Starting with polynomial:
P : 2*t
Extension levels are: 1 2 40
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : 2*t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^43 - 35411093473535666447/40988561757168329*t^41 + 6930950714471408020435/40988561757168329*t^39 - 85834154469284057450055/4314585448122982*t^37 + 27161461233596456941273515/17258341792491928*t^35 - 3063077734441637407449767085/34516683584983856*t^33 + 31833357402938260827767844735/8629170896245964*t^31 - 1991054253294801032959790994825/17258341792491928*t^29 + 379095202259066772119225757647475/138066734339935424*t^27 - 13806249252872268447356943790473525/276133468679870848*t^25 + 192416784264613991730961245490432875/276133468679870848*t^23 - 4088016083931311005286071684846546125/552266937359741696*t^21 + 131265614542177507026601215319459764375/2209067749438966784*t^19 - 1571235685468908541266190508111435450625/4418135498877933568*t^17 + 3438428917617006179267323864303131144375/2209067749438966784*t^15 - 21426998193666641308217295462349433360625/4418135498877933568*t^13 + 732614764596555335100969631108500999714375/70690167982046937088*t^11 - 2036865469423890662057680038540916200590625/141380335964093874176*t^9 + 1703506700447161122318105388201387990340625/141380335964093874176*t^7 - 1514374029519950696534165552373634493784375/282760671928187748352*t^5 + 1145924863808828573664109359893103314034375/1131042687712750993408*t^3 - 111067956871100921542007595344653162040625/2262085375425501986816*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: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-5.6667223867213411319 + 1.6191925420914666386e-793j)  +/-  (5.48e-245, 5.48e-245j)
| (8.3301418303454869051 + 3.77856985773858927e-805j)  +/-  (1.13e-247, 1.13e-247j)
| (7.6495007641817001595 - 4.9368289759526566929e-804j)  +/-  (1.45e-246, 1.45e-246j)
| (6.5775022717201395796 - 7.9532709490512923238e-803j)  +/-  (2.11e-245, 2.11e-245j)
| (-8.3301418303454869051 + 2.2314295603767618574e-804j)  +/-  (1.16e-247, 1.16e-247j)
| (-6.5775022717201395796 + 1.0541177536500193179e-801j)  +/-  (1.95e-245, 1.95e-245j)
| (-6.1087575221793520269 - 1.9543098278762669923e-805j)  +/-  (3.61e-245, 3.61e-245j)
| (4.4450899204149803083 + 1.0155276126374600969e-807j)  +/-  (3.52e-245, 3.52e-245j)
| (-2.9594360115807011771 - 2.2759346402547641447e-816j)  +/-  (7.47e-247, 7.47e-247j)
| (1.5632927683110282087 - 1.9310533130737526169e-825j)  +/-  (8.75e-250, 8.75e-250j)
| (0.8918236445877068427 - 2.9828276219901018033e-827j)  +/-  (9.15e-252, 9.15e-252j)
| (3.3203788395129862137 - 4.6442752935284720738e-827j)  +/-  (2.88e-246, 2.88e-246j)
| (2.252873576275645423 + 5.7300069200482145844e-840j)  +/-  (3.52e-248, 3.52e-248j)
| (-4.8386045825562490109 + 2.3820918604200839444e-847j)  +/-  (5.22e-245, 5.22e-245j)
| (6.1087575221793520269 + 2.6946395842159836254e-856j)  +/-  (3.74e-245, 3.74e-245j)
| (4.0619774388788612116 - 6.1833349450559687906e-856j)  +/-  (1.83e-245, 1.83e-245j)
| (-5.2447914035718727682 - 2.3809889185899507534e-863j)  +/-  (6.03e-245, 6.03e-245j)
