The infinitive expresses an unrealized event e.g., I regret to tell you. . . I am about to tell you. I haven't yet.
The present participle expresses an event that has been realized e.g., I regret telling you. I told you before.
Perfective infinitive example? Hmm. Seems awkward: past connected to an unrealized event. If it works, let me know. I for one can't think of an example at the moment.
Student or Learner