Starting with polynomial:
P : t
Extension levels are: 1 4 6 34
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : t^5 - 10/9*t^3 + 5/21*t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P3 : t^11 - 319/117*t^9 + 15994/5915*t^7 - 219098/186745*t^5 + 23263/112047*t^3 - 383/37349*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^45 - 3470258453034101516809456402859308647747737540832956510306948538793227691807198175708839465213440219496978594060855/304137867791703337053767366515348337904922206202199837779635008471863247359861257974650458997355324807146360379103*t^43 + 146373367068536620848182235610730436508202393241784848026040152656870739679039694878882940755065961636519118293591419752/2407859499306915319454676240702012791193269106502816115701370362071741329348021579385307683882062106498177735121358451*t^41 - 519660622385001954347666524060863103545195889339415405997646151286929840115786379052750004232882684896103581251246906681738/2587286546824234078259557459879842089185291676818422516598979374224742467717713808111226646118928872434128151866091403159*t^39 + 539548369165586631853739459798819905522752225058799634225659046183725967999247306758485064133214533550367608796270722949402839/1170360175133953748648607509095219167266081726458247963170948575904653804307350455506723677314908637380993439636862286428975*t^37 - 4085115835816238756237352908909408995241040548621519782881757566487499664945455515520427233579602698032252216960763019006917642563/5235021063374175117705221388182915335181183562447743139263652980021516466666778587481575008629586335005183655495685007196805175*t^35 + 612699604800044109584651348300822092664375883518915128733874409361982195201023782194849158458533584225714888925900297947329096802/607086476256837114490185337453144803575633051779654246402003454826024598655475163926434748899901608597239785259163471422822785*t^33 - 13824578869429049432596316827083526893780003937975155529379179629226979999279626606642569210854462718301586530093258682389756709576/13558264636402695556947472536453567279855804823078944836311410491114549369972278661023709392097802592005021870787984195109708865*t^31 + 4958548172092375351751475846748840124121499773068731560974605947462588833515491323875610735440381654746719624485836428441282889538/6077842768042587663459211826686081884073291817242285616277528840844453165849642158389938693009359782622940838629096363325041905*t^29 - 6196156758113088411900478648298787734304157649127216646627332918709029893176664264968011640743445461762503244278695391577735185206/11891431502692019341550631834820594990578179642430558814456034688608712715792778135980314834148747400784014684274318971722908075*t^27 + 12668585300879625411883214833278042549722305643025985742928754597878925168022036520223553260920989045768538584948309942071046182552/47531847288538185573206656593314230119034718057920438793965289652757902963695919443818751317124480351281973225176266431131737975*t^25 - 12241270557297234290190825722007435059198271403501420316283343205411973778119795538873176743676015079314153614872045245165590581556/112175159600950117952767709560221583080921934616692235553758083580508650994322369887412253108413773629025456811415988777470901621*t^23 + 3647587610178573544916849689166928180613322408577433831068528809884840210385787331034701722605140907017516787794968681040187388742/102420797896519672913396604381071880204320027258718997679518250225681811777424772505898144142464749835197156219118946275082127567*t^21 - 