It is difficult to know when to use eval and when not, as sometimes it actually slows down the program. However, where you may always have to use it is with stack, augment, max and min. The code has a couple of those functions without eval, including a fairly hidden one where you put eval (max) -min, change that to eval (max-min).

Another detail to correct would be not to call f (x) so many times, because to extract f (x) [k] it actually evaluates all the lines of f (x).

There could be other calls to f (x) that could be stored in intermediate variables to extract its components.

In the main loop of the solver, try to evaluate f only once, in this case for xmid, instead of for x1 and x2, exchanging the values ​​of f1 and f2 when necessary.

Finally he takes the calculation of the flexures out of the loop.

Maybe an independent function for only the first component of f can speed up the process even more, but I don't know how linked the 6 variables of f are.

At the moment the fastest and most efficient purely numerical algorithm available in SMath for nonlinear systems of equations is al_nleqsolve. You can check it here.

This version is around 30 sec for the 63 steps.

FLEXO TRACAO E FLEXO COMPRESSAO OBLIQUAS CORRIGIDO 0.33 AFTER ERROR EVAL.sm (277kb) downloaded 8 time(s).

Best regards.
Alvaro.

Edited by user 17 November 2021 20:06:32(UTC)  | Reason: Not specified

Thank you so very much Alvaro!

I will go over point by point and if you allow me I have a couple of questions.

It is difficult to know when to use eval and when not, as sometimes it actually slows down the program. However, where you may always have to use it is with stack, augment, max and min. The code has a couple of those functions without eval, including a fairly hidden one where you put eval (max) -min, change that to eval (max-min).

I wiil certanly do that. I have two versios of the code using eval() the first with leees eval() and a secondo with more. As I was kind of desperate to solve the issue I inseted eval in every little thing in the second, but the calculation actually became slower so I annexed here the first one.

Another detail to correct would be not to call f (x) so many times, because to extract f (x) [k] it actually evaluates all the lines of f (x).


There could be other calls to f (x) that could be stored in intermediate variables to extract its components.

The problem is that a need to call the function in every step of the loop in order to find the root and I wasn't able to find a way around that. The for autside of the main function was a while that a changed in order to spped up the calculations, adicionally there were two whiles but I combined them in just one in order to do the same.

In the main loop of the solver, try to evaluate f only once, in this case for xmid, instead of for x1 and x2, exchanging the values ​​of f1 and f2 when necessary.

I didn't get this one, because I need to calculate f(x) in the interval in order to find the root. I think that the best way is to change the Algorythm for finding the roots like you did and finding a way around of expanding the interval for the case that the root isn't between the first guesses of x1 and x1.

Finally he takes the calculation of the flexures out of the loop.

Done!

Maybe an independent function for only the first component of f can speed up the process even more, but I don't know how linked the 6 variables of f are.

If you look in the upper parte of the spreadsheet you will see that every part of the code was once separated, but I joined everything since from x2x' y2y' forward everything became a function of ɑ and x.0 and since they were separate behind the line() they kept calling each other and that would slow the calculation a lot, and it was slow before I implemented the algorithm to find the roots. So I kind o had to join everything to improve the calculation time.

I had this same program written in Mathcad 15 when I was in college, but I'm rewriting it in Smath bacause it is free to use and offer so much possibility now. In Mathcad I was able to "transform" a two variable function by evaluating it through a second function that gives value to one of the variables. Like we have f(ɑ;x) would became g(x) assigning values to ɑ, in the case of this program in particular I used a vector of ɑ values and vectorized f(ɑ;x), but I wasn't able to do the same on Smath. If this were possible it would eliminate the external loop and improve the calculation time even further.

I'm sorry for flooding you with issues and once again thank you so very much for your help.