Starting with polynomial:
P : 2*t
Extension levels are: 1 4 8 18
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : 2*t^5 - 10*t^3 + 15/2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P3 : 2*t^13 - 170/3*t^11 + 3251/6*t^9 - 2163*t^7 + 29631/8*t^5 - 20895/8*t^3 + 19215/32*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^31 - 14560699451931256481266962557/40215459959405427123553269*t^29 + 208192419144785290304382557497/7311901810800986749736958*t^27 - 756953499128921200244292865928631/589826746071279597812114612*t^25 + 217319278577776516924500879491609781/5898267460712795978121146120*t^23 - 1671619897514945905401784062267609201/2359306984285118391248458448*t^21 + 16964518509749657889881901613814615919/1814851526373167993268044960*t^19 - 4024742055578418935400646610482615069767/47186139685702367824969168960*t^17 + 50609363231860838759829946716039534848451/94372279371404735649938337920*t^15 - 6648683945405770262471749247986651105227/2903762442197068789228871936*t^13 + 3413745531139248608387179413785123018943/527956807672194325314340352*t^11 - 12232006451373305981873636314656387158043/1055913615344388650628680704*t^9 + 26081017691726688029653205683168621040853/2111827230688777301257361408*t^7 - 29913211028780989772553228386825592222789/4223654461377554602514722816*t^5 + 15504330826220252140491480150362995600035/8447308922755109205029445632*t^3 - 2442872768781915414820215587646931237335/16894617845510218410058891264*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
Positive weights:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-3.2138011329396621797 + 4.2233439016797081556e-286j)  +/-  (1.02e-120, 1.02e-120j)
| (4.5676337907136047146 + 9.5479634334113439658e-297j)  +/-  (2.63e-120, 2.63e-120j)
| (-4.1218345136703474433 + 3.9748630935372165292e-313j)  +/-  (2.68e-120, 2.68e-120j)
| (3.6658316928775966507 - 4.1149492478002821548e-318j)  +/-  (1.99e-120, 1.99e-120j)
| (5.0300859058231312571 - 7.4043413152942846426e-336j)  +/-  (1.43e-120, 1.43e-120j)
| (5.5802830427260621805 + 3.4998219523967901709e-348j)  +/-  (4.25e-121, 4.25e-121j)
| (-5.0300859058231312571 + 4.3056044401473257724e-353j)  +/-  (1.47e-120, 1.47e-120j)
| (2.3778266016550547198 + 1.064477176769666163e-353j)  +/-  (1.83e-121, 1.83e-121j)
| (1.6759041062306479456 + 1.8617134620508875486e-357j)  +/-  (1.52e-122, 1.52e-122j)
| (6.283452026541915845 - 2.4158092824261113476e-358j)  +/-  (5e-122, 5e-122j)
| (0.66944416045059213743 - 1.5922491941406369622e-363j)  +/-  (4.69e-125, 4.69e-125j)
| (-0.66944416045059213743 + 6.2640165276178301373e-365j)  +/-  (4.86e-125, 4.86e-125j)
| (-6.283452026541915845 - 1.2984962734557570279e-362j)  +/-  (5.49e-122, 5.49e-122j)
| (-0.95857246461381850711 + 2.5142694330999293139e-364j)  +/-  (3.2e-124, 3.2e-124j)
| (4.1218345136703474433 - 2.7900563151023998325e-360j)  +/-  (2.43e-120, 2.43e-120j)
| (3.2138011329396621797 - 2.7013374443740525662e-368j)  +/-  (9.71e-121, 9.71e-121j)
| (-3.6658316928775966507 + 1.8986825536191917523e-371j)  +/-  (1.89e-120, 1.89e-120j)
| (-5.5802830427260621805 + 1.7612064935954420403e-372j)  +/-  (4.27e-121, 4.27e-121j)
| (-1.3117288375389628728 + 1.5310513271953365402e-375j)  +/-  (2.26e-123, 2.26e-123j)
| (-1.6759041062306479456 - 3.7754220808763671155e-375j)  +/-  (1.5e-122, 1.5e-122j)
| (-2.3778266016550547198 + 3.7061962704421522099e-373j)  +/-  (1.91e-121, 1.91e-121j)
| (-2.1166067945074977675e-381 - 4.8524888570941059744e-382j)  +/-  (6.73e-380, 6.73e-380j)
