In addition to responses above me (which all point you in the direction you probably want to go in), I'd like to tell you something interesting about the behaviour of die I recently discovered.

This behaviour is documented in the description of die. Allow me to quote.

die LIST
... Inside an eval(), the error message is stuffed into $@ and the eval is terminated with the undefined value. This makes die the way to raise an exception.
...
If the last element of LIST does not end in a newline, the current script line number and input line number
...
(paraphrased: "input line number" means whatever the current value of $/ is. Usually just \n, though.)

Good. Now the underlined part is important there. It implies that if you include $/ at the end of your die message, you can prevent the at line X of Y to be added to the die message. That raises an interesting use of die. Let's see.

my $codeblock = "Important and unimportant stuff";
eval {
    doImportantStuff;
    #if anything goes wrong, it goes `die "invalid important stuff\n";
+`
    #This should be logged

    doUnimportantStuff;
    # `die "invalid unimportant stuff\n";`
    # Should not be logged.
    
    moreImportantStuff;
    #`die "more invalid important stuff\n";`
    # Should be logged
};

log_error("$@", $codeblock) if $@;


sub log_error {
    return unless DEBUG;
    my $error = shift @_;
    my $place = shift @_;

    my @logthese = (
        "invalid important stuff\n",
        "more invalid important stuff\n",
    );

    for my $check (@logthese) {
        if ($error eq "$check") {
            write_to_log("Error '$error' at $place");
            last;  # found! No need to continue searching
        }
    }      
}
[download]

Code is only intended to illustrate a point and therefore untested. Use at own discretion.

Update: spotted a stupidity in the code, fixed that.