Would you confirm that the use of gerund or infinitive in the sentences below is not random (i.e. gerund and infinitive are not interchangeable there) without detriment to the meaning:
regret doing something
regret to do something
regret doing something - feel sorry to have done smth.: I don't regret leaving my last job at all.
regret to do something - be sorry that one must do smth.: Dr. Wimpole regrets to say that he cannot answer readers' letters.
remember doing something
remember to do something
remember doing something - keep in mind smth. that one has done: We remembered seeing many little country churches with ancient horse sheds still at the rear.
remember to do something - bear in mind smth. that one has to do: They kept the Ford out in the street in front of the house. It worked all right if they remembered to get it filled with anti-freeze.
stop doing something
stop to do something
stop doing something - cease or give up doing smth.: The teachers had stopped attending to pupils who would certainly pass or certainly fail and were concentrating on the borderline cases.
stop to do something - pause in order to do smth.: He stopped to watch a half-dozen of the boys playing blackjack.