> They are typically the inputs that matter, and if chosen carefully then they cover all interesting/relevant inputs from the vast space.

The thing is you can have code that passes the tests, but are wrong for the general cases. With manual coding, you will have the knowledge that the code is about right, then add test cases to precisely check that intuition.

Like being aware that you used a linear function so as soon as 2 points in the test are ok, the code is right. But if you don’t read the code and have not noticed the quadratic function, your test cases will pass while the code is incorrect.