Jan8 date format

Format a date in shortest format possible indicating how many days have passed (Past date)

If date1-date2 < 8 Sat, Fri, …
If date1-date2 < 350 Dec24, Jan4, Aug14
Else 2020Feb4

=IF(AND(E34<TODAY(), TODAY()-E34<7), TEXT(E34,"DDD"), IF( AND(E34<TODAY(), TODAY()-E34<365), TEXT(E34, "mmmd"),TEXT(E34,"yyyymmmd")))

Was thinking of this for a while now, trying to simplify as much as possible, and make as user-friendly as possible.