Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 6 20
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P3 : 4*t^11 - 6923/82*t^9 + 97479/164*t^7 - 566685/328*t^5 + 1313235/656*t^3 - 418635/656*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^31 - 121921938457464510034469253163056449697836728231/130766176787098249989292586410434877137605574*t^29 + 46721345774014034094114901782926188977659229853481/523064707148392999957170345641739508550422296*t^27 - 7671336076773682666951258788997282210217001072248115/1627312422239444888755641075329856248823536032*t^25 + 929263510475282351885815567247020275074277395423463225/6044303282603652443949523994082323209915990976*t^23 - 277433414685348288781589388900373518765355616033832188925/84620245956451134215293335917152524938823873664*t^21 + 1137620377287397238822112648626688114672403182510008805975/24177213130414609775798095976329292839663963904*t^19 - 2781209059042065986072630989654046194029486376889037714975/6044303282603652443949523994082323209915990976*t^17 + 148339151584349410226503876051374268756948982602247441719125/48354426260829219551596191952658585679327927808*t^15 - 1335337535407712069995177645993009407403524315341953063631625/96708852521658439103192383905317171358655855616*t^13 + 152791988285748761332482382324727177349994343611564893873375/3719571250833016888584322457896814283025225216*t^11 - 4635584095347505642223792677587578908012764570708037999279125/59513140013328270217349159326349028528403603456*t^9 + 10556175685090291234201524157913883859275654096455353941608625/119026280026656540434698318652698057056807206912*t^7 - 13063732950334203429399596854206267330900742447866011205541875/238052560053313080869396637305396114113614413824*t^5 + 7332115608620337099121646950355075119657811815644263925211875/476105120106626161738793274610792228227228827648*t^3 - 613534018006080977160851631739772482956498672166138016604375/476105120106626161738793274610792228227228827648*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:
| (-4.2176994566372290905 - 1.3196659506710169337e-481j)  +/-  (6.88e-121, 6.88e-121j)
| (-5.3876777250469117179 - 1.6133065925012351251e-494j)  +/-  (2.32e-121, 2.32e-121j)
| (8.8661934365836591045 - 1.07233096146097375e-499j)  +/-  (1.1e-123, 1.1e-123j)
| (4.7724475211158788203 - 7.234632247552475251e-497j)  +/-  (4.79e-121, 4.79e-121j)
| (6.1213478264427165128 - 1.9589572801234918207e-498j)  +/-  (5.18e-122, 5.18e-122j)
| (-8.8661934365836591045 + 6.7898498154908273262e-500j)  +/-  (1.1e-123, 1.1e-123j)
| (-3.7016358998392343543 + 3.4750131782909901599e-496j)  +/-  (6.12e-121, 6.12e-121j)
| (-1.3866480207208212553 - 1.0406271991849037967e-504j)  +/-  (3.9e-123, 3.9e-123j)
| (0.37199049496208924934 - 1.3150959187602404827e-508j)  +/-  (3.59e-126, 3.59e-126j)
| (-6.1213478264427165128 - 2.4181619506880599069e-505j)  +/-  (5.14e-122, 5.14e-122j)
| (0.7071067811865475244 + 5.9922492576759232437e-508j)  +/-  (5.18e-125, 5.18e-125j)
| (1.7320508075688772935 - 2.0631817717699056581e-505j)  +/-  (2.94e-122, 2.94e-122j)
| (-1.9639835885683659009 + 1.342223409900171037e-503j)  +/-  (6.91e-122, 6.91e-122j)
| (-1.7320508075688772935 + 2.1187020706893706699e-506j)  +/-  (3.08e-122, 3.08e-122j)
| (-3.2137281525534003284 - 1.2907447548289317699e-510j)  +/-  (3.84e-121, 3.84e-121j)
| (1.9639835885683659009 + 4.7805068945181624307e-516j)  +/-  (7.89e-122, 7.89e-122j)
| (3.2137281525534003284 + 3.4394692232564697467e-515j)  +/-  (3.86e-121, 3.86e-121j)
| (-4.7724475211158788203 + 3.9317831448397584121e-520j)  +/-  (4.64e-121, 4.64e-121j)
| (-1.0267578413135987289 + 4.1451365466500993944e-530j)  +/-  (4.54e-124, 4.54e-124j)
| (2.7495901630062034467 - 3.3541458238626457834e-526j)  +/-  (2.24e-121, 2.24e-121j)
