I don't think your algorithm for calculating the number of days in the
overlap will work. Picture a scenario where we have one date range that
covers 100 days, and another that covers 10 days, and they overlap by 2
days. Doing "age(<first range>) - age(<second range>)" will return 90
days, not 2 days.
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TIP 9: In versions below 8.0, the planner will ignore your desire to
choose an index scan if your joining column's datatypes do not
match
