a valuation allowance totaling $ 45.4 million , $ 43.9 million and $ 40.4 million as of 2013 , 2012 and 2011 year end , respectively , has been established for deferred income tax assets primarily related to certain subsidiary loss carryforwards that may not be realized . realization of the net deferred income tax assets is dependent on generating sufficient taxable income prior to their expiration . although realization is not assured , management believes it is more- likely-than-not that the net deferred income tax assets will be realized . the amount of the net deferred income tax assets considered realizable , however , could change in the near term if estimates of future taxable income during the carryforward period fluctuate . the following is a reconciliation of the beginning and ending amounts of unrecognized tax benefits for 2013 , 2012 and ( amounts in millions ) 2013 2012 2011 .

----------------------------------------
( amounts in millions ) | 2013 | 2012 | 2011
----------|----------|----------|----------
unrecognized tax benefits at beginning of year | $ 6.8 | $ 11.0 | $ 11.1
gross increases 2013 tax positions in prior periods | 1.5 | 0.7 | 0.5
gross decreases 2013 tax positions in prior periods | -1.6 ( 1.6 ) | -4.9 ( 4.9 ) | -0.4 ( 0.4 )
gross increases 2013 tax positions in the current period | 0.5 | 1.2 | 2.8
settlements with taxing authorities | -2.1 ( 2.1 ) | 2013 | -1.2 ( 1.2 )
lapsing of statutes of limitations | -0.5 ( 0.5 ) | -1.2 ( 1.2 ) | -1.8 ( 1.8 )
unrecognized tax benefits at end of year | $ 4.6 | $ 6.8 | $ 11.0
----------------------------------------

of the $ 4.6 million , $ 6.8 million and $ 11.0 million of unrecognized tax benefits as of 2013 , 2012 and 2011 year end , respectively , approximately $ 4.6 million , $ 4.1 million and $ 9.1 million , respectively , would impact the effective income tax rate if recognized . interest and penalties related to unrecognized tax benefits are recorded in income tax expense . during 2013 and 2012 , the company reversed a net $ 0.6 million and $ 0.5 million , respectively , of interest and penalties to income associated with unrecognized tax benefits . as of 2013 , 2012 and 2011 year end , the company has provided for $ 0.9 million , $ 1.6 million and $ 1.6 million , respectively , of accrued interest and penalties related to unrecognized tax benefits . the unrecognized tax benefits and related accrued interest and penalties are included in 201cother long-term liabilities 201d on the accompanying consolidated balance sheets . snap-on and its subsidiaries file income tax returns in the united states and in various state , local and foreign jurisdictions . it is reasonably possible that certain unrecognized tax benefits may either be settled with taxing authorities or the statutes of limitations for such items may lapse within the next 12 months , causing snap-on 2019s gross unrecognized tax benefits to decrease by a range of zero to $ 1.1 million . over the next 12 months , snap-on anticipates taking certain tax positions on various tax returns for which the related tax benefit does not meet the recognition threshold . accordingly , snap-on 2019s gross unrecognized tax benefits may increase by a range of zero to $ 0.8 million over the next 12 months for uncertain tax positions expected to be taken in future tax filings . with few exceptions , snap-on is no longer subject to u.s . federal and state/local income tax examinations by tax authorities for years prior to 2008 , and snap-on is no longer subject to non-u.s . income tax examinations by tax authorities for years prior to 2006 . the undistributed earnings of all non-u.s . subsidiaries totaled $ 556.0 million , $ 492.2 million and $ 416.4 million as of 2013 , 2012 and 2011 year end , respectively . snap-on has not provided any deferred taxes on these undistributed earnings as it considers the undistributed earnings to be permanently invested . determination of the amount of unrecognized deferred income tax liability related to these earnings is not practicable . 2013 annual report 83 .

Question: from 2011 to 2013 what was the average gross increases 2013 tax positions in prior periods
Program: add(1.5, 0.5), divide(0.7, #0), divide(#1, const_3)
Answer: 0.11667