as logs are almost sorted by date, you could probably limit your search on the error log to a small window:

my $window = 300; # 5 min.
my @errors;
my @timestamps;

while (<ACCESSLOG>) {
  my $timestamp = get_timestamp($_);

  while (!@timestamps
         or $timestamps[-1] < $timestamp + $window) {
    if (defined(my $err = <ERRORLOG>)) {
      push @errors, $err;
      push @timestamps, get_timestamp($err);
    }
    else {
      last;
    }
  }

  while (@timestamps
         and $timestamps[0] < $timestamp - $window) {
    shift @errors;
    shift @timestamps;
  }

  for my $error (@errors) {
    # check if access line $_ matchs
    # with error line $error here:
    ...
  }
}
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