He asked which are the most valuable techniques, which is, admittedly, ambiguous. To answer your question, clearly the table (in the case of a Taylor series or other mathematical function) is derived from the math. Without an understanding of the math, the table could not be generated. So the answer to your question, as you stated it, is obvious.

The answer to his question, as he stated it and as I understood it, is largely a matter of opinion. My previous post was my answer to your question in light of his question: "Which then, is the more valuable (technique)?"