Meaning of at any rate

(adv) used to indicate that a statement explains or supports a previous statement; "Anyhow, he is dead now"; "I think they're asleep; anyhow, they're quiet"; "I don't know what happened to it; anyway, it's gone"; "anyway, there is another factor to consider"; "I don't know how it started; in any case, there was a brief scuffle"; "in any event, the government faced a serious protest"; "but at any rate he got a knighthood for it"

if nothing else (`leastwise' is informal and `leastways' is colloquial); "at least he survived"; "they felt--at any rate Jim felt--relieved though still wary"; "the influence of economists--or at any rate of economics--is far-reaching"