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This is one of the most difficult challenge to Tableau's existing feature,I believe.
You can refer this past thread to get some hints.
I hope this helps. The darker shades are the ones computed inside Tableau. Some of the numbers don't match but looks like those were issues with the Excel formula.E.g. August 6th to October 13th only contains 13 days in October but your Excel calc found 18. October 7, 2014 to November 14th 2015 contains the full month of October 2015 in it so should be 31 days but Excel had 24. Null date to Null date is 0 days but original calc found 346 days etc.