If you change your result constants to -1, 0 and 1 then you can change your test code to:

  $result = $guess <=> $target;
  $min = $guess if $result == -1;
  $max = $guess if $result == 1;
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which uses the numeric comparison operator <=> (or spaceship, see 'Equality Operators' in perlop) to perform the check. You need to change the while loop test of course.

Note too the use of if as a statement modifier to make the code a little clearer.

$guess and $interval should be declared within the loop to make it more obvious that their values are not used outside the loop. You should almost never use variables global to a sub inside the sub - pass them in as parameters.