Granted, my experience is only in the SF Bay and not NYC, and I have no idea where you are, my feeling is if the reading is 3 days of rehearsal and one reading, to me, that sounds very similar to "Periodic Performance" contracts that I've done in the past, which are paid at an hourly rate and, personally, my earnings from 3 days on a PP were quite low, but I only had 15 hours of rehearsal.
I would ask to see the contract from AEA immediately, and as loebtmc said, call your local rep. I had questions over my most recent PP and spoke with my rep, who gave me info that the producer hadn't (the producer gave me the wrong hourly and performance rates), so that I understood what I was getting into, before I signed.