Math is interesting when you can use specific theories and equivalences to prove things. The issue is that for the most part these equations are just meant to plug and chug data.
For equation 4 assuming we have a real (3-dimensional) space, you have to do 6 derivatives, 2*(Mp+1) multiplications, 2*(Mp+1) additions, and one division for each iteration of the equation. Your result will be P equations (the number of groups you want to do the previous amount of algebra(/minimal calculus) for.
Scientifically, Mp is provably infinite, but in the industry, the most precise default to ~1000, in the classroom we generally use less than 10.
Also the above is assuming the other variables are constants that do not also need to be calculated (which is not true). Which is why most of these equations when used in the industry must be run on supercomputers in order to get any answer within a reasonable amount of time. Which then means that at this point I'm just being used as a glorified calculator.