Thanks!
Nice ideas here and elsewhere!
One nitpick: your rule 3 (that the last multiplication can't have a carry so that the numerator is base/2 - 1 digits long) doesn't mean that i < n/2, it's e (the first digit of the denominator) that has to be < n/2. i can't be 1, base/2, base-2 and base-1 (and possibly others are excluded for certain bases).
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