44823261051220045783324552961633454841322009642748552439817323309874511203395899810360546928491141900900287876928361436213658182/4877180852215222519685552589574851438300953678986618937119916677413419608448798690757054482974511896914150296148521251194387027*t^19 + 45175124711537203904461449815381469975794410493667357706569766345017210487819898882997294421466460813481646360792541524922070484/24385904261076112598427762947874257191504768394933094685599583387067098042243993453785272414872559484570751480742606255971935135*t^17 - 295346915094433993672272460138255024416491218733022364303262404106835518561850811636705525529239423388164536844213291553179928/1030390320890539968947651955543982698232595847673229352912658452974666114461013807906419961191798288080454287918701672787546555*t^15 + 2107038580649566002716244470515305628194756182630381932842643130434899743523309841393109241107172360141314639463403103859456923/63403351078797892755912183664473068697912397826826046182558916806374454909834382979841708278668654659883953849930776265527031351*t^13 - 237434695288732146589992802653071547608679149030262642555899528222612183190447518491381014365144374895455713965607829956943589843/85043402520076835075756980504416684529653729300489674406559987104057797712521702770730759019626563946492038713941765057076526589799*t^11 + 17723148359779250057644881917102611019355774718084248510263392197919752873449964580836230181325950415436481874513402055674900048/109341517525813073668830403505678594395269080529201009951291411990931454201813617848082404453805582216918335489353697930526962758313*t^9 - 18046597765186198607491985605310384372401653407196146028244765386226524324483710346019468805057393789282896440240814085673263614/2976519088202689227651494317654583958537880525517138604229599548642022919938259596975576565686929738127221354987961776997678430642965*t^7 + 945195226468862653225549956508047140123182520431830278661502706556396456531899650644291720098441597345849658284716734677304311/7228689214206530981439343342875418185020566990541622324557598903844912805564344735512114516668257935451823290685050029851504760132915*t^5 - 75127444783759921124496344856586008856289681442543532617106893871046137518732202648250717816590130346603384674733932061249673/56383775870810941655226878074428261843160422526224654131549271449990319883401888936994493230012411896524221667343390232841737129036737*t^3 + 76248377325426837750579687259362716036397979681734050423450003460374542870999987043060268747952751669438411725154061393878/18794591956936980551742292691476087281053474175408218043849757149996773294467296312331497743337470632174740555781130077613912376345579*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (0.27963041316178319341 + 5.6668627985667701545e-868j)  +/-  (1.71e-250, 1.71e-250j)
| (0.9934090168285012076 - 1.1338051644225253946e-856j)  +/-  (2.64e-239, 2.64e-239j)
| (-0.9061798459386639928 - 2.0661207398646729494e-884j)  +/-  (4.86e-240, 4.86e-240j)
| (0.99873523456944300581 - 3.2042996720045374395e-880j)  +/-  (9.21e-240, 9.21e-240j)
| (0.95392965771413734692 - 1.2270688321457908155e-897j)  +/-  (2.46e-239, 2.46e-239j)
| (0.9324486125917015422 + 1.4789602231937803012e-912j)  +/-  (1.31e-239, 1.31e-239j)
| (-0.9934090168285012076 + 4.4903596819982194645e-916j)  +/-  (2.95e-239, 2.95e-239j)
| (-0.87506136954646878575 - 1.2660167788614164097e-920j)  +/-  (1.87e-240, 1.87e-240j)
| (-0.9840853600948424645 - 2.1640013105909277528e-917j)  +/-  (3.63e-239, 3.63e-239j)
| (-0.99873523456944300581 - 2.6794912782161933674e-919j)  +/-  (8.22e-240, 8.22e-240j)
