Hart, Computer Approximations
The approximants for arctan are based on the relative error criterion.
arctan(x) approx x * P(x^2) / Q(x^2), range [0, tan pi/12]

precision 13.70
p00 = 48.70107004404898384
p01 = 49.5326263772254345
p02 =  9.40604244231624
q00 = 48.70107004404996165
q01 = 65.7663163908956299
q02 = 21.587934067020262
q03 =  1.0

precision 16.06
p00 = 12.82297680061262709335
p01 = 16.2428078151342213662
p02 =  4.923443373635526899
p03 =   .205608723964456163
q00 = 12.82297680061262821474
q01 = 20.517133415336848884
q02 =  9.197892485655692716
q03 =  1.0