In order to remember what part matched, I created a named capture groups and retrieved the names from the special %- hash. Without your data, I can't test whether it's faster or not.

#!/usr/bin/perl
use warnings;
use strict;

...

my @pat_array = split /@@@/, $InListOfPatterns;
my $i;
my $regex = join '|', map +($i++, "(?<m$i>$_)")[1], map quotemeta, @pa
+t_array;

open my $LOG,'<', $InLogFilePath or die "can not open file :$!";
my %matched;
while (<$LOG>) {
    chomp;
    if ( $. > $InStartLineNumber) {
        $matched{ (grep defined $-{$_}[0], keys %-)[0] }++ if /$regex/
+;
    }
}
close $LOG;

for my $pattern (keys %matched) {
    print "$pattern\t$matched{$pattern}\n";
}
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Beware! You have a precedence issue in your code:

open LOG_READ,'<',"$InLogFilePath" || die "can not open file :$!";
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This will never die if you can't open the file, it will only die if the file name is empty.

($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
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