Trevor_Blake comments on The greatest good for the greatest number - starting soonest, or ending last, or lasting longest? - Less Wrong Discussion
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How much time does it take to compute over all time?
Depends how gnarly the functions you're integrating are. The greatest goods in the top-level post sound time-independent (except for when they start & stop); if so one just integrates exp(-rt) over different t intervals, which is extremely fast & straightforward.