10389! 4570! 44289! 11800!
------------------------------
56089! 989! 9400! 43300! 2400!

##</code><code>##

8.070604647867604097576877675243109941805e-7030
8.070604647867604097576877675243109941729476950993498765160880e-7030

##</code><code>##

#!/your/perl/here

use strict;
use warnings;
use Benchmark;
use Math::Big::Factors;

my $ORDER = 5;

# preserve this many significant digits
Math::BigFloat->accuracy(40);
my $ONE = Math::BigFloat->new(1);

my $t0 = new Benchmark;

my @num = ( 10389, 45700, 44289, 11800 );
my @den = ( 56089, 989, 9400, 43300, 2400 );

my $t1 = new Benchmark;
time_delta("startup", $t1, $t0);

# expand terms
my (@num_fac, @den_fac);
foreach my $n ( @num )
{
	push @num_fac, 2..$n;
}
foreach my $n ( @den )
{
	push @den_fac, 2..$n;
}
my $t2 = new Benchmark;
time_delta("expand", $t2, $t1);
my $quotient = cancel_quotient( \@num_fac, \@den_fac );
my $t3 = new Benchmark;
time_delta("cancel_quotient", $t3, $t2);

warn "factoring ", scalar keys %{$quotient}, " terms\n";
my $factors = prime_factor_hash( $quotient );
my $t4 = new Benchmark;
time_delta("prime_factor_hash", $t4, $t3);

# evaluate terms
my $q = $ONE->copy();
#print "Factors\n";
foreach my $t ( sort { $factors->{$b} <=> $factors->{$a} } keys %{$factors} )
{
	my $bft = $ONE->copy()->bmul($t)->bpow($factors->{$t});
	$q->bmul($bft);
#	print "$t**$factors->{$t}:  $q\n";
}

print $q->bsstr(), "\n";
my $t5 = new Benchmark;
time_delta("multiply", $t5, $t4 );
time_delta("All", $t5, $t0 );
exit;

########################################
# cancel like terms between 2 arrays
# similar to unique array element

sub cancel_quotient
{
	my $num = shift;
	my $den = shift;
	
	my %quotient;
	
	# determine the residual terms after cancelling
	# positive terms are in numerator
	# negative terms are in denominator
	# zero terms are filtered
	foreach my $n ( @{$num} )
	{
		$quotient{$n}++;
	}
	foreach my $n ( @{$den} )
	{
		$quotient{$n}--;
	}
	foreach my $n ( keys %quotient )
	{
		delete $quotient{$n} unless $quotient{$n};
	}

	return \%quotient;
}

#######################################
# factor keys of hash, and duplicate "value" times

sub prime_factor_hash
{
	my $quotient = shift;
	my %factors;
	
	foreach my $n ( keys %{$quotient} )
	{
		my @factors = Math::Big::Factors::factors_wheel($n,$ORDER);
		foreach my $f ( @factors )
		{
			$factors{$f} += $quotient->{$n};
		}
	}

	return \%factors;
}

###########################################
# nice benchmark timestamp printer

sub time_delta
{
	print +shift, ": ", timestr(timediff(@_)), "\n";
}

##</code><code>##

foreach my $t ( keys %{$factors} )
{
    my $bft = $ONE->copy()->bmul($t)->bpow($factors->{$t});
    $q->bmul($bft);
}

##</code><code>##

my $s = '$q';
foreach my $t ( keys %{$factors} )
{
    next if ( $factors->{$t} == 0 );
    if ( $factors->{$t} > 0 )
    {
        $s .= "->bmul($t)" x $factors->{$t};
    }
    else
    {
        $s .= "->bdiv($t)" x abs($factors->{$t});
    }
}
eval $s;
die "Error on eval: $@" if $@;