| (5.2447914035718727682 + 3.4452670354979592181e-866j)  +/-  (5.78e-245, 5.78e-245j)
| (-1.5632927683110282087 + 1.9755584754029726297e-875j)  +/-  (8.82e-250, 8.82e-250j)
| (-7.0839614215359299484 + 4.9794774898379625458e-870j)  +/-  (6.36e-246, 6.36e-246j)
| (2.9594360115807011771 - 3.708834935800588272e-870j)  +/-  (8.3e-247, 8.3e-247j)
| (5.6667223867213411319 + 8.0714503620357393913e-875j)  +/-  (5.55e-245, 5.55e-245j)
| (7.0839614215359299484 - 1.0845193397265536941e-878j)  +/-  (6.32e-246, 6.32e-246j)
| (-3.3203788395129862137 - 3.6124553768087771573e-880j)  +/-  (2.83e-246, 2.83e-246j)
| (-4.4450899204149803083 + 5.0690973053018220678e-890j)  +/-  (3.48e-245, 3.48e-245j)
| (3.6875290402641298639 - 2.6624580788361564484e-895j)  +/-  (7.76e-246, 7.76e-246j)
| (4.8386045825562490109 + 5.8819574948830791383e-901j)  +/-  (4.83e-245, 4.83e-245j)
| (1.2247448713915890491 - 4.1927933114755754004e-904j)  +/-  (9.25e-251, 9.25e-251j)
| (-3.6875290402641298639 + 2.5411357555911490715e-900j)  +/-  (8.35e-246, 8.35e-246j)
| (-0.56880747067627256077 + 1.239087415865555547e-916j)  +/-  (7.41e-253, 7.41e-253j)
| (-1.9060963443483750325 + 3.4350660575341769998e-911j)  +/-  (6.45e-249, 6.45e-249j)
| (1.9060963443483750325 - 2.2296081798681665118e-912j)  +/-  (6.16e-249, 6.16e-249j)
| (2.6038276896566423711 - 2.0262453626448335746e-912j)  +/-  (1.94e-247, 1.94e-247j)
| (-7.6495007641817001595 - 1.1488311988352147511e-910j)  +/-  (1.34e-246, 1.34e-246j)
| (-1.2247448713915890491 + 1.0083609357103998826e-914j)  +/-  (9.19e-251, 9.19e-251j)
| (-0.8918236445877068427 + 7.2982504689287372911e-916j)  +/-  (8.74e-252, 8.74e-252j)
| (-2.6038276896566423711 + 8.4304962246750556012e-912j)  +/-  (1.9e-247, 1.9e-247j)
| (0.56880747067627256077 - 1.888910422863193644e-921j)  +/-  (7.41e-253, 7.41e-253j)
| (-4.0619774388788612116 - 9.3400965002179215756e-919j)  +/-  (1.88e-245, 1.88e-245j)
| (-2.252873576275645423 + 5.7003343935001115339e-927j)  +/-  (3.97e-248, 3.97e-248j)
| (-0.26735899932296462609 - 6.5332670115139267292e-932j)  +/-  (5.95e-254, 5.95e-254j)
| (-1.4693369116415631551e-938 + 9.8536180303216801413e-939j)  +/-  (7.61e-937, 7.61e-937j)
| (0.26735899932296462609 + 6.2219139539288916342e-932j)  +/-  (5.95e-254, 5.95e-254j)
-------------------------------------------------
The weights are:
| (2.7546325063580257355e-15 + 2.6058684264460761325e-807j)  +/-  (4.81e-85, 1.45e-206j)
| (3.2358980539046204018e-31 - 2.3523874580635746414e-817j)  +/-  (2.29e-92, 6.92e-214j)
| (1.3261049227294303999e-26 + 5.4498438108479552582e-815j)  +/-  (6.04e-91, 1.83e-212j)
| (4.4488279249433285811e-20 + 1.2619670510994703134e-811j)  +/-  (9.91e-89, 2.99e-210j)
| (3.2358980539046204018e-31 + 1.2362321645089891883e-816j)  +/-  (1.7e-94, 5.13e-216j)
| (4.4488279249433285811e-20 - 1.6965469191497476077e-810j)  +/-  (3.27e-90, 9.89e-212j)
| (1.5921155212764320595e-17 + 7.1183274145793994647e-809j)  +/-  (8.71e-89, 2.63e-210j)
| (5.7423941729063554554e-10 - 2.5637837544412845238e-806j)  +/-  (1.15e-85, 3.47e-207j)
