Starting with polynomial:
P : 2*t
Extension levels are: 1 2 10 22
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P2 : 2*t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P3 : 2*t^13 - 629/8*t^11 + 17435/16*t^9 - 105435/16*t^7 + 557865/32*t^5 - 2248785/128*t^3 + 1133055/256*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^35 - 1957041419687385592031338609712681/4164678192223993000091454933360*t^33 + 9696925531202360372178218788670551037/199904553226751664004389836801280*t^31 - 1628711726900995036250757940878068631175/559732749034904659212291543043584*t^29 + 1645753115556151343311476511346938655560321/14553051474907521139519580119133184*t^27 - 1388943929942253011288467747493161262291763/462001634124048290143478733940736*t^25 + 364058719364688754622059593697669282458715983/6468022877736676062008702275170304*t^23 - 9741581530050132770614861112085974602118495199/12936045755473352124017404550340608*t^21 + 26734943282103985962448371008342813155030180035/3696013072992386321147829871525888*t^19 - 367490989508181877492439611443021093684722990895/7392026145984772642295659743051776*t^17 + 3574790272569616860466666857790935831422103074055/14784052291969545284591319486103552*t^15 - 1856580885973061254279193935525200350848071389835/2274469583379930043783279920939008*t^13 + 8443231975521404105849581423801946507307883011105/4548939166759860087566559841878016*t^11 - 24729747304468654744069032643480689722775482051325/9097878333519720175133119683756032*t^9 + 43562151113534219814435895926332963425659001577775/18195756667039440350266239367512064*t^7 - 41264607072279405372992746846401841045937885148975/36391513334078880700532478735024128*t^5 + 17063544790674883176058839445684896043546200760725/72783026668157761401064957470048256*t^3 - 1868015204665759955430194668363779739204907275425/145566053336315522802129914940096512*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (4.5865593477740438902 + 1.1711628420377010995e-438j)  +/-  (1e-119, 1e-119j)
| (5.0856944272315831692 - 3.0884663025100054472e-442j)  +/-  (6.93e-120, 6.93e-120j)
| (-6.2296452683399182222 - 1.8406828245907533372e-449j)  +/-  (9.39e-121, 9.39e-121j)
| (-5.0856944272315831692 + 3.077174992818056173e-459j)  +/-  (6.69e-120, 6.69e-120j)
| (5.62600862113280669 + 3.5594467301278716594e-468j)  +/-  (3.31e-120, 3.31e-120j)
| (2.8759177223792773828 - 1.6703288390493593135e-467j)  +/-  (2.9e-120, 2.9e-120j)
| (6.9560846948478366174 - 2.2853092093082073211e-470j)  +/-  (1.22e-121, 1.22e-121j)
| (-5.62600862113280669 - 6.5557540395854509957e-469j)  +/-  (3.3e-120, 3.3e-120j)
| (-2.5296025834934300893 - 1.1712895975329974982e-470j)  +/-  (1.37e-120, 1.37e-120j)
| (-4.5865593477740438902 + 3.0232774430793939914e-473j)  +/-  (9.03e-120, 9.03e-120j)
| (1.2247448713915890491 + 2.0348998023220650653e-480j)  +/-  (3.6e-123, 3.6e-123j)
| (-6.9560846948478366174 - 1.7450921873527275284e-479j)  +/-  (1.08e-121, 1.08e-121j)
| (4.1180864274630133413 - 5.3171019195907469249e-476j)  +/-  (1.06e-119, 1.06e-119j)
| (-4.1180864274630133413 + 2.1796959697394769046e-476j)  +/-  (1.01e-119, 1.01e-119j)
| (3.2595330824338197843 + 1.0661040549701146341e-479j)  +/-  (5.19e-120, 5.19e-120j)
| (1.5269352718982998336 + 8.2599021820072643729e-484j)  +/-  (2.28e-122, 2.28e-122j)
| (2.1992932081871996471 - 7.882438411822244469e-482j)  +/-  (4.48e-121, 4.48e-121j)
| (-1.8602834494799461889 + 8.1190466070731787443e-483j)  +/-  (9.59e-122, 9.59e-122j)
| (-0.92966640114313345589 - 3.2154060002488872813e-485j)  +/-  (5.1e-124, 5.1e-124j)
| (-3.2595330824338197843 + 3.1805742204284846096e-480j)  +/-  (5.12e-120, 5.12e-120j)
| (2.5296025834934300893 + 1.8892733438090275932e-488j)  +/-  (1.3e-120, 1.3e-120j)
| (3.6756353218886387545 + 1.2835819745319876515e-488j)  +/-  (8.05e-120, 8.05e-120j)
| (6.001133736022263191e-499 - 6.9301570266326642238e-499j)  +/-  (3.21e-497, 3.21e-497j)
| (-1.2247448713915890491 - 9.6090448351334051507e-492j)  +/-  (3.88e-123, 3.88e-123j)
| (-1.5269352718982998336 + 4.4911786750083379353e-490j)  +/-  (1.97e-122, 1.97e-122j)
