I’m trying to make a parser focusing on getting all the expressions into a list.
Given the following math functions:

1. f(x) = (3x^2) + 2/x + 10
2. f(x) = (-3)x^e + (2(x^x))
3. f(x) = log(10^e+x^(10-x))

I want to find a regex to split these approaches as follows:

1. ['(3x^2)', '+2/x', '+10']
2. ['(-3)x^e', '+(2(x^x))']
3. ['log(10^e+x^(10-x)']

I have found something, but doesn’t work as expected.
((?:^|[+-])[0-9]*)(?:\*?x(?:\^[0-9]+)?)?
It works only for polynomials such as 3x^2 + 2x - 1 etc.

For example, let’s consider the following match (-3x&25) where & could be one of the following symbols ['-', '+', "https://stackoverflow.com/", '*', '^']

• (-3x&25) should be part of a group 1

• -3x should be part of a group 2

• 25 should be part of a group 3

For example, if we have an expression like (expression1&expression2)
expression1 can be (3x&e^10) where & could be one of the following symbols ['-', '+', "https://stackoverflow.com/", '*', '^'] and then apply the rules described above.

But if the expression has '(', ')' (ex. (3x-2(3x-2))) the matches should be: ['3x', '-2(3x-2)'], not ['3x', '-2(3x', '-2)']