| (0.87506136954646878575 - 2.4444538059329169752e-919j)  +/-  (1.73e-240, 1.73e-240j)
| (-0.21082683075469763596 - 1.4517683482137568019e-937j)  +/-  (9.55e-252, 9.55e-252j)
| (-0.9324486125917015422 + 7.9383618712356021094e-924j)  +/-  (1.34e-239, 1.34e-239j)
| (-0.83921207487737441643 + 3.4586250876421670853e-928j)  +/-  (5.49e-241, 5.49e-241j)
| (0.9840853600948424645 + 9.1577125921597563097e-925j)  +/-  (3.9e-239, 3.9e-239j)
| (0.9061798459386639928 - 5.9982746004257807052e-941j)  +/-  (5.12e-240, 5.12e-240j)
| (0.79883268131626945437 - 4.389814182472018105e-948j)  +/-  (1.24e-241, 1.24e-241j)
| (-0.97097943968239305255 + 2.4373067738823687497e-944j)  +/-  (3.44e-239, 3.44e-239j)
| (-0.70548804714027908278 + 3.4401603017891711087e-952j)  +/-  (4.47e-243, 4.47e-243j)
| (-0.95392965771413734692 + 1.6337140828009031221e-947j)  +/-  (2.51e-239, 2.51e-239j)
| (0.83921207487737441643 + 6.7160696622106783197e-949j)  +/-  (5.01e-241, 5.01e-241j)
| (0.70548804714027908278 + 9.7054128863463216248e-955j)  +/-  (4.31e-243, 4.31e-243j)
| (0.21082683075469763596 - 8.1786616978317754149e-966j)  +/-  (9.44e-252, 9.44e-252j)
| (-0.79883268131626945437 + 1.362185835890794239e-955j)  +/-  (1.2e-241, 1.2e-241j)
| (-0.75416672657084922044 - 3.1019027158205163497e-957j)  +/-  (2.43e-242, 2.43e-242j)
| (0.14107220146080813369 + 1.1380507362412459521e-967j)  +/-  (4.61e-253, 4.61e-253j)
| (0.75416672657084922044 + 4.5100332388433675014e-956j)  +/-  (2.68e-242, 2.68e-242j)
| (0.97097943968239305255 + 2.9085786649045501516e-962j)  +/-  (3.34e-239, 3.34e-239j)
| (-0.47692330950443648685 + 5.8081715289737477375e-990j)  +/-  (6.49e-247, 6.49e-247j)
| (-0.65309570580320731722 - 1.5049245282955959961e-987j)  +/-  (6.49e-244, 6.49e-244j)
| (-0.27963041316178319341 - 8.5475838097666475945e-997j)  +/-  (1.74e-250, 1.74e-250j)
| (0.47692330950443648685 + 1.0111440270936393592e-988j)  +/-  (7.42e-247, 7.42e-247j)
| (0.65309570580320731722 - 4.1006380470769837564e-988j)  +/-  (5.93e-244, 5.93e-244j)
| (0.070691365143326506046 - 3.1240796151942736478e-999j)  +/-  (2.01e-254, 2.01e-254j)
| (-0.59731019807931748754 + 9.2796533709801860151e-991j)  +/-  (7.03e-245, 7.03e-245j)
| (-0.41302956639847532004 - 2.7648696791390409043e-995j)  +/-  (4.8e-248, 4.8e-248j)
| (-1.5848432189285352601e-1000 - 1.0302677064693961853e-999j)  +/-  (4.69e-998, 4.69e-998j)
| (0.59731019807931748754 + 3.379385862602648692e-990j)  +/-  (7.14e-245, 7.14e-245j)
| (0.41302956639847532004 - 7.0090434888426222507e-994j)  +/-  (4.87e-248, 4.87e-248j)
| (-0.34714693243573225245 + 1.4778995593253484358e-996j)  +/-  (3.12e-249, 3.12e-249j)
| (-0.53846931010568309104 - 8.3498454803458793278e-994j)  +/-  (7.72e-246, 7.72e-246j)
| (-0.14107220146080813369 - 1.277006070061202614e-1001j)  +/-  (5.31e-253, 5.31e-253j)
| (0.34714693243573225245 + 4.3479723951977349907e-996j)  +/-  (3.28e-249, 3.28e-249j)
| (0.53846931010568309104 + 3.3959287371132533335e-994j)  +/-  (7.5e-246, 7.5e-246j)
| (-0.070691365143326506046 + 2.0490850694445780831e-1004j)  +/-  (2.01e-254, 2.01e-254j)
-------------------------------------------------
The weights are:
| (0.068217006621484546451 - 3.3878621161371802792e-858j)  +/-  (8.17e-74, 1.22e-188j)
| (0.0073741865251355972441 + 6.4934685590445015579e-857j)  +/-  (4.01e-74, 5.99e-189j)
| (0.028702944778344868856 - 1.5109255357910931779e-858j)  +/-  (1.4e-75, 2.1e-190j)
| (0.0032372332517993424487 + 4.4833554114509035746e-857j)  +/-  (2.97e-74, 4.44e-189j)
