Up to you. In my own case, I just wait and, if the IRS sends a letter about it, I reply documenting why there was no change. They have all the numbers from the original filing and so can calculate on their own if that would change the tax. They also have plenty of more pressing demands on their staff than pursuing math differences that don't change revenue.
But, this reminds me: I no longer file in April, but pay the tax due (plus a few bucks more margin that I can direct down the road towards estimated taxes) with the automatic extension form. This is for multiple reasons (yes, mostly learned the hard way):
(a) Sometimes corrected 1099's end up being sent out after the April filing date and one is forced to amend federal and state taxes, taking up time and unnecessary postage.
(b) One may realized after the April filing date that there was an overlooked deduction or alternate calculation (in my case the one time ability to split a Roth conversion across two years back ~2010) that lowered the tax bill and negated an underpayment which had added Form 2210 penalty interest in the original return. Federal law prevents the IRS from refunding that penalty interest. They can only send you the tax refund plus some (small) overpayment interest.
(c) The state of CA assesses underpayment penalty interest purely on the amounts of the original filing. So if one later determines as in (b) that one wasn't underpaid, tough cookies ... you're still out of pocket that penalty interest.
(d) Young folks, e.g. college students, who are due a refund, may not find the time before the April filing date to actually prepare the paperwork. By sending in the automatic extension form (without any payment, of course), they extend the 3 year deadline for claiming refunds by another 6 months. It was rather surprising to find out how many college seniors attending a financial literacy class we taught had not bothered to file for refunds during college.
