at any rate (Adverb) — Used to indicate that a statement explains or supports a previous statement. ex. "but at any rate he got a knighthood for it"
at any rate (Adverb) — If nothing else ('leastwise' is informal and 'leastways' is colloquial). ex. "they felt--at any rate Jim felt--relieved though still wary" ex. "the influence of economists--or at any rate of economics--is far-reaching"