Average Error: 17.7 → 18.9
Time: 22.9s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;U \le -3.440264728937229717785528289539985872593 \cdot 10^{213} \lor \neg \left(U \le -1.468679264294656491917272404167659060091 \cdot 10^{122}\right):\\ \;\;\;\;\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{\frac{U}{2 \cdot J}}{\cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \frac{\sqrt{0.25} \cdot U}{J \cdot \cos \left(0.5 \cdot K\right)}\right)\\ \end{array}\]
\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}\;U \le -3.440264728937229717785528289539985872593 \cdot 10^{213} \lor \neg \left(U \le -1.468679264294656491917272404167659060091 \cdot 10^{122}\right):\\
\;\;\;\;\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{\frac{U}{2 \cdot J}}{\cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)\\

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

\end{array}
double f(double J, double K, double U) {
        double r117729 = -2.0;
        double r117730 = J;
        double r117731 = r117729 * r117730;
        double r117732 = K;
        double r117733 = 2.0;
        double r117734 = r117732 / r117733;
        double r117735 = cos(r117734);
        double r117736 = r117731 * r117735;
        double r117737 = 1.0;
        double r117738 = U;
        double r117739 = r117733 * r117730;
        double r117740 = r117739 * r117735;
        double r117741 = r117738 / r117740;
        double r117742 = pow(r117741, r117733);
        double r117743 = r117737 + r117742;
        double r117744 = sqrt(r117743);
        double r117745 = r117736 * r117744;
        return r117745;
}
↓
double f(double J, double K, double U) {
        double r117746 = U;
        double r117747 = -3.44026472893723e+213;
        bool r117748 = r117746 <= r117747;
        double r117749 = -1.4686792642946565e+122;
        bool r117750 = r117746 <= r117749;
        double r117751 = !r117750;
        bool r117752 = r117748 || r117751;
        double r117753 = -2.0;
        double r117754 = J;
        double r117755 = r117753 * r117754;
        double r117756 = K;
        double r117757 = 2.0;
        double r117758 = r117756 / r117757;
        double r117759 = cos(r117758);
        double r117760 = 1.0;
        double r117761 = r117757 * r117754;
        double r117762 = r117746 / r117761;
        double r117763 = r117762 / r117759;
        double r117764 = pow(r117763, r117757);
        double r117765 = r117760 + r117764;
        double r117766 = sqrt(r117765);
        double r117767 = r117759 * r117766;
        double r117768 = r117755 * r117767;
        double r117769 = 0.25;
        double r117770 = sqrt(r117769);
        double r117771 = r117770 * r117746;
        double r117772 = 0.5;
        double r117773 = r117772 * r117756;
        double r117774 = cos(r117773);
        double r117775 = r117754 * r117774;
        double r117776 = r117771 / r117775;
        double r117777 = r117759 * r117776;
        double r117778 = r117755 * r117777;
        double r117779 = r117752 ? r117768 : r117778;
        return r117779;
}

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 U < -3.44026472893723e+213 or -1.4686792642946565e+122 < U

    1. Initial program 16.5

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

    3. Applied associate-*l*16.5

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

    5. Applied associate-/r*16.5

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

    if -3.44026472893723e+213 < U < -1.4686792642946565e+122

    1. Initial program 33.2

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

    3. Applied associate-*l*33.2

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

    4. Taylor expanded around inf 48.8

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

  4. Final simplification18.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;U \le -3.440264728937229717785528289539985872593 \cdot 10^{213} \lor \neg \left(U \le -1.468679264294656491917272404167659060091 \cdot 10^{122}\right):\\ \;\;\;\;\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{\frac{U}{2 \cdot J}}{\cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \frac{\sqrt{0.25} \cdot U}{J \cdot \cos \left(0.5 \cdot K\right)}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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)))))