Average Error: 17.9 → 8.3
Time: 8.6s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \mathsf{hypot}\left(\sqrt{1}, {\left(\frac{\frac{U}{2 \cdot J}}{\cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}\right)\right)\]
\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 \mathsf{hypot}\left(\sqrt{1}, {\left(\frac{\frac{U}{2 \cdot J}}{\cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}\right)\right)
double f(double J, double K, double U) {
        double r265703 = -2.0;
        double r265704 = J;
        double r265705 = r265703 * r265704;
        double r265706 = K;
        double r265707 = 2.0;
        double r265708 = r265706 / r265707;
        double r265709 = cos(r265708);
        double r265710 = r265705 * r265709;
        double r265711 = 1.0;
        double r265712 = U;
        double r265713 = r265707 * r265704;
        double r265714 = r265713 * r265709;
        double r265715 = r265712 / r265714;
        double r265716 = pow(r265715, r265707);
        double r265717 = r265711 + r265716;
        double r265718 = sqrt(r265717);
        double r265719 = r265710 * r265718;
        return r265719;
}
↓
double f(double J, double K, double U) {
        double r265720 = -2.0;
        double r265721 = J;
        double r265722 = r265720 * r265721;
        double r265723 = K;
        double r265724 = 2.0;
        double r265725 = r265723 / r265724;
        double r265726 = cos(r265725);
        double r265727 = 1.0;
        double r265728 = sqrt(r265727);
        double r265729 = U;
        double r265730 = r265724 * r265721;
        double r265731 = r265729 / r265730;
        double r265732 = r265731 / r265726;
        double r265733 = 2.0;
        double r265734 = r265724 / r265733;
        double r265735 = pow(r265732, r265734);
        double r265736 = hypot(r265728, r265735);
        double r265737 = r265726 * r265736;
        double r265738 = r265722 * r265737;
        return r265738;
}

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. Using strategy rm

  3. Applied sqr-pow17.9

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

  4. Applied add-sqr-sqrt17.9

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

  5. Applied hypot-def8.3

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

  7. Applied associate-*l*8.4

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

  9. Applied associate-/r*8.3

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

  10. Final simplification8.3

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

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(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)))))