Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 3 6 22
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : 3/2*t^5 - 25/14*t^3 + 3/7*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P3 : 3/2*t^11 - 2114365/488852*t^9 + 2243043/488852*t^7 - 1964259/907868*t^5 + 386565/907868*t^3 - 11007/453934*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^33 - 1091440979681711949266504212092221591850539799353275489123549379392162943277/84117781012297110491838099713215007234797347483436444745854392432879500164*t^31 + 11635957220154610263081919816100279133793721423295809518043933482652154526798205/227370362076239089659438383524820164555657230247728710148044422746073288943292*t^29 - 449922355341614896684719778942452357282850624872887150397312626812954915548665660881/3693290476385389652883087382785416342959818219528981303289759580875841468950363602*t^27 + 603965855509790655258138294774258723794435774381984069502694236579271638221876455077/3093525356288616974209765500110861552222753722340514254037576401075491144932783188*t^25 - 16174277655464599575661475399837501946714706861353630665970112745823212266839598890705/72697845872782498893929489252605246477234712475002084969883045425274041905920404918*t^23 + 23144748437051958362531005270963563421897167318855506622880250460461372956797930085/124696133572525727090788146230883784695085270111495857581274520455015509272590746*t^21 - 9334774843432909818987334654827805226984040575623408086900146626508322406688543900625/81194996689081752011401767217195470091456951595456874122207037747708670180638374324*t^19 + 2946540726207180877281105866177856249514897806320433937159936627388471178644023815/55536933439864399460603123951570088981844700133691432368130668774082537743254702*t^17 - 1126295616583104281114155685210178877570330597725385900406586963524196132438032014985/62090291585768398596954292577855359481702374749467021387570087689424277196958756836*t^15 + 10400486083774457409614479812024719181533320705388413010284932300750371661623194656315/2297340788673430748087308825380648300822987865730279791340093244508698256287474002932*t^13 - 10191239010380356756345607815002304061065393054282373955092122353347746009426355486195/12679553968255281244251108324697039660311490720472890386819360791807623068355866131567*t^11 + 163106240987400354353652521925943499768349624273414063350225225700857821082224583312075/1673701123809697124241146298860009235161116775102421531060155624518606245022974329366844*t^9 - 81201864550519466101928863837839983797646832546507563511485597733500710160832392835/10728853357754468745135553197820572020263569071169368788847151439221834903993425188249*t^7 + 6751669592360047029789204762173221180442579638119580036051984889366107488056470095/19925013378686870526680313081666776609060913989314542036430424101411979107416361063891*t^5 - 574449286268733881171857537996532271387353828626921438594795043722293598497430255/79700053514747482106721252326667106436243655957258168145721696405647916429665444255564*t^3 + 24000084121202117430494764251962242492787199148139994536477814775298404880860047/518050347845858633693688140123336191835583763722178092947191026636711456792825387661166*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:
| (0.98785368285261173498 - 8.6723622598502992599e-416j)  +/-  (8.73e-116, 8.73e-116j)
| (-0.10321575447435615671 - 7.399548596545630677e-437j)  +/-  (1.08e-126, 1.08e-126j)
| (-0.88972209068447914916 - 1.9385129634462422187e-425j)  +/-  (1.97e-116, 1.97e-116j)
| (-0.95247411416333978885 - 3.1090259520440811301e-427j)  +/-  (1.09e-115, 1.09e-115j)
| (0.95247411416333978885 - 9.9125854532584201957e-428j)  +/-  (1.14e-115, 1.14e-115j)
| (0.92582009977255146157 - 2.9450460179489420009e-437j)  +/-  (6.19e-116, 6.19e-116j)
| (-0.98785368285261173498 + 1.0977948434846237925e-440j)  +/-  (9.36e-116, 9.36e-116j)
| (-0.92582009977255146157 - 6.9496439262200945335e-446j)  +/-  (5.76e-116, 5.76e-116j)
| (-0.99761564752831530681 + 4.9020653312903308166e-443j)  +/-  (2.92e-116, 2.92e-116j)
| (0.99761564752831530681 - 5.2068779197888903976e-442j)  +/-  (2.97e-116, 2.97e-116j)
| (0.88972209068447914916 - 1.6923992025841040001e-447j)  +/-  (1.86e-116, 1.86e-116j)
| (0.97220928203468039914 - 2.523339439400241619e-459j)  +/-  (1.36e-115, 1.36e-115j)
| (-0.49192212771516655197 - 1.8493485381830538855e-471j)  +/-  (1.69e-121, 1.69e-121j)
| (-0.79008322340119373077 + 8.822489943555550135e-467j)  +/-  (1.03e-117, 1.03e-117j)
| (0.40070877258142725562 - 1.8174273348313155547e-473j)  +/-  (9.72e-123, 9.72e-123j)
