Serving notice period now, need early release from project, but HR refusing it.

Hi, I've got offer from other company and their Joining Date is june 26th, I've already resigned from TCS and HR called me , i've asked for ealry release and instead of serving 90 days(LWD IN TCS Officialy is July 29th) as notice i said can we bring it down to 45-50 days as most of my deliverables/other things can be completed even before but she is refusing.

I spoke with my manager as well earlier he said Early release might not be possible as there are some constraints bla bla bla.. is that really true or they just want to play around by keeping me here. He also said there might be 10-15% of chance to get release early but dont keep hope on it. What to do now? what are the other ways and how to convince this guy? any ideas please?