AI testing 101

so ive been working on better ways of hand simulating my AI
and what ive found is that you can convert a basic neural net into a mathematical function via calculus.

now im not fully into calculus yet i only know a few things here and there about it

but for example we have 3 total neurons in 3 layers
this is to just make it easier

N1=5v
N1 - R1 = x (this is assuming instead of multiplying a neurons output by a specific factor you instead use resistors to limit a literal electrical signal)

x - N2 = y (this is the function that says if the next neuron fires or not based on its bias if its negative then it naturally will not

y - N3 = output (this is from the output of the AI

now in a normal neural net your going to add multiple X values together because of the interconnecting neurons, same for y values. and by doing this you can kind of reduce a AI neural net from a complex thing to something somewhat easier to work on by hand without going insane like i