Average Error: 17.9 → 17.9
Time: 26.7s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\left(\sqrt{1 + \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)} \cdot \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot -2\right)\right) \cdot J\]
\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}}
↓
\left(\sqrt{1 + \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)} \cdot \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot -2\right)\right) \cdot J
double f(double J, double K, double U) {
        double r2213815 = -2.0;
        double r2213816 = J;
        double r2213817 = r2213815 * r2213816;
        double r2213818 = K;
        double r2213819 = 2.0;
        double r2213820 = r2213818 / r2213819;
        double r2213821 = cos(r2213820);
        double r2213822 = r2213817 * r2213821;
        double r2213823 = 1.0;
        double r2213824 = U;
        double r2213825 = r2213819 * r2213816;
        double r2213826 = r2213825 * r2213821;
        double r2213827 = r2213824 / r2213826;
        double r2213828 = pow(r2213827, r2213819);
        double r2213829 = r2213823 + r2213828;
        double r2213830 = sqrt(r2213829);
        double r2213831 = r2213822 * r2213830;
        return r2213831;
}
↓
double f(double J, double K, double U) {
        double r2213832 = 1.0;
        double r2213833 = U;
        double r2213834 = 2.0;
        double r2213835 = J;
        double r2213836 = r2213834 * r2213835;
        double r2213837 = K;
        double r2213838 = r2213837 / r2213834;
        double r2213839 = cos(r2213838);
        double r2213840 = r2213836 * r2213839;
        double r2213841 = r2213833 / r2213840;
        double r2213842 = r2213841 * r2213841;
        double r2213843 = r2213832 + r2213842;
        double r2213844 = sqrt(r2213843);
        double r2213845 = -2.0;
        double r2213846 = r2213839 * r2213845;
        double r2213847 = r2213844 * r2213846;
        double r2213848 = r2213847 * r2213835;
        return r2213848;
}

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. Initial program 17.9

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

  2. Simplified17.9

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

  4. Applied associate-*l*17.9

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

  5. Final simplification17.9

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

Reproduce

herbie shell --seed 2019153 
(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)))))