Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formal Verification of Medina's Sequence of Polynomials for
  Approximating Arctangent   The verification of many algorithms for calculating transcendental functions
is based on polynomial approximations to these functions, often Taylor series
approximations. However, computing and verifying approximations to the
arctangent function are very challenging problems, in large part because the
Taylor series converges very slowly to arctangent-a 57th-degree polynomial is
needed to get three decimal places for arctan(0.95). Medina proposed a series
of polynomials that approximate arctangent with far faster convergence-a
7th-degree polynomial is all that is needed to get three decimal places for
arctan(0.95). We present in this paper a proof in ACL2(r) of the correctness
and convergence rate of this sequence of polynomials. The proof is particularly
beautiful, in that it uses many results from real analysis. Some of these
necessary results were proven in prior work, but some were proven as part of
this effort.

15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con