#!/usr/bin/perl -w

sub objective {
    return sqrt(2);
}

my $N = 100;          # size of each run
my $candidates = 10;  # size of the best's list 
my $min = 0;
my $max = +100;
my (@matrix, @list);

print "Value            Error\n";
while (1) {
    for my $i (0..$N-1) {
	$matrix[$i][0] = $min + rand()*($max-$min);                   # value
	$matrix[$i][1] = 2 - $matrix[$i][0]*$matrix[$i][0] ;      # signed error
    }
    @list = sort { abs($a->[1]) <=> abs($b->[1]) } @matrix;
    ;  
    $min = $list[$candidates-1][0];   # value of the worst candidate
    for my $i (reverse 0..$candidates-2){
	if ($list[$candidates-1][1] * $list[$i][1] < 0) { # value of a better candidate
	    $max = $list[$i][0];                          # by the other side
	    last;
	}
    }
    if ($max < $min ) {
	($min , $max ) = ( $max, $min);
    }
    print "$list[0][0] $list[0][1]\n";
    if ($list[0][1] == 0 || "$list[0][0]" eq "$list[$candidates-1][0]") {
	print objective(), "\n";
	exit 0;
    }
}

__END__

Monte Carlo simulation