Average Error: 18.5 → 7.9
Time: 25.4s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \mathsf{hypot}\left(\sqrt{1}, {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}\right)\]
\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(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\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)
double f(double J, double K, double U) {
        double r128463 = -2.0;
        double r128464 = J;
        double r128465 = r128463 * r128464;
        double r128466 = K;
        double r128467 = 2.0;
        double r128468 = r128466 / r128467;
        double r128469 = cos(r128468);
        double r128470 = r128465 * r128469;
        double r128471 = 1.0;
        double r128472 = U;
        double r128473 = r128467 * r128464;
        double r128474 = r128473 * r128469;
        double r128475 = r128472 / r128474;
        double r128476 = pow(r128475, r128467);
        double r128477 = r128471 + r128476;
        double r128478 = sqrt(r128477);
        double r128479 = r128470 * r128478;
        return r128479;
}
↓
double f(double J, double K, double U) {
        double r128480 = -2.0;
        double r128481 = J;
        double r128482 = r128480 * r128481;
        double r128483 = K;
        double r128484 = 2.0;
        double r128485 = r128483 / r128484;
        double r128486 = cos(r128485);
        double r128487 = r128482 * r128486;
        double r128488 = 1.0;
        double r128489 = sqrt(r128488);
        double r128490 = U;
        double r128491 = r128484 * r128481;
        double r128492 = r128491 * r128486;
        double r128493 = r128490 / r128492;
        double r128494 = 2.0;
        double r128495 = r128484 / r128494;
        double r128496 = pow(r128493, r128495);
        double r128497 = hypot(r128489, r128496);
        double r128498 = r128487 * r128497;
        return r128498;
}

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 18.5

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

  3. Applied sqr-pow18.5

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

  4. Applied add-sqr-sqrt18.5

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

  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. Final simplification7.9

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

Reproduce

herbie shell --seed 2019303 +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)))))