I took this sentence below from Oxford English Grammar Intermediate by Swan.
I've been to sleep three times during this lesson.
I've never seen that construction before. What I've seen so far is
(Has/Have/Had) + been + (adjective/gerund)
Why do they use infinitive there? Does it still have the same meaning if the infinitive form is replaced by gerund?
I mean:
I've been sleeping three times during this lesson.