Economic policy is more complicated than that. Regan had the second highest government spending as % of GDP of any recent president, 21.6% of GDP. Second only to Obama and not by much. He nearly tripled the Federal debt in dollar terms and as a % of GDP it went from 26% to 41%. Household debt almost doubled during the Regan administration. 

Inflation during his administration was around 62%. 

Regan's first act reduced taxes. His second TEFRA--while not increasing income tax--was one of the largest tax increases in history. Regan's own administration estimated that taxes were 19.4% of GDP while the historic average was 18.3%. 

Regan was not a free market economist. He followed the same Keynesian strategy that FDR and LBJ did. He just painted it better. 

And this isn't boiler plate liberal nonsense but comes from the libertarian Mises institute and you can find similar analysis from FEE and many others. Regan did not cut taxes.
https://mises.org/library/sad-legacy-ronald-reagan-0