It is something of an axiom that any recursive solution can be rewritten as an iterative one. Often a finite infinite loop is useful:

#!/usr/bin/perl -w

use constant HIGH => 10_000;
my $ans = int(rand(HIGH)) + 1;
my ( $lower, $higher ) = (1, HIGH);
while(1) {
    my $guess = int(($lower + $higher)/2);
    print "Guessing: $guess\n";
  last if $ans == $guess;
    if ( $guess > $ans ) {
        print "Lower...";
        $higher = $guess -1;
    }
    else {
        print "Higher...";
        $lower = $guess +1;
    }
}
print "The guess was correct!";
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FWIW, with your code &function(args) syntax is not considered best style, you can drop the & - which you actually do in the sub. A consistent style is a good idea. You could declare and set $ans in one call.

It is worth noting that while an iterative solution will almost inevitably run faster than a recursive solution, a good recursive solution is often quite terse. A classic very simple example is the calculation of factorial n! The factorial is defined n! = 1 x 2 x 3 x .... (n-1) x n You can code using either iteration or recursion.....

sub fact_rec{ 
    my ($num) = @_;
    $num ? $num*fact_rec($num-1) : 1 
}

sub fact_it{
    my ($num) = @_;
    my $fac = 1;
    for my $i( 1 .. $num ) {
        $fac *= $i;
    }
  return $fac;
}

for (1..10){
    printf"%d!\t%10d\t%10d\n", $_, fact_rec($_), fact_it($_);
}
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As you can see the recursive solution is short and sweet. It also has a bug that can cause it to go infinite. One gotcha with recursion is that you need to be *positive* that your exit condition (ie stop recursing when we are done) will be *always* be met. A typical real world use for recursion is in dealing with tree like structures

The bug:

Negative numbers or floats mean that $num -1 will never equal 0, and so always it will always be true.