how to normalize a `scala.reflect.api.Types.Type`

How to implement the function normalize(type: Type): Type such that:

A =:= B if and only if normalize(A) == normalize(B) and normalize(A).hashCode == normalize(B).hashCode.

There is a deprecated method called normalize in the TypeApi, but it does not the same.

In my particular case I only need to normalize types that represent a class or a trait (tpe.typeSymbol.isClass == true).