Problems with SetPrecision and ReplaceAll

Questions
1

I’m working with the complex equation in figure (Prova1). This equation is function of different variables. If I evaluate the equation in all the variables except A and wel4, I obtain an equation in function of A and wel4 (Prova2). If now evaluate this second expression in A = 1 and wel4 = -1 setting the precision to 64 digits, I obtain a result (Prova3). If I evaluate the same expression without setting the precision, the result is different (Prova4).

If now I try to replace in the equation Prova1 all the variables except A, I obtain an equation in function only of A (Prova5). If I evaluate this equation in A = 1, the final result is different from those obtained previously.

Can someone help me to understand why it happens?
Thanks

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2

I add the Notebook with the code if someone wants to do some tests

Wolfram Notebook
[1]: https://www.wolframcloud.com/obj/1de33499-fc03-4859-b124-2398b6eb0c5b

3

Get conclusions from my attached file:

Open in Wolfram Cloud ↗
4

Thank You for the Notebook.

Sorry, but I don’t understand which is the rule of N in the equations.
I attach a new Notebook with some additional tests.

You can notice that the formats 0.005 or 5/1000 have a strong impact on the result! And N is a command that impacts only in the representation format of the number. Is it correct?

Than I want to ask you an other question.
If now I want to transfer the Prova1 equation from Mathematica to Matlab, I use the package ToMatlab’ which writes a .m file with the equation in Matlab format.
If then I calculate the expression Prova 1 in Matlab in the same values of the variables, I obtain a different result respect to Mathematica. Do you know the reason?

Open in Wolfram Cloud ↗