Average Error: 17.7 → 7.9
Time: 24.0s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\left(-2 \cdot J\right) \cdot \left(\mathsf{hypot}\left(\sqrt{1}, {\left(\frac{\frac{U}{2 \cdot J}}{\cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}\right) \cdot \cos \left(\frac{K}{2}\right)\right)\]
\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(-2 \cdot J\right) \cdot \left(\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) \cdot \cos \left(\frac{K}{2}\right)\right)
double f(double J, double K, double U) {
        double r150004 = -2.0;
        double r150005 = J;
        double r150006 = r150004 * r150005;
        double r150007 = K;
        double r150008 = 2.0;
        double r150009 = r150007 / r150008;
        double r150010 = cos(r150009);
        double r150011 = r150006 * r150010;
        double r150012 = 1.0;
        double r150013 = U;
        double r150014 = r150008 * r150005;
        double r150015 = r150014 * r150010;
        double r150016 = r150013 / r150015;
        double r150017 = pow(r150016, r150008);
        double r150018 = r150012 + r150017;
        double r150019 = sqrt(r150018);
        double r150020 = r150011 * r150019;
        return r150020;
}
↓
double f(double J, double K, double U) {
        double r150021 = -2.0;
        double r150022 = J;
        double r150023 = r150021 * r150022;
        double r150024 = 1.0;
        double r150025 = sqrt(r150024);
        double r150026 = U;
        double r150027 = 2.0;
        double r150028 = r150027 * r150022;
        double r150029 = r150026 / r150028;
        double r150030 = K;
        double r150031 = r150030 / r150027;
        double r150032 = cos(r150031);
        double r150033 = r150029 / r150032;
        double r150034 = 2.0;
        double r150035 = r150027 / r150034;
        double r150036 = pow(r150033, r150035);
        double r150037 = hypot(r150025, r150036);
        double r150038 = r150037 * r150032;
        double r150039 = r150023 * r150038;
        return r150039;
}

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 17.7

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

  3. Applied sqr-pow17.7

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

  4. Applied add-sqr-sqrt17.7

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

  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. Using strategy rm

  7. Applied associate-*l*8.0

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

  8. Simplified8.0

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

  10. Applied associate-/r*7.9

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

  11. Final simplification7.9

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

Reproduce

herbie shell --seed 2019325 +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)))))