Average Error: 18.0 → 18.0
Time: 10.3s
Precision: binary64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[-2 \cdot \left(J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{U}{J \cdot \left(2 \cdot \cos \left(\frac{K}{2}\right)\right)}\right)}^{2}}\right)\right)\]
\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}}
↓
-2 \cdot \left(J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{U}{J \cdot \left(2 \cdot \cos \left(\frac{K}{2}\right)\right)}\right)}^{2}}\right)\right)
(FPCore (J K U)
 :precision binary64
 (*
  (* (* -2.0 J) (cos (/ K 2.0)))
  (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
↓
(FPCore (J K U)
 :precision binary64
 (*
  -2.0
  (*
   J
   (*
    (cos (/ K 2.0))
    (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))))
double code(double J, double K, double U) {
	return ((double) (((double) (((double) (-2.0 * J)) * ((double) cos((K / 2.0))))) * ((double) sqrt(((double) (1.0 + ((double) pow((U / ((double) (((double) (2.0 * J)) * ((double) cos((K / 2.0)))))), 2.0))))))));
}
↓
double code(double J, double K, double U) {
	return ((double) (-2.0 * ((double) (J * ((double) (((double) cos((K / 2.0))) * ((double) sqrt(((double) (1.0 + ((double) pow((U / ((double) (J * ((double) (2.0 * ((double) cos((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 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

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

  3. Final simplification18.0

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

Reproduce

herbie shell --seed 2020198 
(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)))))