@cclauss , plz review this.

while executing this test print(f"The root of sin(x) = 0 with precision 0 is {newton_raphson('sin(x)', 2, precision=0)}") it took too much time and still not executed...so cancelled that. Same with precision=-1.

Also precision is initially defined in function argument (precision: float = 10**-10) then why we should make a test case with different precisions??

why we should make a test case with different precisions??

Because the caller might choose to change the default. Why are there no tests that change the default precision?

How does scipy.optimize.newton() deal with a precision of 0 and -1?

@QuantumNovice your review of these changes please.

How does scipy.optimize.newton() deal with a precision of 0 and -1?

for -1 it is throwing error.

The newton method implemented in scipy is entirely a numerical method.
https://github.com/scipy/scipy/blob/cfe80116aaa145061246b8aec0e98248fbefb835/scipy/optimize/_zeros_py.py#L105

@QuantumNovice What would be a valid test to replace

    >>> all(newton_raphson("log(x) - 1", 2) == newton("log(x) - 1", 2)
    ...     for precision in (10, 100, 1000, 10000))
    True

Why does this test not pass?

>>> from math import log
>>> from scipy.optimize import newton
>>>
>>> def log_x_minus_one(x):
...     return log(x) - 1
...
>>> def compare(precision):
...         a = newton_raphson("log(x) - 1", 2, precision=1)
...         b = newton(log_x_minus_one, 2, tol=1)
...         assert a == b, f"{a = } != {b = }"
...         return a == b
...
>>> all(compare(precision) for precision in (1, 10, 100, 1000, 10000))
True

Closing due to lack of fixes in response to code review. We need to clear out our backlog of PRs as much as possible before Hacktoberfest, and this PR still has failing tests.