Approximate any real number $x with chain fractions.

I'm not the first one offering code on this, see Continued Fractions. 

#use bignum "a", 32; # uncomment for greater precision
$x = 2**(1/12); # change this to any number you like
print $x, "\n"; ($p, $q, $r, $s) = (0, 1, 1, 0); 
{ 
$n = int(($p - $x*$q) / ($x*$s - $r)); ($p, $q) = ($p + $n*$r, $q + $n
+*$s); print $p, "/", $q, " = ", $y = $p/$q, "\n"; $y == $x and last; 
$n = int(($r - $x*$s) / ($x*$q - $p)); ($r, $s) = ($r + $p*$n, $s + $q
+*$n); print $r, "/", $s, " = ", $y = $r/$s, "\n"; $y == $x and last; 
redo; }

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In reply to Approximation with chain fractions by ambrus

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