First, users don't use string.indexOf(string). Users use software that uses string.indexOf(string). Second, I would write a test that takes generates a variety of inputs to cover the domain of string.indexOf(string) and have it call the old version and the new version. I would then collect stats around the performance of each call and make sure the new implementation is faster by the threshold I meant for it to be. Since the PURPOSE OF THE REFACTOR WAS PERFORMANCE. Then I would delete the test after I'm satisfied it worked well on the target hardware, etc.

Let's look at the chrome unit tests.

https://chromium.googlesource.com/v8/v8/+/3.0.12.1/test/mjsu...

This test checks one case and then does a loop over to make sure various sizes work. This is a POOR test because it doesn't cover the domain of the function and exceptional cases. This test is pointless to have and run every build. Why keep it, it does nothing useful.

My point is that if you are refactoring a function, you are going to have to write a NEW TEST anyway because the purpose of a refactor is different each time. The old tests are going to be useless. This is why contracts are so useful because they will ALERT YOU when the software does something you didn't assume. Unit tests don't do this.

From an information theory perspective, the old tests would not provide you with new information. If you want to make sure your refactor works like the old function, then compare the outputs of your new function with the old one over the domain of the function. Then if it's good, delete the tests because why keep them.

Experience shows that users will do things to your program you did NOT expect and therefore your tests will not cover. And more likely than not, refactoring requires rewriting tests anyway so the old tests are usually always useless.

Now SYSTEM tests ARE useful. Tests that wire up many components and test them are useful. But a UNIT test, which tests one function is often just a waste of time to keep.