in reply to Grep matches all elements if compiled regex is passed as EXPR

The following works: 

grep $_=~$re, ...

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Your problem is unrelated to grep. In 

if (/re/     ) { ...a... }
if ($re      ) { ...b... }
if (/$re/    ) { ...c... }
if ($_=~$re  ) { ...d... }
if ($_=~/$re/) { ...e... }

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...b... will always be executed if $re contains a compiled regexp. Others have already explained why.

In Section Seekers of Perl Wisdom