Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 10 19
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Trying to find an order 10 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 19 Kronrod extension for:
P2 : 16*t^14 - 3816/7*t^12 + 44964/7*t^10 - 225630/7*t^8 + 68715*t^6 - 108945/2*t^4 + 46845/4*t^2 - 2835/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^33 - 6978881355496824168728920184/2495856217653108003195383*t^31 + 2635754801841352274187490948572/12479281088265540015976915*t^29 - 1249919337187246528948724165848686/137272091970920940175746065*t^27 + 34219750611530818721219158999289259/137272091970920940175746065*t^25 - 250654077180855141828633011491865145/54908836788368376070298426*t^23 + 900308297364693042806082770570484435/15688239082390964591513836*t^21 - 15704757515709116263320063828337714977/31376478164781929183027672*t^19 + 189898734204661971894897774788765528067/62752956329563858366055344*t^17 - 143093424272692843545447606337655841771/11409628423557065157464608*t^15 + 8743611889380386209892869759276280665485/251011825318255433464221376*t^13 - 31339865344802557315448172883482762568695/502023650636510866928442752*t^11 + 6194946759310778915531538349515120163545/91277027388456521259716864*t^9 - 7387845987458637803702228754706664432895/182554054776913042519433728*t^7 + 4141897815661356296102379763005147426435/365108109553826085038867456*t^5 - 937953319370154974082928714110788757825/730216219107652170077734912*t^3 + 24340633132581997593423752999883945825/730216219107652170077734912*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (4.9706362245996210627 + 1.0145723182722810356e-448j)  +/-  (6.63e-121, 6.63e-121j)
| (3.911506869286660161 - 9.1288082632952704591e-457j)  +/-  (1.88e-120, 1.88e-120j)
| (-4.4182967047772646168 + 6.099681267640912566e-467j)  +/-  (1.24e-120, 1.24e-120j)
| (-3.0486879132310133212 + 7.383851129673470728e-467j)  +/-  (1.52e-120, 1.52e-120j)
| (-6.328235033607170872 - 2.3512605362771919725e-468j)  +/-  (3.03e-122, 3.03e-122j)
| (5.5877295593217517919 + 7.4802788205923349419e-466j)  +/-  (2.27e-121, 2.27e-121j)
| (-5.5877295593217517919 - 4.1049012244763323713e-472j)  +/-  (2.56e-121, 2.56e-121j)
| (6.328235033607170872 + 5.9886802435305432048e-471j)  +/-  (3.52e-122, 3.52e-122j)
| (-4.9706362245996210627 - 5.9589553648415750345e-473j)  +/-  (5.99e-121, 5.99e-121j)
| (3.449013085632172285 - 3.220434403374524791e-472j)  +/-  (1.74e-120, 1.74e-120j)
| (1.6506801238857845559 + 2.1574445925452191644e-476j)  +/-  (5.43e-122, 5.43e-122j)
| (1.8923999220321492703 + 4.0819733694299206581e-476j)  +/-  (1.01e-121, 1.01e-121j)
| (-1.8923999220321492703 - 1.4878858425088399484e-478j)  +/-  (9.89e-122, 9.89e-122j)
| (-0.52464762327529031788 + 3.7599127068054070497e-480j)  +/-  (8.67e-125, 8.67e-125j)
| (-3.911506869286660161 + 7.3002836039561630775e-477j)  +/-  (1.95e-120, 1.95e-120j)
| (2.3166778458612639611 + 1.4815964857406565609e-475j)  +/-  (2.48e-121, 2.48e-121j)
| (3.0486879132310133212 + 1.3096004359096777646e-476j)  +/-  (1.29e-120, 1.29e-120j)
| (-3.449013085632172285 - 7.293431746350957941e-483j)  +/-  (1.98e-120, 1.98e-120j)
| (-1.0363502036603261655 - 1.4081770404562925658e-486j)  +/-  (4.25e-124, 4.25e-124j)
| (2.6988820822996506013 - 1.6913822471451585697e-483j)  +/-  (6.76e-121, 6.76e-121j)
| (1.299570539370358132e-498 + 2.6306201874563674913e-497j)  +/-  (8.69e-496, 8.69e-496j)
| (0.47761512394723076755 + 3.8860068718560256843e-491j)  +/-  (7.02e-125, 7.02e-125j)
| (-2.6988820822996506013 + 5.1416067331603561763e-487j)  +/-  (7.15e-121, 7.15e-121j)
| (-1.6506801238857845559 - 4.9976297982162545327e-493j)  +/-  (6.2e-122, 6.2e-122j)
