The Lookups

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The dumb or simple lookup is a program that looks in the huge tables to see if there is a match between the input X (your number) and an entry in the tables.

The smart lookup is a set of variations of K with elementary functions. The functions we took in that level are (if K is the input) :

We had to be sure that the output is always positive, so this is why there are 'abs' in many of them. Also we had to choose to limit the input (X) to be between 1/1000 and 1000.