Average Error: 16.7 → 16.0
Time: 2.0m
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;J \le -3.412047028071739 \cdot 10^{-146}:\\ \;\;\;\;\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left(-2 \cdot \sqrt{1 + \frac{U}{2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)} \cdot \frac{U}{2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)}}\right)\\ \mathbf{elif}\;J \le 1.722601909069302 \cdot 10^{-268}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left(-2 \cdot \sqrt{1 + \frac{U}{2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)} \cdot \frac{U}{2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)}}\right)\\ \end{array}\]
\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}\;J \le -3.412047028071739 \cdot 10^{-146}:\\
\;\;\;\;\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left(-2 \cdot \sqrt{1 + \frac{U}{2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)} \cdot \frac{U}{2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)}}\right)\\

\mathbf{elif}\;J \le 1.722601909069302 \cdot 10^{-268}:\\
\;\;\;\;-U\\

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

\end{array}
double f(double J, double K, double U) {
        double r30793835 = -2.0;
        double r30793836 = J;
        double r30793837 = r30793835 * r30793836;
        double r30793838 = K;
        double r30793839 = 2.0;
        double r30793840 = r30793838 / r30793839;
        double r30793841 = cos(r30793840);
        double r30793842 = r30793837 * r30793841;
        double r30793843 = 1.0;
        double r30793844 = U;
        double r30793845 = r30793839 * r30793836;
        double r30793846 = r30793845 * r30793841;
        double r30793847 = r30793844 / r30793846;
        double r30793848 = pow(r30793847, r30793839);
        double r30793849 = r30793843 + r30793848;
        double r30793850 = sqrt(r30793849);
        double r30793851 = r30793842 * r30793850;
        return r30793851;
}
↓
double f(double J, double K, double U) {
        double r30793852 = J;
        double r30793853 = -3.412047028071739e-146;
        bool r30793854 = r30793852 <= r30793853;
        double r30793855 = K;
        double r30793856 = 2.0;
        double r30793857 = r30793855 / r30793856;
        double r30793858 = cos(r30793857);
        double r30793859 = r30793858 * r30793852;
        double r30793860 = -2.0;
        double r30793861 = 1.0;
        double r30793862 = U;
        double r30793863 = r30793856 * r30793859;
        double r30793864 = r30793862 / r30793863;
        double r30793865 = r30793864 * r30793864;
        double r30793866 = r30793861 + r30793865;
        double r30793867 = sqrt(r30793866);
        double r30793868 = r30793860 * r30793867;
        double r30793869 = r30793859 * r30793868;
        double r30793870 = 1.722601909069302e-268;
        bool r30793871 = r30793852 <= r30793870;
        double r30793872 = -r30793862;
        double r30793873 = r30793871 ? r30793872 : r30793869;
        double r30793874 = r30793854 ? r30793869 : r30793873;
        return r30793874;
}

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 < -3.412047028071739e-146 or 1.722601909069302e-268 < J

    1. Initial program 12.6

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

    2. Simplified12.6

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

    if -3.412047028071739e-146 < J < 1.722601909069302e-268

    1. Initial program 38.7

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

    2. Simplified38.7

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

    4. Applied add-cube-cbrt38.9

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

    5. Applied associate-*l*38.9

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

    6. Taylor expanded around -inf 34.3

      \[\leadsto \color{blue}{-1 \cdot U}\]

    7. Simplified34.3

      \[\leadsto \color{blue}{-U}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification16.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;J \le -3.412047028071739 \cdot 10^{-146}:\\ \;\;\;\;\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left(-2 \cdot \sqrt{1 + \frac{U}{2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)} \cdot \frac{U}{2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)}}\right)\\ \mathbf{elif}\;J \le 1.722601909069302 \cdot 10^{-268}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left(-2 \cdot \sqrt{1 + \frac{U}{2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)} \cdot \frac{U}{2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019104 
(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)))))