It is a valid performance note. True But it isn't producing (visibly) wrong answers to take the naive approach.

And the improvement is subtle. For instance consider the following slightly different version of your code: 

sub not_so_nice {
  my ($n, $r) = @_;
  my $res = 1;
  for my $i (1..$r) {
    $res *= ($n-- / $i);
  }
  return $res;
}

[download]
Someone was trying to simplify. But oops. In Perl you have just slowed down instead. In other languages you are going to get wrong answers. It takes a fair amount of knowledge to understand what changed. In fact it takes a fair amount of knowledge to understand why the original formula can be sped up by using your alternate approach.

Now I appreciate that you have both pieces of knowledge. In fact the necessary analysis is probably almost a reflex for you, just like it is for me. But not everyone has the math background that we do...

In reply to Re (tilly) 3: In theory, theory and practice are the same... by tilly
in thread Binomial Expansion by crazyinsomniac

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