| (0.84436108167932387319 - 4.3961734686169959592e-468j)  +/-  (4.83e-117, 4.83e-117j)
| (0.65603855443711485605 + 3.5417958465556683728e-470j)  +/-  (2.08e-119, 2.08e-119j)
| (-0.97220928203468039914 - 3.6865871423875668248e-468j)  +/-  (1.31e-115, 1.31e-115j)
| (-0.84436108167932387319 - 1.4923261120515375913e-477j)  +/-  (5.33e-117, 5.33e-117j)
| (-0.40070877258142725562 - 6.5566349089745542115e-484j)  +/-  (8.87e-123, 8.87e-123j)
| (0.57735026918962576451 - 2.2216331961240598153e-479j)  +/-  (1.99e-120, 1.99e-120j)
| (0.79008322340119373077 - 4.3502696731151093894e-479j)  +/-  (1.11e-117, 1.11e-117j)
| (0.10321575447435615671 - 1.3317213594056053261e-488j)  +/-  (1.08e-126, 1.08e-126j)
| (-0.72716455684343167249 - 1.2357499913792305653e-481j)  +/-  (1.52e-118, 1.52e-118j)
| (-0.57735026918962576451 - 1.5569372280445722233e-484j)  +/-  (2.06e-120, 2.06e-120j)
| (5.3977380171418804554e-494 - 3.4127328887745187658e-494j)  +/-  (2.11e-492, 2.11e-492j)
| (0.72716455684343167249 + 1.787522519617309131e-484j)  +/-  (1.62e-118, 1.62e-118j)
| (0.30476216915276288265 - 4.6265320584214710621e-490j)  +/-  (5.25e-124, 5.25e-124j)
| (-0.30476216915276288265 + 1.1739225521775541243e-489j)  +/-  (5.15e-124, 5.15e-124j)
| (-0.65603855443711485605 - 4.035818015445934169e-487j)  +/-  (1.92e-119, 1.92e-119j)
| (-0.20520608093988050927 + 4.8304071587157211345e-493j)  +/-  (2.25e-125, 2.25e-125j)
| (0.20520608093988050927 - 4.5286176556631297135e-493j)  +/-  (1.9e-125, 1.9e-125j)
| (0.49192212771516655197 - 7.5713592740740134975e-491j)  +/-  (1.59e-121, 1.59e-121j)
-------------------------------------------------
The weights are:
| (0.013147763365967416954 + 6.3768270765426145727e-416j)  +/-  (1.46e-22, 2.35e-77j)
| (0.10280645014591217442 + 4.1266610874550378819e-418j)  +/-  (8.36e-23, 1.35e-77j)
| (0.040807335406438890483 + 1.298942801230443964e-417j)  +/-  (2.53e-23, 4.08e-78j)
| (0.02243088409207871799 + 1.6399887323574881298e-417j)  +/-  (2.01e-23, 3.25e-78j)
| (0.02243088409207871799 + 8.9942184433162642925e-416j)  +/-  (8.5e-24, 1.37e-78j)
| (0.03130498241460519073 - 4.8824725779494529755e-416j)  +/-  (5.92e-24, 9.56e-79j)
| (0.013147763365967416954 + 5.7712072928570060564e-418j)  +/-  (6.86e-25, 1.11e-79j)
| (0.03130498241460519073 - 1.5827006473815044565e-417j)  +/-  (1.04e-24, 1.69e-79j)
| (0.0060750594197512826818 - 1.4842699491248740827e-418j)  +/-  (3.48e-25, 5.61e-80j)
| (0.0060750594197512826818 + 3.0188312926982263626e-416j)  +/-  (3.53e-26, 5.7e-81j)
| (0.040807335406438890483 + 2.4852990439014949791e-416j)  +/-  (5.74e-27, 9.28e-82j)
| (0.017684938741950986718 - 1.5140953217861573467e-415j)  +/-  (9.05e-26, 1.46e-80j)
| (0.08848894054999431176 + 4.3860736842664413117e-418j)  +/-  (2.29e-29, 3.7e-84j)
| (0.058652939843178116356 + 8.3168120325557834823e-418j)  +/-  (9.85e-29, 1.59e-83j)
| (0.093762027734295761821 - 9.6352674479479473272e-418j)  +/-  (3.43e-30, 5.54e-85j)
| (0.049860988742013293671 - 1.3233873711279654556e-416j)  +/-  (2.86e-28, 4.62e-83j)
| (0.075031051078520205134 + 2.8128479308588271468e-417j)  +/-  (7.49e-30, 1.21e-84j)
| (0.017684938741950986718 - 1.2084874161047253836e-417j)  +/-  (9.14e-28, 1.48e-82j)
| (0.049860988742013293671 - 1.03643032153874084e-417j)  +/-  (7.4e-29, 1.2e-83j)
| (0.093762027734295761821 - 4.0742123010912072258e-418j)  +/-  (4.34e-31, 7.01e-86j)
| (0.082207662355583170862 - 1.8692902106707733193e-417j)  +/-  (3.72e-31, 6e-86j)
| (0.058652939843178116356 + 7.4767319555421573521e-417j)  +/-  (3.26e-30, 5.26e-85j)
| (0.10280645014591217442 + 5.0896232763973465643e-418j)  +/-  (1.83e-32, 2.96e-87j)
| (0.067112697396088174295 - 6.7858545948766521078e-418j)  +/-  (3.88e-31, 6.26e-86j)
| (0.082207662355583170862 - 4.9025560561730289816e-418j)  +/-  (8.63e-32, 1.39e-86j)
| (0.10342054450520905714 - 4.4892747324410905709e-418j)  +/-  (6.81e-33, 1.1e-87j)
| (0.067112697396088174295 - 4.4642692312131173719e-417j)  +/-  (1.04e-31, 1.68e-86j)
| (0.097943553121584302905 + 7.4434767884367102813e-418j)  +/-  (2.18e-33, 3.52e-88j)
| (0.097943553121584302905 + 3.933555213636902337e-418j)  +/-  (1.45e-33, 2.35e-88j)
| (0.075031051078520205134 + 5.6776561999851189682e-418j)  +/-  (6.13e-33, 9.9e-88j)
| (0.10097245333943347465 - 3.9496824539065181291e-418j)  +/-  (8.43e-34, 1.36e-88j)
| (0.10097245333943347465 - 6.0208543482121034879e-418j)  +/-  (2.22e-34, 3.61e-89j)
| (0.08848894054999431176 + 1.3087301425421691976e-417j)  +/-  (2.45e-34, 3.92e-89j)
