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 precision 20.78 p00 = 41.0662918134876242247734962 p01 = 72.468559121745017145904169 p02 = 39.07257269452817173492684 p03 = 6.5293765452906963960675 p04 = .1624170218722279659508 q00 = 41.0662918134876242248414084 q01 = 86.15732305957422506242472 q02 = 59.57842201835544930322456 q03 = 15.0239990556978858274928 q04 = 1.0 precision 25.51 p00 = 137.772398556992967072803545 p01 = 311.6092089800060900355248812 p02 = 243.2657933898208264206733648 p03 = 76.11794408121611233450964866 p04 = 8.1327059582002624490996398 p05 = .1342077928230059190697038 q00 = 137.7723985569929670728035493 q01 = 357.5333418323370790597777492 q02 = 334.8890942892012593679882767 q03 = 135.9227450335766811043244001 q04 = 22.23061618444266557469256796 q05 = 1.0