| (-4.5676337907136047146 + 9.5686205783560293314e-375j)  +/-  (2.36e-120, 2.36e-120j)
| (-2.0201828704560856329 - 7.1650557483675650797e-376j)  +/-  (6.6e-122, 6.6e-122j)
| (1.3117288375389628728 + 5.0324078808709880056e-378j)  +/-  (2.06e-123, 2.06e-123j)
| (0.36489753082497850202 + 1.0411866446973354051e-380j)  +/-  (3.45e-126, 3.45e-126j)
| (2.0201828704560856329 - 2.3438969608685670316e-375j)  +/-  (6.7e-122, 6.7e-122j)
| (2.7796084806380178827 + 2.0314198444566006672e-379j)  +/-  (5.27e-121, 5.27e-121j)
| (-2.7796084806380178827 + 1.5617343334693241126e-387j)  +/-  (4.73e-121, 4.73e-121j)
| (-0.36489753082497850202 + 1.6810381879616321864e-392j)  +/-  (3.98e-126, 3.98e-126j)
| (0.95857246461381850711 - 1.0241913823862386838e-391j)  +/-  (3.25e-124, 3.25e-124j)
-------------------------------------------------
The weights are:
| (8.2097150069527193094e-06 + 1.4928432057563797263e-290j)  +/-  (5.83e-33, 2.51e-92j)
| (2.1743789160486536259e-10 - 8.1008658311998922221e-295j)  +/-  (6.19e-38, 2.67e-97j)
| (1.067175723856318507e-08 - 6.7307537665246428937e-293j)  +/-  (7.2e-37, 3.1e-96j)
| (3.7575093070999641843e-07 - 7.1202029230087682189e-293j)  +/-  (1.11e-35, 4.79e-95j)
| (2.8716270238524123759e-12 + 4.9345007702201386249e-296j)  +/-  (1.67e-39, 7.17e-99j)
| (1.0353126064146174029e-14 - 1.1973338100921674503e-297j)  +/-  (2.42e-41, 1.04e-100j)
| (2.8716270238524123759e-12 - 2.2397075365025411706e-295j)  +/-  (3.89e-42, 1.68e-101j)
| (0.00075046701771312638609 + 1.9847057913922934862e-290j)  +/-  (1.48e-33, 6.36e-93j)
| (0.012052477087118081332 + 2.1796669817954151474e-289j)  +/-  (9.06e-31, 3.9e-90j)
| (3.3177961699321545724e-18 + 7.5250437730687074394e-300j)  +/-  (1.11e-43, 4.78e-103j)
| (0.097804961185288988799 - 2.4042629961017099499e-288j)  +/-  (9.13e-29, 3.93e-88j)
| (0.097804961185288988799 - 3.6694312412260595383e-288j)  +/-  (5e-29, 2.15e-88j)
| (3.3177961699321545724e-18 - 2.3281880652320805574e-299j)  +/-  (4.11e-46, 1.77e-105j)
| (0.073271003559178610325 + 2.6064498855711314087e-288j)  +/-  (4.09e-29, 1.76e-88j)
| (1.067175723856318507e-08 + 8.3315875977849276365e-294j)  +/-  (3.04e-38, 1.31e-97j)
| (8.2097150069527193094e-06 + 5.3943054306974952904e-292j)  +/-  (1.04e-36, 4.48e-96j)
| (3.7575093070999641843e-07 + 1.0836519938433565634e-291j)  +/-  (3.85e-40, 1.66e-99j)
| (1.0353126064146174029e-14 + 4.4494125515207427982e-297j)  +/-  (1.24e-44, 5.36e-104j)
| (0.037166144911795968764 - 1.3328447470645935461e-288j)  +/-  (1.86e-34, 7.98e-94j)
| (0.012052477087118081332 + 6.930196804745560013e-289j)  +/-  (4.9e-36, 2.11e-95j)
| (0.00075046701771312638609 + 1.3275208194557769897e-289j)  +/-  (1.34e-38, 5.79e-98j)
| (0.21135949920373546605 - 2.8493554180370655736e-288j)  +/-  (4.6e-35, 1.98e-94j)
| (2.1743789160486536259e-10 + 4.6561412097623995833e-294j)  +/-  (7.18e-43, 3.1e-102j)
| (0.0032529807987924527137 - 3.3796080947766441509e-289j)  +/-  (1.01e-37, 4.33e-97j)
| (0.037166144911795968764 - 5.6019230543172919716e-289j)  +/-  (3.08e-37, 1.33e-96j)
| (0.1699088743761760496 + 2.7432297537595007756e-288j)  +/-  (4.1e-36, 1.75e-95j)
| (0.0032529807987924527137 - 7.707249275786914833e-290j)  +/-  (9.53e-39, 4.12e-98j)
| (0.00010474510405421269945 - 3.6037875425762815161e-291j)  +/-  (3.64e-40, 1.59e-99j)
| (0.00010474510405421269945 - 4.9745141444584848246e-290j)  +/-  (2.52e-40, 1.12e-99j)
| (0.1699088743761760496 + 3.4459546637136265011e-288j)  +/-  (2.77e-37, 1.24e-96j)
| (0.073271003559178610325 + 1.4088241062456137099e-288j)  +/-  (7.29e-38, 2.56e-97j)