| (1.8602834494799461889 - 1.0966501627218648084e-490j)  +/-  (9.8e-122, 9.8e-122j)
| (0.60808265691331281929 - 9.0569804831404706963e-495j)  +/-  (3.83e-125, 3.83e-125j)
| (-3.6756353218886387545 - 3.1429774024188792513e-487j)  +/-  (8.35e-120, 8.35e-120j)
| (6.2296452683399182222 - 6.6733869433204397385e-495j)  +/-  (9.72e-121, 9.72e-121j)
| (-0.60808265691331281929 + 1.6860221296403983994e-497j)  +/-  (3.58e-125, 3.58e-125j)
| (0.28691220005817625052 + 2.8821320556190871607e-498j)  +/-  (2.9e-126, 2.9e-126j)
| (-0.28691220005817625052 - 5.2287915938213716714e-498j)  +/-  (2.14e-126, 2.14e-126j)
| (0.92966640114313345589 + 1.0282032481509406342e-496j)  +/-  (4.86e-124, 4.86e-124j)
| (-2.8759177223792773828 + 3.010259305397239955e-497j)  +/-  (3.13e-120, 3.13e-120j)
| (-2.1992932081871996471 - 3.3011635068664302118e-504j)  +/-  (4.24e-121, 4.24e-121j)
-------------------------------------------------
The weights are:
| (1.990605388259805749e-10 - 1.3499366966375394985e-447j)  +/-  (3.42e-32, 1.27e-91j)
| (1.7079298063876292677e-12 - 2.4735799590174388701e-449j)  +/-  (8.65e-34, 3.22e-93j)
| (5.1199078722220798243e-18 + 7.0384541819086864163e-454j)  +/-  (1.85e-38, 6.91e-98j)
| (1.7079298063876292677e-12 + 1.2767055840009596185e-450j)  +/-  (1.09e-35, 4.06e-95j)
| (5.7346787621540178101e-15 + 4.0730218085995713942e-451j)  +/-  (3.32e-36, 1.24e-95j)
| (5.260810344469944737e-05 - 1.1411026816443631566e-444j)  +/-  (1e-28, 3.75e-88j)
| (4.5735526921276173753e-22 + 1.8037164385707286639e-455j)  +/-  (4.41e-40, 1.65e-99j)
| (5.7346787621540178101e-15 - 4.1454060205094870412e-452j)  +/-  (1e-37, 3.74e-97j)
| (0.00031165920298949983544 + 1.2988254654305468926e-444j)  +/-  (8.03e-30, 2.99e-89j)
| (1.990605388259805749e-10 - 2.5415756534770687908e-449j)  +/-  (8.35e-36, 3.11e-95j)
| (0.036370169937916793081 + 1.6819137110154701569e-442j)  +/-  (2.83e-23, 1.05e-82j)
| (4.5735526921276173753e-22 - 3.7027006267586108024e-456j)  +/-  (7.62e-42, 2.84e-101j)
| (1.1078361998241356542e-08 + 6.818696705009291041e-447j)  +/-  (4.95e-35, 1.85e-94j)
| (1.1078361998241356542e-08 + 3.6698078588105520918e-448j)  +/-  (2.43e-35, 9.08e-95j)
| (5.5051000870902684479e-06 + 2.2005586598764205287e-445j)  +/-  (3.32e-33, 1.24e-92j)
| (0.017542010785325942435 - 8.5933211148541834211e-443j)  +/-  (7.6e-28, 2.84e-87j)
| (0.0014937001783885241605 - 1.3410884018132895604e-443j)  +/-  (1.14e-30, 4.25e-90j)
| (0.0060452072997491820322 + 1.4860409998928319519e-443j)  +/-  (3.02e-31, 1.13e-90j)
| (0.073401297802322352439 - 1.6397303549047490409e-442j)  +/-  (1.47e-27, 5.48e-87j)
| (5.5051000870902684479e-06 + 3.7218855119344539921e-446j)  +/-  (3.63e-35, 1.36e-94j)
| (0.00031165920298949983544 + 4.4933375724122413465e-444j)  +/-  (4.92e-32, 1.84e-91j)
| (3.2902944052028258171e-07 - 3.7389924259139752765e-446j)  +/-  (4.77e-35, 1.78e-94j)
| (0.15485588496170529248 + 4.5062572563968959642e-442j)  +/-  (3.98e-29, 1.49e-88j)
| (0.036370169937916793081 + 9.7298192776941132072e-443j)  +/-  (2.38e-30, 8.88e-90j)
| (0.017542010785325942435 - 4.3007161302066408202e-443j)  +/-  (2.92e-31, 1.09e-90j)
| (0.0060452072997491820322 + 3.5140386197062566223e-443j)  +/-  (1.44e-31, 5.35e-91j)
| (0.12807203158896278002 + 3.1972231580029754613e-442j)  +/-  (7.9e-31, 2.95e-90j)
| (3.2902944052028258171e-07 - 4.1223686709241708796e-447j)  +/-  (6.78e-37, 2.53e-96j)
| (5.1199078722220798243e-18 - 4.6334109510993793352e-453j)  +/-  (1.5e-42, 5.6e-102j)
| (0.12807203158896278002 + 2.4486943923338300661e-442j)  +/-  (2.87e-31, 1.07e-90j)
| (0.15927752721138376309 - 4.1276667133937491418e-442j)  +/-  (3.34e-31, 1.25e-90j)
| (0.15927752721138376309 - 3.6416584479361438517e-442j)  +/-  (1.39e-31, 5.17e-91j)
| (0.073401297802322352439 - 2.4734408673864866496e-442j)  +/-  (6.12e-32, 2.29e-91j)
| (5.260810344469944737e-05 - 2.615795445050248614e-445j)  +/-  (3.13e-36, 1.17e-95j)
| (0.0014937001783885241605 - 4.7179763847421005983e-444j)  +/-  (6.07e-35, 2.24e-94j)
