#!/usr/bin/perl -wTl

use strict;
use warnings;

use bignum 'bexp';  ## get the latest from CPAN
use Memoize;

use constant MAX_POWER  => 30;
use constant MAX_DIGITS => 50;

my $X = shift || 1;
memoize('my_factorial');

my $best = bexp( $X, MAX_DIGITS );

my $estimate = 1;
for my $i (1 .. MAX_POWER) {
    $estimate += ($X ** $i) / my_factorial( $i );

    print join "\n", ($i, $best, $estimate,
                      abs( $best - $estimate ), q());
}

exit( 0 );

##--------------------------------------------------+
sub my_factorial {
    my ($n) = @_;
    return 1 if $n == 1;
    $n * my_factorial( $n - 1 );
}
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