Average Error: 18.0 → 8.1
Time: 35.4s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\mathsf{hypot}\left({\left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot 2}\right)}^{\left(\frac{2}{2}\right)}, \sqrt{1}\right) \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\right)\]
\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}}
↓
\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(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\right)
double f(double J, double K, double U) {
        double r6075914 = -2.0;
        double r6075915 = J;
        double r6075916 = r6075914 * r6075915;
        double r6075917 = K;
        double r6075918 = 2.0;
        double r6075919 = r6075917 / r6075918;
        double r6075920 = cos(r6075919);
        double r6075921 = r6075916 * r6075920;
        double r6075922 = 1.0;
        double r6075923 = U;
        double r6075924 = r6075918 * r6075915;
        double r6075925 = r6075924 * r6075920;
        double r6075926 = r6075923 / r6075925;
        double r6075927 = pow(r6075926, r6075918);
        double r6075928 = r6075922 + r6075927;
        double r6075929 = sqrt(r6075928);
        double r6075930 = r6075921 * r6075929;
        return r6075930;
}
↓
double f(double J, double K, double U) {
        double r6075931 = U;
        double r6075932 = K;
        double r6075933 = 2.0;
        double r6075934 = r6075932 / r6075933;
        double r6075935 = cos(r6075934);
        double r6075936 = J;
        double r6075937 = r6075935 * r6075936;
        double r6075938 = r6075937 * r6075933;
        double r6075939 = r6075931 / r6075938;
        double r6075940 = 2.0;
        double r6075941 = r6075933 / r6075940;
        double r6075942 = pow(r6075939, r6075941);
        double r6075943 = 1.0;
        double r6075944 = sqrt(r6075943);
        double r6075945 = hypot(r6075942, r6075944);
        double r6075946 = -2.0;
        double r6075947 = r6075946 * r6075937;
        double r6075948 = r6075945 * r6075947;
        return r6075948;
}

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

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

  4. Applied add-sqr-sqrt18.0

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

  5. Applied sqr-pow18.0

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

  6. Applied hypot-def8.1

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

  7. Final simplification8.1

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

Reproduce

herbie shell --seed 2019169 +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)))))