It has been a tough journey

If you read my previous devlog, it almost feels like i was foreshadowing what was about to happen to me.

While making the solve_node function which would solve the inequality for x, i got lost in the mess of symbolic mathematics and started handling cases with fallbacks upon fallbacks. It has really a hot mess, I got to find out that there can be many types of questions and to solve every type of domain question, I would need fallback logic for every type of question which would mean I would have to encompass all the techniques in domain finding into the file and manage the interaction of the techniques and orchestrate them at a high level and basically making my own sympy (which took decades to build).

I even thought of quitting a few times and the project was basically at a halt for 1-2 days. I then decided to solve a simple domain question by hand to check what really are the steps of finding the domain of a function. I found out that my logic up until making the constraints was fine. The next steps were finding critical points for example: (x-2)(x+3)>0 would have critical points 2 and -3 (they are just the points where the function is zero). Now, I also know that critical points also occur when the sign of the function changes or when its nature changes (going from defined to undefined and vice-versa) so instead of making a symbolic critical point finding function I thought of a more brute force method.

If I have a number line (range of numbers) and i simply walk through them one by one, noting sign change between 2 numbers as a sign “there is a critical point here” and then use another function to basically go into each of those marked intervals and continuously half the interval (think of it as taking an interval and then zooming into the interval until you find the critical point) until about 9 decimal places (could be anything, it is just the amount of accuracy), you would get the critical point pretty accurately without having to solve anything using logic or symbolically, just substitute values of x. After finding the critical points, turning it into domain is as simple as just substituting points and see if the inequality holds.