Average Error: 18.7 → 18.7
Time: 26.7s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)\]
\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(-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)
double f(double J, double K, double U) {
        double r101552 = -2.0;
        double r101553 = J;
        double r101554 = r101552 * r101553;
        double r101555 = K;
        double r101556 = 2.0;
        double r101557 = r101555 / r101556;
        double r101558 = cos(r101557);
        double r101559 = r101554 * r101558;
        double r101560 = 1.0;
        double r101561 = U;
        double r101562 = r101556 * r101553;
        double r101563 = r101562 * r101558;
        double r101564 = r101561 / r101563;
        double r101565 = pow(r101564, r101556);
        double r101566 = r101560 + r101565;
        double r101567 = sqrt(r101566);
        double r101568 = r101559 * r101567;
        return r101568;
}
↓
double f(double J, double K, double U) {
        double r101569 = -2.0;
        double r101570 = J;
        double r101571 = r101569 * r101570;
        double r101572 = K;
        double r101573 = 2.0;
        double r101574 = r101572 / r101573;
        double r101575 = cos(r101574);
        double r101576 = 1.0;
        double r101577 = U;
        double r101578 = r101573 * r101570;
        double r101579 = r101578 * r101575;
        double r101580 = r101577 / r101579;
        double r101581 = pow(r101580, r101573);
        double r101582 = r101576 + r101581;
        double r101583 = sqrt(r101582);
        double r101584 = r101575 * r101583;
        double r101585 = r101571 * r101584;
        return r101585;
}

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 18.7

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

  3. Applied associate-*l*18.7

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

  4. Final simplification18.7

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

Reproduce

herbie shell --seed 2019298 
(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)))))