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Instead of working with full polynomials, we can use a linear approximation.
And instead of computing with decimals, we approximate the lunation length by a vulgar fraction.
Moreover it is sufficient to keep track of just the numerator by adding once every lunation, an integer constant to a variable that is called the accumulator.
This is similar to calculating the molad in the Hebrew calendar.
It works as follows:

1.860 seconds.