Building Hash Tables

A more detailed version of the sample analysis just described is carried out on all 90,000 identities of the Wolfram Functions site. This one-time processing procedure takes a few hours. Then the connections identity->listOfIngredients are reversed and large hash tables of the form ingredient->listOfIdentities are constructed. While quite large, such tables allow for a very fast lookup, which is of constant time and independent of the length of the table. The ingredients are sorted into four categories: functions (such as Sin, BesselJ), constants (such as Pi, E), numbers (such as (2, 3, 1729), and operations (such as Sum, Integrate). Integrals are classified as definite versus indefinite.

Here are a few example counts.

Ingredient	Occurrences in the Left-Hand Side	Occurrences in the Right-Hand Side	Occurrences in Conditions
Cos	9517	6234	66
Pi	2566	42730	12237
Hypergeometric2F1	4088	1421	209
D	2372	358	39
11	596	211	19