Change

gbacktrack  => q{ $input =~ /$bregexp/g },
gpossessive => q{ $input =~ /$regexp/g }
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to

gbacktrack  => q{ use strict; use warnings; $input =~ /$bregexp/g },
gpossessive => q{ use strict; use warnings; $input =~ /$regexp/g }
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and you'll see what you're doing wrong. Code compiled inside of Benchmark can't see your lexicals, so you're benchmarking

'' =~ //g
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against

'' =~ //g
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It's no surprise you get the same results. You'll need to use package variables. (Switch my to our.)