at any rate vs at least

at any rate and at least both are adverbs.

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

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

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

Other synonyms of at any rate include leastways, leastwise.

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