Average Error: 17.7 → 7.9
Time: 25.2s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\left(-2 \cdot J\right) \cdot \left(\mathsf{hypot}\left(\sqrt{1}, {\left(\frac{\frac{U}{2 \cdot J}}{\cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}\right) \cdot \cos \left(\frac{K}{2}\right)\right)\]
\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(\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) \cdot \cos \left(\frac{K}{2}\right)\right)
double f(double J, double K, double U) {
        double r133649 = -2.0;
        double r133650 = J;
        double r133651 = r133649 * r133650;
        double r133652 = K;
        double r133653 = 2.0;
        double r133654 = r133652 / r133653;
        double r133655 = cos(r133654);
        double r133656 = r133651 * r133655;
        double r133657 = 1.0;
        double r133658 = U;
        double r133659 = r133653 * r133650;
        double r133660 = r133659 * r133655;
        double r133661 = r133658 / r133660;
        double r133662 = pow(r133661, r133653);
        double r133663 = r133657 + r133662;
        double r133664 = sqrt(r133663);
        double r133665 = r133656 * r133664;
        return r133665;
}
↓
double f(double J, double K, double U) {
        double r133666 = -2.0;
        double r133667 = J;
        double r133668 = r133666 * r133667;
        double r133669 = 1.0;
        double r133670 = sqrt(r133669);
        double r133671 = U;
        double r133672 = 2.0;
        double r133673 = r133672 * r133667;
        double r133674 = r133671 / r133673;
        double r133675 = K;
        double r133676 = r133675 / r133672;
        double r133677 = cos(r133676);
        double r133678 = r133674 / r133677;
        double r133679 = 2.0;
        double r133680 = r133672 / r133679;
        double r133681 = pow(r133678, r133680);
        double r133682 = hypot(r133670, r133681);
        double r133683 = r133682 * r133677;
        double r133684 = r133668 * r133683;
        return r133684;
}

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 17.7

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

  3. Applied sqr-pow17.7

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

  4. Applied add-sqr-sqrt17.7

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

  5. Applied hypot-def7.9

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

  7. Applied associate-*l*8.0

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

  8. Simplified8.0

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

  10. Applied associate-/r*7.9

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

  11. Final simplification7.9

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

Reproduce

herbie shell --seed 2019325 +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)))))