| (0.01918133222811505049 - 7.0220347301786649708e-857j)  +/-  (7.19e-75, 1.07e-189j)
| (0.023842189218222908621 + 4.7913367239390922422e-857j)  +/-  (2.58e-75, 3.85e-190j)
| (0.0073741865251355972441 + 4.2081814359380499656e-859j)  +/-  (1.9e-76, 2.85e-191j)
| (0.033512568024971637492 + 1.4685077825457320601e-858j)  +/-  (3e-76, 4.48e-191j)
| (0.011229298755450869691 - 8.0713839012226282431e-859j)  +/-  (1.13e-76, 1.69e-191j)
| (0.0032372332517993424487 - 1.1986745997561408695e-859j)  +/-  (8.48e-77, 1.27e-191j)
| (0.033512568024971637492 + 2.3184772716514757475e-857j)  +/-  (3.69e-78, 5.52e-193j)
| (0.069334148942641515964 + 2.0382329498515949878e-858j)  +/-  (1.03e-79, 1.54e-194j)
| (0.023842189218222908621 + 1.5166324814038273228e-858j)  +/-  (2.28e-77, 3.4e-192j)
| (0.038152018316431882339 - 1.4241574353430914516e-858j)  +/-  (1.47e-78, 2.2e-193j)
| (0.011229298755450869691 - 1.7118944566711124662e-856j)  +/-  (2.33e-77, 3.49e-192j)
| (0.028702944778344868856 - 3.2903411678693072486e-857j)  +/-  (6.74e-78, 1.01e-192j)
| (0.042566010217433294068 + 1.2822429740088832234e-857j)  +/-  (7.71e-80, 1.15e-194j)
| (0.015010001853183767955 + 1.1776800398579717334e-858j)  +/-  (6.93e-78, 1.04e-192j)
| (0.050587267937995836128 + 1.3802138386966829023e-858j)  +/-  (1.73e-81, 2.59e-196j)
| (0.01918133222811505049 - 1.4236117962306932085e-858j)  +/-  (3.04e-78, 4.55e-193j)
| (0.038152018316431882339 - 1.6926022791469413756e-857j)  +/-  (4.91e-80, 7.34e-195j)
| (0.050587267937995836128 + 8.1440446684380722643e-858j)  +/-  (3.72e-82, 5.56e-197j)
| (0.069334148942641515964 + 3.1364286434894899196e-858j)  +/-  (1.99e-83, 2.97e-198j)
| (0.042566010217433294068 + 1.3920786431056692211e-858j)  +/-  (7.54e-81, 1.13e-195j)
| (0.046720186759934449317 - 1.377027493675393499e-858j)  +/-  (1.52e-81, 2.27e-196j)
| (0.070121004190021381076 - 2.9146144608746335761e-858j)  +/-  (1.45e-84, 2.17e-199j)
| (0.046720186759934449317 - 1.0058672500021029968e-857j)  +/-  (1.48e-82, 2.22e-197j)
| (0.015010001853183767955 + 1.031415376505396979e-856j)  +/-  (1.01e-80, 1.51e-195j)
| (0.062779744011821579905 + 1.5739055128791462227e-858j)  +/-  (1.42e-85, 2.13e-200j)
| (0.054143930282476030032 - 1.4017101258850922307e-858j)  +/-  (4.9e-84, 7.33e-199j)
| (0.068217006621484546451 - 1.8995354219119838358e-858j)  +/-  (3.08e-86, 4.6e-201j)
| (0.062779744011821579905 + 4.4805966964717614139e-858j)  +/-  (2.04e-86, 3.04e-201j)
| (0.054143930282476030032 - 6.7817574780676294707e-858j)  +/-  (3.28e-85, 4.9e-200j)
| (0.070588124415944907596 + 2.7133944696533671725e-858j)  +/-  (1.49e-86, 2.23e-201j)
| (0.057370707049116947669 + 1.4413161493048997822e-858j)  +/-  (1.17e-85, 1.75e-200j)
| (0.064947843084942799064 - 1.6662234199639214385e-858j)  +/-  (1.06e-86, 1.59e-201j)
| (0.070742939712152473948 - 2.5271266802794193381e-858j)  +/-  (1.74e-87, 2.6e-202j)
| (0.057370707049116947669 + 5.7882760180505865262e-858j)  +/-  (2.13e-87, 3.19e-202j)
| (0.064947843084942799064 - 4.0377737429163986951e-858j)  +/-  (6.36e-88, 9.51e-203j)
| (0.066758183146113024707 + 1.775097758215414486e-858j)  +/-  (9.53e-88, 1.42e-202j)
| (0.060252600532341525912 - 1.4988026504193910197e-858j)  +/-  (1.96e-87, 2.93e-202j)
| (0.070121004190021381076 - 2.1897526088755320597e-858j)  +/-  (9.29e-89, 1.39e-203j)
| (0.066758183146113024707 + 3.6821251274422041489e-858j)  +/-  (6.47e-89, 9.81e-204j)
| (0.060252600532341525912 - 5.0467858981467532692e-858j)  +/-  (5.93e-89, 9.04e-204j)
| (0.070588124415944907596 + 2.3528766792090094834e-858j)  +/-  (5.89e-89, 8.73e-204j)
