We proposed a general method for efficiently recording trajectories of states for analyzing the time correlation functions (TCFs) A ( t ) of arbitrary quantities from short to long times, for computer simulations, to reproduce dynamic behaviors. If the quantities for TCF are defined, then on-the-fly calculations are efficient; otherwise, we have to record the trajectories of the states of the system in study. Although the multiple-tau method is popular as an efficient method for error accumulation in calculation of TCFs of defined values for longer t , the problem of the large storage capacity required for recording the trajectories needed to calculate TCFs of arbitrary quantities for shorter t remains. To solve this problem, we propose a method to reduce data size and/or computing times... to compute A ( t ) for shorter t by recording multiple trajectories with different intervals. We named the proposed method multi-interval trajectory recording (MITR). The combination of MITR and recurrence-averages was confirmed to be necessary for precise connection to the multiple-tau method for longer t . In the present paper, we demonstrate an example of a stress autocorrelation function of melts of Kremer–Grest chains.