at any rate vs anyway

at any rate and anyway both are adverbs.

Word	Noun	Adjective	Verb	Adverb
at any rate	No	No	No	Yes
anyway	No	No	No	Yes

As adverbs, at any rate and anyway are synonyms defined as:

at any rate and anyway: used to indicate that a statement explains or supports a previous statement

Other synonyms of at any rate include anyhow, anyways, in any case, in any event.

at any rate (adverb)	anyway (adverb)
used to indicate that a statement explains or supports a previous statement	used to indicate that a statement explains or supports a previous statement
if nothing else (`leastwise' is informal and `leastways' is colloquial)	in any way whatsoever