Average Error: 18.0 → 7.8
Time: 48.5s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[-2 \cdot \left(\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \mathsf{hypot}\left({\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{\left(\frac{2}{2}\right)}, \sqrt{1}\right)\right)\]
\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}}
↓
-2 \cdot \left(\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \mathsf{hypot}\left({\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{\left(\frac{2}{2}\right)}, \sqrt{1}\right)\right)
double f(double J, double K, double U) {
        double r5742504 = -2.0;
        double r5742505 = J;
        double r5742506 = r5742504 * r5742505;
        double r5742507 = K;
        double r5742508 = 2.0;
        double r5742509 = r5742507 / r5742508;
        double r5742510 = cos(r5742509);
        double r5742511 = r5742506 * r5742510;
        double r5742512 = 1.0;
        double r5742513 = U;
        double r5742514 = r5742508 * r5742505;
        double r5742515 = r5742514 * r5742510;
        double r5742516 = r5742513 / r5742515;
        double r5742517 = pow(r5742516, r5742508);
        double r5742518 = r5742512 + r5742517;
        double r5742519 = sqrt(r5742518);
        double r5742520 = r5742511 * r5742519;
        return r5742520;
}
↓
double f(double J, double K, double U) {
        double r5742521 = -2.0;
        double r5742522 = K;
        double r5742523 = 2.0;
        double r5742524 = r5742522 / r5742523;
        double r5742525 = cos(r5742524);
        double r5742526 = J;
        double r5742527 = r5742525 * r5742526;
        double r5742528 = U;
        double r5742529 = r5742527 * r5742523;
        double r5742530 = r5742528 / r5742529;
        double r5742531 = 2.0;
        double r5742532 = r5742523 / r5742531;
        double r5742533 = pow(r5742530, r5742532);
        double r5742534 = 1.0;
        double r5742535 = sqrt(r5742534);
        double r5742536 = hypot(r5742533, r5742535);
        double r5742537 = r5742527 * r5742536;
        double r5742538 = r5742521 * r5742537;
        return r5742538;
}

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. Simplified18.0

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

  4. Applied add-sqr-sqrt18.0

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

  5. Applied sqr-pow18.0

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

  6. Applied hypot-def7.8

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

  7. Final simplification7.8

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))