The Test::More is_deeply() test acts like all of the other tests in Test::More by comparing values, not references. If two independent variables (meaning I change one and the other stays as it was) happen to have the same values, I expect is_deeply to pass.

What I don't expect, and don't want to test with is_deeply, is that the same operations will produce the same results.

I can see what you want to test, but I don't think is_deeply should be the thing to do that. It lives in its own community of tests in Test::More that all have the same idea and the same way of looking at things. If you changed how is_deeply works you have to change a lot more in Test::More.

In fairness, there are notes in the is_deeply docs pointing at other modules. If those don't work for you, make another one that does and then send in a doc patch. (Along with that doc patch could be something to remove the word "equivalent" from the docs, since I think that's where the confusion starts).