        double r105974 = r105969 * r105973;
        double r105975 = 1.0;
        double r105976 = U;
        double r105977 = r105971 * r105968;
        double r105978 = r105977 * r105973;
        double r105979 = r105976 / r105978;
        double r105980 = pow(r105979, r105971);
        double r105981 = r105975 + r105980;
        double r105982 = sqrt(r105981);
        double r105983 = r105974 * r105982;
        return r105983;
}
↓
double f(double J, double K, double U) {
        double r105984 = U;
        double r105985 = J;
        double r105986 = 2.0;
        double r105987 = r105985 * r105986;
        double r105988 = K;
        double r105989 = r105988 / r105986;
        double r105990 = cos(r105989);
        double r105991 = r105987 * r105990;
        double r105992 = r105984 / r105991;
        double r105993 = pow(r105992, r105986);
        double r105994 = 1.0;
        double r105995 = r105993 + r105994;
        double r105996 = sqrt(r105995);
        double r105997 = -2.0;
        double r105998 = r105997 * r105985;
        double r105999 = r105990 * r105998;
        double r106000 = r105996 * r105999;
        double r106001 = -inf.0;
        bool r106002 = r106000 <= r106001;
        double r106003 = 2.046657204468815e+296;
        bool r106004 = r106000 <= r106003;
        double r106005 = !r106004;
        bool r106006 = r106002 || r106005;
        double r106007 = cbrt(r105990);
        double r106008 = r106007 * r105985;
        double r106009 = r105997 * r106008;
        double r106010 = r106009 * r106007;
        double r106011 = r106007 * r106010;
        double r106012 = 0.25;
        double r106013 = sqrt(r106012);
        double r106014 = r106013 * r105984;
        double r106015 = r106014 / r105985;
        double r106016 = 0.5;
        double r106017 = r106016 * r105988;
        double r106018 = cos(r106017);
        double r106019 = r106015 / r106018;
        double r106020 = r106011 * r106019;
        double r106021 = r106006 ? r106020 : r106000;
        return r106021;
}

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 2.046657204468815e+296 < (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

    1. Initial program 61.0

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

    3. Applied add-cube-cbrt61.0

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

    4. Applied associate-*r*61.0

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

    5. Simplified61.0

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

    6. Taylor expanded around inf 46.1

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

    7. Simplified46.1

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

    if -inf.0 < (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) < 2.046657204468815e+296

    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 simplification13.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) = -\infty \lor \neg \left(\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) \le 2.046657204468815031699915225739490531069 \cdot 10^{296}\right):\\ \;\;\;\;\left(\sqrt[3]{\cos \left(\frac{K}{2}\right)} \cdot \left(\left(-2 \cdot \left(\sqrt[3]{\cos \left(\frac{K}{2}\right)} \cdot J\right)\right) \cdot \sqrt[3]{\cos \left(\frac{K}{2}\right)}\right)\right) \cdot \frac{\frac{\sqrt{0.25} \cdot U}{J}}{\cos \left(0.5 \cdot K\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(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)))))