Is there a grammar formula in a grammar book?

Lots of people refer to "subject + verb + adjective" as a formula.

Does there exist this kind of grammar formulas in grammar books? In other words, is this kind of formula a well recognized term?

"Grammar" by definition incorporates the structure of a language. The rules of grammar dictate how sentences are constructed. There is no single "grammar formula", although the "rules" for constructing the most basic of sentences could, I suppose, be called a "formula", and perhaps are when teaching English as a foreign language, but during my own education as a native British English speaker, I never heard the term "grammar formula".

A formula is a list of ingredients with which something is made. In a mathematical context, if an "ingredient" or element of the formula was omitted, it would be an incomplete formula.

The example "formula" you gave of "Subject + Verb + Adjective" is very basic and does not give all the "ingredients" of a complete sentence. It does not mention articles, for example, and even in the most basic sentence, the subject would require one.

At best, I would suggest "subject-verb-adjective" is a guide to the order in which these appear within a sentence.