Help with conditional formatting formula

Hi,
I'm sure this will be easy for someone, but it has me going bold!

I'm trying to format a cell based on a calculation of days from today + a date in a cell, plus the text in another cell. There's an "or" in that the cell needs to be highlighted based on;

The text cell not stating "Rarely" and the date being over 360 days old

OR

The text cell being equal to "Rarely" and the date being over 720 days old

I've tried:

=IF((E4-TODAY())<-360,B4<>"Rarely")=OR((E4-TODAY())<-720,B4="Rarely")

And

=IF(E4-TODAY()<-360,B4<>"Rarely",IF(E4-TODAY()<-720,B4="Rarely"))

But they don't work completely. Any help much appreciated.

Thanks!