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while(<$fh_big_file>) {
  print if (/MY_HUGE_REGEX_JUST_PLAIN/../^END_OF_BLOCK/o);
}

while(<$fh_big_file>) {
  print if (/MY_HUGE_REGEX_JUST_PLAIN/o .. /^END_OF_BLOCK/);
}

while(<$fh_big_file>) {
  print if (/$regex/o .. /^END_OF_BLOCK/);
}