This tool converts an Opus Magnum solution into a number — its Continued Fraction Cycles, or CFC. This number encodes every cycle on which the solution outputs a product.

If a solution A has a lower Continued Fraction Cycles than a solution B, that means either A outputs its first product before B; or A and B are tied on the first product, but A outputs its second product before B; or A and B are tied on the first two products, but A outputs its third product before B; or so on. Solutions with equal CFCs output all products on the same cycles to infinity.

A solution that outputs a certain number of products and then stops has a rational CFC; a solution that loops and continues to output products has a quadratic irrational CFC.

Lexicographic cycles, or LexC, is the sequence of intervals between the cycles on which the solution drops a product. This sequence is converted into a continued fraction according to the order-preserving continued fraction representation described at https://oscarcunningham.com/494/a-better-representation-for-real-numbers/. The real number corresponding to this continued fraction is the Continued Fraction Cycles of the solution.