Average Error: 17.9 → 17.9
Time: 7.4s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)\]
\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 r121343 = -2.0;
        double r121344 = J;
        double r121345 = r121343 * r121344;
        double r121346 = K;
        double r121347 = 2.0;
        double r121348 = r121346 / r121347;
        double r121349 = cos(r121348);
        double r121350 = r121345 * r121349;
        double r121351 = 1.0;
        double r121352 = U;
        double r121353 = r121347 * r121344;
        double r121354 = r121353 * r121349;
        double r121355 = r121352 / r121354;
        double r121356 = pow(r121355, r121347);
        double r121357 = r121351 + r121356;
        double r121358 = sqrt(r121357);
        double r121359 = r121350 * r121358;
        return r121359;
}
↓
double f(double J, double K, double U) {
        double r121360 = -2.0;
        double r121361 = J;
        double r121362 = r121360 * r121361;
        double r121363 = K;
        double r121364 = 2.0;
        double r121365 = r121363 / r121364;
        double r121366 = cos(r121365);
        double r121367 = 1.0;
        double r121368 = U;
        double r121369 = r121364 * r121361;
        double r121370 = r121369 * r121366;
        double r121371 = r121368 / r121370;
        double r121372 = pow(r121371, r121364);
        double r121373 = r121367 + r121372;
        double r121374 = sqrt(r121373);
        double r121375 = r121366 * r121374;
        double r121376 = r121362 * r121375;
        return r121376;
}

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 associate-*l*17.9

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

  4. Final simplification17.9

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

Reproduce

herbie shell --seed 2020001 
(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)))))