"at" / "in" any rate

[sunsunmoon]

at any rate
— used to indicate that something is true or certain regardless of what else has happened or been said
▪ This restaurant has the best food—or at any rate, the best pasta dishes—in the city. ▪ At any rate [=in any case], cooking with fresh ingredients makes everything taste better. ▪ It is possible that she was nervous. At any rate, her singing was still good.


Are "at any rate" and "in any rate" interchangeable only in the second example?

[billmcd]

at any rate
— used to indicate that something is true or certain regardless of what else has happened or been said
▪ This restaurant has the best food—or at any rate, the best pasta dishes—in the city. ▪ At any rate [=in any case], cooking with fresh ingredients makes everything taste better. ▪ It is possible that she was nervous. At any rate, her singing was still good.


Are "at any rate" and "in any rate" interchangeable only in the second example?

I think either expression is acceptable/understood your three examples.

[Hedwig]

But can you say in any rate? I mean, in any case, in any event, I'm familiar with, but the question specifies in any rate, if I understand correctly. I would have thought this phrase could only be used with at.

[5jj]

But can you say in any rate? I mean, in any case, in any event, I'm familiar with, but the question specifies in any rate, if I understand correctly. I would have thought this phrase could only be used with at.

My view, too.

[billmcd]

But can you say in any rate? I mean, in any case, in any event, I'm familiar with, but the question specifies in any rate, if I understand correctly. I would have thought this phrase could only be used with at.

Sorry, I misread, misunderstood or simply didn't read the complete post. I didn't mean to imply that "in any rate" was a correct phrase, which it is not in AmE.