Simplify! :-)

#! perl
use strict;
use warnings;
use bignum;

my ($even, $odd) = (1, 1);

for (1 .. 47)
{
    $even += $odd;
    $odd  += $even;
    print "phi = ", ($odd / $even), "\n";
}
[download]

47 iterations gives phi correct to 38 decimal places:

phi = 1.61803398874989484820458683436563811772
[download]

Update: Timed (with Time::HiRes) at less than 0.3 seconds.

Hope that helps,