1.Prepositional phraseIn any case: anyway, anyhow, regardless; used to discard a previous thought or discount its importance.
"Jim broke the window — or maybe it was John? At any rate, the window’s broken now.; He's stinking rich — or, at any rate, pretty well off."
2.Prepositional phraseIn any case: by any measure, any way one slices it; used to emphasize that a point matters no matter which instance is operative or how one looks at the situation.
"At any rate, no aircraft can leave this hangar until no fewer than three inspectors have signed off on it."
3.Prepositional phraseUsed other than figuratively or idiomatically: see at, any, rate.
"Mr Chairman, I'd point out here that taxation without representation is an affront at any rate, low or high, but it is especially galling at the rate that Mr Smith proposes."