| (5.3876777250469117179 - 7.7009431472733484909e-528j)  +/-  (2.12e-121, 2.12e-121j)
| (1.3866480207208212553 - 2.3224993878943771255e-529j)  +/-  (4.28e-123, 4.28e-123j)
| (3.7016358998392343543 - 1.063926160543928094e-527j)  +/-  (6e-121, 6e-121j)
| (-2.7495901630062034467 - 2.4687164983624900539e-528j)  +/-  (2.43e-121, 2.43e-121j)
| (6.1606184662518051268e-541 + 5.6737952500875301305e-542j)  +/-  (1.92e-539, 1.92e-539j)
| (4.2176994566372290905 + 1.5389162407570363393e-534j)  +/-  (6.38e-121, 6.38e-121j)
| (1.0267578413135987289 + 3.732374579849303596e-537j)  +/-  (4.49e-124, 4.49e-124j)
| (2.3142743884833336815 + 6.6228262713704174739e-538j)  +/-  (1.22e-121, 1.22e-121j)
| (-0.37199049496208924934 + 2.691520396632807813e-541j)  +/-  (3.59e-126, 3.59e-126j)
| (-0.7071067811865475244 - 2.0304055335675069572e-543j)  +/-  (4.61e-125, 4.61e-125j)
| (-2.3142743884833336815 + 1.670845655168457505e-545j)  +/-  (1.48e-121, 1.48e-121j)
-------------------------------------------------
The weights are:
| (5.6559921992320875826e-09 - 3.8973650229759187734e-489j)  +/-  (1.76e-38, 4.09e-98j)
| (9.2007616549074520819e-14 + 9.6872694459879438077e-493j)  +/-  (9.78e-42, 2.28e-101j)
| (7.4050344422321839669e-29 - 1.7033222492635478697e-501j)  +/-  (2.45e-49, 5.7e-109j)
| (4.198810196518653544e-11 + 4.3030802837552255255e-492j)  +/-  (6.22e-42, 1.45e-101j)
| (2.5291679923743924957e-17 + 1.1548651890972475875e-495j)  +/-  (7.6e-45, 1.77e-104j)
| (7.4050344422321839669e-29 + 4.7942593812418281019e-501j)  +/-  (3.26e-50, 7.59e-110j)
| (3.1646970266369076293e-07 + 1.9132751691309516401e-488j)  +/-  (2.5e-39, 5.81e-99j)
| (0.03073258577415638431 + 4.9216977888947220649e-485j)  +/-  (7.18e-31, 1.67e-90j)
| (0.17605209841741741463 - 7.9775155149046603983e-485j)  +/-  (2.99e-30, 6.95e-90j)
| (2.5291679923743924957e-17 - 6.2722748513054119508e-495j)  +/-  (3.33e-45, 7.76e-105j)
| (0.10765358406947887892 + 6.9334663176531403041e-485j)  +/-  (2.27e-30, 5.28e-90j)
| (0.0079216757889067689649 - 1.5036806518215351596e-485j)  +/-  (1.38e-34, 3.22e-94j)
| (0.0030794756938060059339 + 1.9398247557132655414e-485j)  +/-  (1.58e-34, 3.69e-94j)
| (0.0079216757889067689649 - 3.599271505572622914e-485j)  +/-  (1.72e-33, 4.01e-93j)
| (8.7783865454721804058e-06 - 1.0053415266406322243e-487j)  +/-  (8.02e-39, 1.87e-98j)
| (0.0030794756938060059339 + 7.0722063898350248845e-486j)  +/-  (1.66e-36, 3.86e-96j)
| (8.7783865454721804058e-06 - 1.3581966973650451828e-488j)  +/-  (1.33e-41, 3.1e-101j)
| (4.198810196518653544e-11 - 6.9734942192879717325e-491j)  +/-  (5.84e-43, 1.36e-102j)
| (0.066490568513662931539 - 7.5625822232646960314e-485j)  +/-  (7.22e-35, 1.68e-94j)
| (0.00013280532864853856659 + 1.2678779939695753336e-487j)  +/-  (1.95e-40, 4.54e-100j)
| (9.2007616549074520819e-14 - 1.1799531155993547024e-493j)  +/-  (6.88e-47, 1.6e-106j)
| (0.03073258577415638431 + 2.4862090811980552356e-485j)  +/-  (1.92e-37, 4.47e-97j)
| (3.1646970266369076293e-07 + 1.2467859289574252448e-489j)  +/-  (1.41e-43, 3.28e-103j)
| (0.00013280532864853856659 + 6.0170405736691250661e-487j)  +/-  (1.29e-41, 2.96e-101j)
| (0.2136603451633979328 + 8.4884393361507459787e-485j)  +/-  (6.85e-38, 1.6e-97j)
| (5.6559921992320875826e-09 - 8.8484497287279883494e-491j)  +/-  (8.5e-45, 1.98e-104j)
| (0.066490568513662931539 - 4.6013833204345146339e-485j)  +/-  (1.36e-38, 3.18e-98j)
| (0.0010979332779036407517 - 1.1310041844691506605e-486j)  +/-  (9.17e-41, 2.14e-100j)
| (0.17605209841741741463 - 9.5208252008589015904e-485j)  +/-  (4.13e-39, 9.76e-99j)
| (0.10765358406947887892 + 9.7265565469043409167e-485j)  +/-  (1.94e-39, 4.69e-99j)
| (0.0010979332779036407517 - 3.8812611409177448127e-486j)  +/-  (2.42e-41, 5.17e-101j)
