Well actually I was thinking more like... 
#! /usr/bin/perl
use strict;
use Getopt::Std;
getopts('v');
use vars qw($opt_v @find_in);

# Set up my array of hashes of how to find various numbers with
# n 9's.
@find_in =(
  {},                                   # None of size 0!
  { 9 => '9' },                         # 2 with 1 9
  map {}, 2..9
);

foreach my $i (1..9) {
  print "Searching depth $i\n" if $opt_v;
  my $find_in_a = $find_in[$i];

  foreach my $j (1..$i) {
    next if 9 < $i + $j;
    print "  Searching combinations of $i, $j\n" if $opt_v;

    my $find_in_b = $find_in[$j];
    my $find_in_sum = $find_in[ $i+$j ];

    foreach my $val_a (keys %$find_in_a) {
      my $expr_a = $find_in_a->{$val_a};

      foreach my $val_b (keys %$find_in_b) {
        my $expr_b = $find_in_b->{$val_b};

        $find_in_sum->{$val_a + $val_b} = "($expr_a + $expr_b)";
        $find_in_sum->{$val_a * $val_b} = "($expr_a * $expr_b)";
    if ($val_a < $val_b) {
          $find_in_sum->{$val_b - $val_a} = "($expr_b - $expr_a)";
    }
    else {
          $find_in_sum->{$val_a - $val_b} = "($expr_a - $expr_b)";
    }
        if (0 != $val_b) {
          $find_in_sum->{$val_a / $val_b} = "($expr_a / $expr_b)";
        }
        if (0 != $val_a) {
          $find_in_sum->{$val_b / $val_a} = "($expr_b / $expr_a)";
        }
      }
    }
  }
}

my $ans = 0;
while (exists $find_in[9]{$ans}) {
  print "$ans\t$find_in[9]{$ans}\n" if $opt_v;
  $ans++;
}
print "ANSWER: $ans\n";

[download]
There are several optimizations here, primarily the (ab)use of the fact that there is a +- symmetry in values reached, so you can actually avoid worrying about the negative values you can reach. (You know that they are mirrored on the positive side.)

You can optimize further by not tracking information about the expressions that lead to specific values. But not as much as you would expect. You can optimize more by switching languages to use data structures that avoid stringification of values...

In reply to Re (tilly) 1: As per Tilly, The 9 nines solution by tilly
in thread As per Tilly, The 9 nines solution by dfog

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