Average Error: 18.6 → 8.2
Time: 8.5s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \mathsf{hypot}\left(\sqrt{1}, {\left(\frac{\frac{U}{2 \cdot J}}{\cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}\right)\right)\]
\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 r264030 = -2.0;
        double r264031 = J;
        double r264032 = r264030 * r264031;
        double r264033 = K;
        double r264034 = 2.0;
        double r264035 = r264033 / r264034;
        double r264036 = cos(r264035);
        double r264037 = r264032 * r264036;
        double r264038 = 1.0;
        double r264039 = U;
        double r264040 = r264034 * r264031;
        double r264041 = r264040 * r264036;
        double r264042 = r264039 / r264041;
        double r264043 = pow(r264042, r264034);
        double r264044 = r264038 + r264043;
        double r264045 = sqrt(r264044);
        double r264046 = r264037 * r264045;
        return r264046;
}
↓
double f(double J, double K, double U) {
        double r264047 = -2.0;
        double r264048 = J;
        double r264049 = r264047 * r264048;
        double r264050 = K;
        double r264051 = 2.0;
        double r264052 = r264050 / r264051;
        double r264053 = cos(r264052);
        double r264054 = 1.0;
        double r264055 = sqrt(r264054);
        double r264056 = U;
        double r264057 = r264051 * r264048;
        double r264058 = r264056 / r264057;
        double r264059 = r264058 / r264053;
        double r264060 = 2.0;
        double r264061 = r264051 / r264060;
        double r264062 = pow(r264059, r264061);
        double r264063 = hypot(r264055, r264062);
        double r264064 = r264053 * r264063;
        double r264065 = r264049 * r264064;
        return r264065;
}

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 18.6

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

  3. Applied sqr-pow18.6

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

  4. Applied add-sqr-sqrt18.6

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

  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. Using strategy rm

  7. Applied associate-*l*8.3

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

  9. Applied associate-/r*8.2

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

  10. Final simplification8.2

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

Reproduce

herbie shell --seed 2019347 +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)))))