~/.bashrc

function timestamp()
  { perl -MPOSIX -MTime::HiRes -n -e '
      BEGIN {$|=1; $dp=0; $t0=Time::HiRes::time};
      $t=Time::HiRes::time; $dt=$t-$t0; printf("%s%06.3f %4.3f %4.3f %s",
        POSIX::strftime("%H:%M:",localtime($t)), $t-int($t/60)*60,
        $dt, $dt-$dp, $_); $dp=$dt' $*
  }

ls -Al | timestamp

11:54:12.060 0.030 0.030 -rw-r--r--  1 tester users 1091262 Mar 20 11:54 logfile.log
11:54:12.061 0.031 0.001 -rw-r--r--  1 tester users 2048199 Mar 20 11:54 logfile.log.1
11:54:12.061 0.031 0.000 -rw-r--r--  1 tester users 2048326 Mar 20 11:48 logfile.log.10
11:54:12.062 0.031 0.000 -rw-r--r--  1 tester users 2048145 Mar 20 10:35 logfile.log.100
11:54:12.062 0.032 0.000 -rw-r--r--  1 tester users 2048023 Mar 18 19:02 logfile.log.1000
11:54:12.062 0.032 0.000 -rw-r--r--  1 tester users 2048229 Mar 18 19:01 logfile.log.1001
11:54:12.062 0.032 0.000 -rw-r--r--  1 tester users 2048175 Mar 18 19:00 logfile.log.1002
11:54:12.062 0.032 0.000 -rw-r--r--  1 tester users 2048082 Mar 18 18:58 logfile.log.1003
11:54:12.062 0.032 0.000 -rw-r--r--  1 tester users 2048100 Mar 18 18:55 logfile.log.1004
11:54:12.062 0.032 0.000 -rw-r--r--  1 tester users 2048074 Mar 18 18:54 logfile.log.1005
11:54:12.063 0.032 0.000 -rw-r--r--  1 tester users 2048049 Mar 18 18:53 logfile.log.1006
11:54:12.063 0.033 0.000 -rw-r--r--  1 tester users 2048209 Mar 18 18:53 logfile.log.1007
11:54:12.063 0.033 0.000 -rw-r--r--  1 tester users 2048175 Mar 18 18:53 logfile.log.1008
11:54:12.063 0.033 0.000 -rw-r--r--  1 tester users 2048177 Mar 18 18:48 logfile.log.1009
11:54:12.063 0.033 0.000 -rw-r--r--  1 tester users 2048054 Mar 20 10:35 logfile.log.101