Average Error: 18.1 → 8.1
Time: 8.9s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \mathsf{hypot}\left(\sqrt{1}, {\left(\frac{\frac{U}{2 \cdot J}}{\cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}\right)\right)\]
\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 \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)\right)
double f(double J, double K, double U) {
        double r183974 = -2.0;
        double r183975 = J;
        double r183976 = r183974 * r183975;
        double r183977 = K;
        double r183978 = 2.0;
        double r183979 = r183977 / r183978;
        double r183980 = cos(r183979);
        double r183981 = r183976 * r183980;
        double r183982 = 1.0;
        double r183983 = U;
        double r183984 = r183978 * r183975;
        double r183985 = r183984 * r183980;
        double r183986 = r183983 / r183985;
        double r183987 = pow(r183986, r183978);
        double r183988 = r183982 + r183987;
        double r183989 = sqrt(r183988);
        double r183990 = r183981 * r183989;
        return r183990;
}
↓
double f(double J, double K, double U) {
        double r183991 = -2.0;
        double r183992 = J;
        double r183993 = r183991 * r183992;
        double r183994 = K;
        double r183995 = 2.0;
        double r183996 = r183994 / r183995;
        double r183997 = cos(r183996);
        double r183998 = 1.0;
        double r183999 = sqrt(r183998);
        double r184000 = U;
        double r184001 = r183995 * r183992;
        double r184002 = r184000 / r184001;
        double r184003 = r184002 / r183997;
        double r184004 = 2.0;
        double r184005 = r183995 / r184004;
        double r184006 = pow(r184003, r184005);
        double r184007 = hypot(r183999, r184006);
        double r184008 = r183997 * r184007;
        double r184009 = r183993 * r184008;
        return r184009;
}

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 18.1

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

  3. Applied sqr-pow18.1

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

  4. Applied add-sqr-sqrt18.1

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

  5. Applied hypot-def8.1

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

  7. Applied associate-/r*8.1

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

  9. Applied associate-*l*8.1

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

  10. Final simplification8.1

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

Reproduce

herbie shell --seed 2019356 +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)))))