Average Error: 17.9 → 13.0
Time: 29.2s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} = -\infty \lor \neg \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \le 1.792215731407936430111562169642558319512 \cdot 10^{308}\right):\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \frac{\sqrt{0.25} \cdot U}{J \cdot \cos \left(0.5 \cdot K\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}\right) \cdot {\left(1 + \left(\sqrt[3]{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)}^{\left(\frac{1}{4}\right)}\\ \end{array}\]
\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}\;\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 1.792215731407936430111562169642558319512 \cdot 10^{308}\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(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}\right) \cdot {\left(1 + \left(\sqrt[3]{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)}^{\left(\frac{1}{4}\right)}\\

\end{array}
double f(double J, double K, double U) {
        double r130008 = -2.0;
        double r130009 = J;
        double r130010 = r130008 * r130009;
        double r130011 = K;
        double r130012 = 2.0;
        double r130013 = r130011 / r130012;
        double r130014 = cos(r130013);
        double r130015 = r130010 * r130014;
        double r130016 = 1.0;
        double r130017 = U;
        double r130018 = r130012 * r130009;
        double r130019 = r130018 * r130014;
        double r130020 = r130017 / r130019;
        double r130021 = pow(r130020, r130012);
        double r130022 = r130016 + r130021;
        double r130023 = sqrt(r130022);
        double r130024 = r130015 * r130023;
        return r130024;
}
↓
double f(double J, double K, double U) {
        double r130025 = -2.0;
        double r130026 = J;
        double r130027 = r130025 * r130026;
        double r130028 = K;
        double r130029 = 2.0;
        double r130030 = r130028 / r130029;
        double r130031 = cos(r130030);
        double r130032 = r130027 * r130031;
        double r130033 = 1.0;
        double r130034 = U;
        double r130035 = r130029 * r130026;
        double r130036 = r130035 * r130031;
        double r130037 = r130034 / r130036;
        double r130038 = pow(r130037, r130029);
        double r130039 = r130033 + r130038;
        double r130040 = sqrt(r130039);
        double r130041 = r130032 * r130040;
        double r130042 = -inf.0;
        bool r130043 = r130041 <= r130042;
        double r130044 = 1.7922157314079364e+308;
        bool r130045 = r130041 <= r130044;
        double r130046 = !r130045;
        bool r130047 = r130043 || r130046;
        double r130048 = 0.25;
        double r130049 = sqrt(r130048);
        double r130050 = r130049 * r130034;
        double r130051 = 0.5;
        double r130052 = r130051 * r130028;
        double r130053 = cos(r130052);
        double r130054 = r130026 * r130053;
        double r130055 = r130050 / r130054;
        double r130056 = r130032 * r130055;
        double r130057 = sqrt(r130040);
        double r130058 = r130032 * r130057;
        double r130059 = cbrt(r130038);
        double r130060 = r130059 * r130059;
        double r130061 = r130060 * r130059;
        double r130062 = r130033 + r130061;
        double r130063 = 1.0;
        double r130064 = 4.0;
        double r130065 = r130063 / r130064;
        double r130066 = pow(r130062, r130065);
        double r130067 = r130058 * r130066;
        double r130068 = r130047 ? r130056 : r130067;
        return r130068;
}

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 1.7922157314079364e+308 < (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

    1. Initial program 64.0

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

    2. Taylor expanded around inf 46.0

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

    if -inf.0 < (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) < 1.7922157314079364e+308

    1. Initial program 0.1

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

    3. Applied add-sqr-sqrt0.1

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

    4. Applied sqrt-prod0.3

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

    5. Applied associate-*r*0.3

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

    7. Applied pow10.3

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

    8. Applied sqrt-pow10.3

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

    9. Applied sqrt-pow10.3

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

    10. Simplified0.3

      \[\leadsto \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}\right) \cdot {\left(1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}\right)}^{\color{blue}{\left(\frac{1}{4}\right)}}\]
    11. Using strategy rm

    12. Applied add-cube-cbrt0.3

      \[\leadsto \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}\right) \cdot {\left(1 + \color{blue}{\left(\sqrt[3]{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}\right)}^{\left(\frac{1}{4}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification13.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} = -\infty \lor \neg \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \le 1.792215731407936430111562169642558319512 \cdot 10^{308}\right):\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \frac{\sqrt{0.25} \cdot U}{J \cdot \cos \left(0.5 \cdot K\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}\right) \cdot {\left(1 + \left(\sqrt[3]{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)}^{\left(\frac{1}{4}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019294 
(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)))))