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The modified accuracy assurance scheme for the Binary Interaction Approximation (BIA) to N-body problemsis proposed. The present error-tolerance-adjusting scheme, implemented into the BIA introduced in thisstudy significantly reduces the CPU times and numerical errors in invariants of the motion compared to theprevious one.This article is based on the presentation at the 22nd International Toki Conference (ITC22

Accuracy Assurance in Binary Interaction Approximation for N-Body Problems II