| (-1.484410709015204834 + 1.7205680091768753996e-494j)  +/-  (1.7e-122, 1.7e-122j)
| (4.4182967047772646168 + 1.1720652896524607314e-496j)  +/-  (1.27e-120, 1.27e-120j)
| (1.484410709015204834 + 1.9270597758673932509e-511j)  +/-  (1.65e-122, 1.65e-122j)
| (0.18980675578014987883 - 3.3126200247170485358e-515j)  +/-  (1.2e-126, 1.2e-126j)
| (-0.18980675578014987883 + 5.0365847054920752795e-515j)  +/-  (1.2e-126, 1.2e-126j)
| (-0.47761512394723076755 - 7.5171712793808968852e-514j)  +/-  (6.66e-125, 6.66e-125j)
| (-2.3166778458612639611 - 2.2354223413136317825e-513j)  +/-  (2.61e-121, 2.61e-121j)
| (1.0363502036603261655 + 1.3909260492616693045e-515j)  +/-  (4.36e-124, 4.36e-124j)
| (0.52464762327529031788 + 1.4645994781731676348e-517j)  +/-  (9.95e-125, 9.95e-125j)
-------------------------------------------------
The weights are:
| (6.0872226903508367605e-12 - 4.0812849731419053185e-459j)  +/-  (9.3e-42, 7.51e-101j)
| (6.2138324101753005416e-08 - 4.6058831849728951255e-457j)  +/-  (1.73e-38, 1.4e-97j)
| (9.9084430748838375798e-10 + 2.2393784438318103238e-459j)  +/-  (2.19e-41, 1.77e-100j)
| (1.8874846123207666629e-05 - 1.1144655775048578989e-455j)  +/-  (7.04e-37, 5.68e-96j)
| (1.9495211162262390229e-18 - 4.6361111378229543807e-465j)  +/-  (7.81e-47, 6.31e-106j)
| (1.0300326755700778521e-14 - 1.6163488553247443462e-461j)  +/-  (3.21e-45, 2.59e-104j)
| (1.0300326755700778521e-14 + 9.4468977434831342784e-463j)  +/-  (3.41e-45, 2.75e-104j)
| (1.9495211162262390229e-18 + 3.8584908764593544182e-464j)  +/-  (1.63e-47, 1.32e-106j)
| (6.0872226903508367605e-12 - 6.212410800093580047e-461j)  +/-  (1.01e-43, 8.17e-103j)
| (1.6764637478376596062e-06 + 5.4689601328029102351e-456j)  +/-  (1.78e-40, 1.44e-99j)
| (-0.0023991596214200767641 - 4.5917581771083961052e-452j)  +/-  (1.75e-34, 1.42e-93j)
| (0.0069900512246426819825 + 1.1266927365947153165e-452j)  +/-  (8.79e-36, 7.1e-95j)
| (0.0069900512246426819825 + 5.0534873305017415157e-453j)  +/-  (4.94e-37, 3.99e-96j)
| (0.6574203622799573268 + 2.6073421830491964373e-450j)  +/-  (4.95e-35, 4.01e-94j)
| (6.2138324101753005416e-08 - 5.4921758684841852251e-458j)  +/-  (8.22e-43, 6.64e-102j)
| (0.0010720902258381459934 - 1.1823210878069519416e-453j)  +/-  (2.31e-38, 1.87e-97j)
| (1.8874846123207666629e-05 - 4.6501040304005156786e-455j)  +/-  (8.28e-41, 6.69e-100j)
| (1.6764637478376596062e-06 + 9.8836638609093184661e-457j)  +/-  (2.89e-42, 2.34e-101j)
| (0.086237557678992302338 - 4.9354624558308938329e-452j)  +/-  (1.04e-35, 8.41e-95j)
| (0.00013767807204930280251 + 2.397028533888052096e-454j)  +/-  (4.51e-40, 3.64e-99j)
| (-0.22398049750309532533 - 3.4842970129341518784e-450j)  +/-  (9.89e-36, 8.01e-95j)
| (-0.56053898150992365437 - 4.1242848509905661638e-450j)  +/-  (3.05e-36, 2.46e-95j)
| (0.00013767807204930280251 + 7.100132935042874927e-455j)  +/-  (4.82e-41, 3.9e-100j)
| (-0.0023991596214200767641 - 2.3023270998783856317e-452j)  +/-  (8.95e-39, 7.24e-98j)
| (0.029342806654525620925 + 3.0593547113930014549e-452j)  +/-  (1.31e-38, 1.06e-97j)
| (9.9084430748838375798e-10 + 3.8066042132435979892e-458j)  +/-  (6.76e-46, 5.47e-105j)
| (0.029342806654525620925 + 5.6646587000739318215e-452j)  +/-  (7.4e-39, 6e-98j)
| (0.39370722930174903343 + 2.7362253399469198937e-450j)  +/-  (4.6e-37, 3.75e-96j)
| (0.39370722930174903343 + 2.5349426063523074394e-450j)  +/-  (2.81e-37, 2.28e-96j)
| (-0.56053898150992365437 - 3.401182841937903052e-450j)  +/-  (3.07e-37, 2.51e-96j)
| (0.0010720902258381459934 - 4.3058815734701544711e-454j)  +/-  (2.99e-41, 2.4e-100j)
| (0.086237557678992302338 - 7.535612637104441909e-452j)  +/-  (1.02e-39, 7.99e-99j)
| (0.6574203622799573268 + 3.2226995041975257015e-450j)  +/-  (6.24e-38, 5.14e-97j)
