Math functions execution time

Question

Where can I go for information on the computation time of mathematical functions? Has any (general) research been done with any amount of rigor?

For example, calculation time

constant + constant

usually takes O (1).

Suppose I want to start using mathematics as integrals, and I would like to get an asymptotic approximation to various integrals. Was this a standard study of this issue, or should I take the information I have and figure out my own approximation. I would be very interested in a standard approach to this, and I would like to know if it already exists.

Here is my motivation: I am in the middle of writing an article that points to the equivalence between the complex problems of NP and some types of mathematical equations. It seems that it can be used to study mathematical time, which is generalized as a new science.

EDIT: I guess I'm wondering if there is standard computational complexity for any math that cannot be avoided. I am wondering if anyone has studied this issue. I would like to see what others have tried.

EDIT 2: Wikipedia lists "Theory of Computational Complexity" in its encyclopedia, which I think might fit the bill. I'm still wondering if anyone who has studied this can confirm this.

Answer 1

, . , , sin (x) , log (x) 1/epsilon. ( ), .

Answer 2

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. , , .

, - . , .

" " ? ? " " ? ?

, , ?

Answer 3

, ( ) . .

, n- Θ (n), Θ (n log n) ( ), gcd Θ (n ²) Θ (n (log n) ² (log log n)) .. , , , , .

Answer 4

user389117,

, .

. , (x ^ 2), ( ), x ^ 2, - O (n ^ 2) .

, .

: , .

, .

, , .

Even if you calculate the complexity and you find that the form is similar to the form of the calculated equation, then I think it would be difficult, at least in the first place, so that you can convert this remark from pseudoscience to science.

Good luck