| (3.1755656824418669464e-05 - 3.366718136489687112e-803j)  +/-  (6.08e-80, 1.83e-201j)
| (0.016693090685981494239 - 5.3586808166483174448e-802j)  +/-  (3.29e-71, 9.94e-193j)
| (0.083817038992493321902 - 2.1948397969955376756e-801j)  +/-  (3.29e-71, 9.94e-193j)
| (3.3444774539518696631e-06 + 2.9385596335350440035e-804j)  +/-  (6.11e-82, 1.84e-203j)
| (0.0012296248512786100783 - 9.3519039690754760216e-803j)  +/-  (7.58e-77, 2.29e-198j)
| (1.5314695576012162741e-11 + 4.699338954906769078e-806j)  +/-  (1.63e-87, 4.93e-209j)
| (1.5921155212764320595e-17 - 2.6721210919573812637e-810j)  +/-  (1.22e-90, 3.68e-212j)
| (1.4581727714690399084e-08 + 1.4683854185522155224e-805j)  +/-  (3.14e-85, 9.49e-207j)
| (2.6385042338165460378e-13 - 1.117393027466598041e-806j)  +/-  (3.19e-89, 9.64e-211j)
| (2.6385042338165460378e-13 - 4.3207821362580720015e-808j)  +/-  (4.49e-89, 1.36e-210j)
| (0.016693090685981494239 - 9.4416980715836909765e-802j)  +/-  (4.93e-78, 1.49e-199j)
| (4.8142279762745858616e-23 + 3.3309104720345437958e-812j)  +/-  (7.11e-95, 2.15e-216j)
| (3.1755656824418669464e-05 - 1.0566314365210612023e-803j)  +/-  (4.09e-83, 1.23e-204j)
| (2.7546325063580257355e-15 + 3.9355028412094253651e-809j)  +/-  (3.27e-90, 9.86e-212j)
| (4.8142279762745858616e-23 - 3.7023083725082224186e-813j)  +/-  (4.88e-94, 1.47e-215j)
| (3.3444774539518696631e-06 + 1.1255441649440790207e-803j)  +/-  (1.07e-87, 3.23e-209j)
| (5.7423941729063554554e-10 - 2.1221194453097343992e-805j)  +/-  (4.14e-90, 1.25e-211j)
| (2.5992432447107276173e-07 - 7.0957448340505109239e-805j)  +/-  (1.28e-86, 3.87e-208j)
| (1.5314695576012162741e-11 + 3.7044123115986694206e-807j)  +/-  (5.05e-89, 1.52e-210j)
| (0.042312150259821031852 + 1.1226023812016555206e-801j)  +/-  (2.99e-82, 9.02e-204j)
| (2.5992432447107276173e-07 - 3.3536582646424013716e-804j)  +/-  (2.42e-89, 7.3e-211j)
| (0.12862632677767112403 + 4.9501624843183353385e-801j)  +/-  (2.26e-83, 6.84e-205j)
| (0.0051415594269414952537 + 4.7335054701231800278e-802j)  +/-  (9.01e-86, 2.72e-207j)
| (0.0051415594269414952537 + 2.3506364769854671575e-802j)  +/-  (2.54e-84, 7.68e-206j)
| (0.00022643545820968799392 + 3.3367326010373063827e-803j)  +/-  (1.38e-85, 4.16e-207j)
| (1.3261049227294303999e-26 - 3.6600831011925184216e-814j)  +/-  (4.74e-99, 1.43e-220j)
| (0.042312150259821031852 + 1.7416516691457432594e-801j)  +/-  (3.56e-85, 1.07e-206j)
| (0.083817038992493321902 - 3.0147147860663219648e-801j)  +/-  (8.08e-85, 2.44e-206j)
| (0.00022643545820968799392 + 9.0099780754257078459e-803j)  +/-  (2.37e-88, 7.15e-210j)
| (0.12862632677767112403 + 4.0470509712635716991e-801j)  +/-  (9.66e-86, 2.92e-207j)
| (1.4581727714690399084e-08 + 8.9020258225691743305e-805j)  +/-  (1.04e-90, 3.13e-212j)
| (0.0012296248512786100783 - 2.1694956347276643322e-802j)  +/-  (5.74e-88, 1.73e-209j)
| (0.14942095101960515291 - 7.3925400925217071116e-801j)  +/-  (1.33e-86, 4.02e-208j)
| (0.1449948945956935831 + 8.4589149818745877763e-801j)  +/-  (5.72e-87, 1.73e-208j)
| (0.14942095101960515291 - 6.7264008898428836784e-801j)  +/-  (4.25e-87, 1.27e-208j)
