Average Error: 18.0 → 8.2
Time: 23.8s
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 r125301 = -2.0;
        double r125302 = J;
        double r125303 = r125301 * r125302;
        double r125304 = K;
        double r125305 = 2.0;
        double r125306 = r125304 / r125305;
        double r125307 = cos(r125306);
        double r125308 = r125303 * r125307;
        double r125309 = 1.0;
        double r125310 = U;
        double r125311 = r125305 * r125302;
        double r125312 = r125311 * r125307;
        double r125313 = r125310 / r125312;
        double r125314 = pow(r125313, r125305);
        double r125315 = r125309 + r125314;
        double r125316 = sqrt(r125315);
        double r125317 = r125308 * r125316;
        return r125317;
}
↓
double f(double J, double K, double U) {
        double r125318 = -2.0;
        double r125319 = J;
        double r125320 = r125318 * r125319;
        double r125321 = K;
        double r125322 = 2.0;
        double r125323 = r125321 / r125322;
        double r125324 = cos(r125323);
        double r125325 = r125320 * r125324;
        double r125326 = 1.0;
        double r125327 = sqrt(r125326);
        double r125328 = U;
        double r125329 = r125322 * r125319;
        double r125330 = r125329 * r125324;
        double r125331 = r125328 / r125330;
        double r125332 = 2.0;
        double r125333 = r125322 / r125332;
        double r125334 = pow(r125331, r125333);
        double r125335 = hypot(r125327, r125334);
        double r125336 = r125325 * r125335;
        return r125336;
}

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 18.0

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

  3. Applied sqr-pow18.0

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

  4. Applied add-sqr-sqrt18.0

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

  5. Applied hypot-def8.2

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

  6. Final simplification8.2

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

Reproduce

herbie shell --seed 2019323 +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)))))