Note B::Deparse can be a useful tool:

$ perl -MO=Deparse -we 'use strict; my $value=1; my $lower_limit = 0;
  my $upper_limit = 2; if ( ( $value <= $upper_limit )
    && ( $value => $lower_limit ) )
      { print "the value is in the range!\n"}'

Useless use of private variable in void context at -e line 4.
BEGIN { $^W = 1; }
use strict;
my $value = 1;
my $lower_limit = 0;
my $upper_limit = 2;
if ($value <= $upper_limit and $value, $lower_limit) {
    print "the value is in the range!\n";
}
-e syntax OK
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Say perl -MO=Deparse,-p ... to add parentheses and see the precedence better.