Average Error: 17.9 → 18.0
Time: 12.6s
Precision: binary64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\left(J \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{\sqrt{1 + {\left(\frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)}^{2}}}\right)\right)\right) \cdot \sqrt{\left|\sqrt[3]{1 + {\left(\frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)}^{2}}\right| \cdot \sqrt{\sqrt[3]{1 + {\left(\frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)}^{2}}}}\]
\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(J \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{\sqrt{1 + {\left(\frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)}^{2}}}\right)\right)\right) \cdot \sqrt{\left|\sqrt[3]{1 + {\left(\frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)}^{2}}\right| \cdot \sqrt{\sqrt[3]{1 + {\left(\frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)}^{2}}}}
double code(double J, double K, double U) {
	return ((double) (((double) (((double) (-2.0 * J)) * ((double) cos(((double) (K / 2.0)))))) * ((double) sqrt(((double) (1.0 + ((double) pow(((double) (U / ((double) (((double) (2.0 * J)) * ((double) cos(((double) (K / 2.0)))))))), 2.0))))))));
}
↓
double code(double J, double K, double U) {
	return ((double) (((double) (J * ((double) (-2.0 * ((double) (((double) cos(((double) (K / 2.0)))) * ((double) sqrt(((double) sqrt(((double) (1.0 + ((double) pow(((double) (U / ((double) (2.0 * ((double) (J * ((double) cos(((double) (K / 2.0)))))))))), 2.0)))))))))))))) * ((double) sqrt(((double) (((double) fabs(((double) cbrt(((double) (1.0 + ((double) pow(((double) (U / ((double) (2.0 * ((double) (J * ((double) cos(((double) (K / 2.0)))))))))), 2.0)))))))) * ((double) sqrt(((double) cbrt(((double) (1.0 + ((double) pow(((double) (U / ((double) (2.0 * ((double) (J * ((double) cos(((double) (K / 2.0)))))))))), 2.0))))))))))))));
}

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 17.9

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

  3. Applied add-sqr-sqrt17.9

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

  4. Applied sqrt-prod18.0

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

  5. Applied associate-*r*18.0

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

  6. Simplified18.0

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

  8. Applied add-cube-cbrt18.0

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

  9. Applied sqrt-prod18.0

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

  10. Simplified18.0

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

  11. Simplified18.0

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

  12. Final simplification18.0

    \[\leadsto \left(J \cdot \left(-2 \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{\sqrt{1 + {\left(\frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)}^{2}}}\right)\right)\right) \cdot \sqrt{\left|\sqrt[3]{1 + {\left(\frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)}^{2}}\right| \cdot \sqrt{\sqrt[3]{1 + {\left(\frac{U}{2 \cdot \left(J \cdot \cos \left(\frac{K}{2}\right)\right)}\right)}^{2}}}}\]

Reproduce

herbie shell --seed 2020179 
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  :precision binary64
  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))