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  • $\begingroup$ Please reduce the post to a minimal example. The first half of it is not about NIntegrate at all. $\endgroup$ Commented Aug 4, 2018 at 22:31
  • $\begingroup$ Using working precision less than machine precision is only a good idea for educational/didactic purposes. $\endgroup$ Commented Aug 5, 2018 at 0:35
  • $\begingroup$ Might you want to integrate from -Infinity to Infinity? $\endgroup$ Commented Aug 5, 2018 at 2:08