at least vs at any rate

at least and at any rate both are adverbs.

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

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

at least and at any rate: if nothing else (`leastwise' is informal and `leastways' is colloquial)

Other synonyms of at least include leastways, leastwise.

at least (adverb)	at any rate (adverb)
not less than	used to indicate that a statement explains or supports a previous statement
if nothing else (`leastwise' is informal and `leastways' is colloquial)	if nothing else (`leastwise' is informal and `leastways' is colloquial)