Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 8 18
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : t^9 - 21*t^7 + 108*t^5 - 135*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P3 : t^17 - 979083/11003*t^15 + 163166982/55015*t^13 - 2614614867/55015*t^11 + 107801282178/275075*t^9 - 454972876533/275075*t^7 + 922004635734/275075*t^5 - 157900293621/55015*t^3 + 44369803107/55015*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^35 - 4611254612384396200628821496619401700287067798765368954420624586719919849997665706514626/11615349195169249864339020252241967790286614071155670645859947248410514583036436453807*t^33 + 1337443309138559419560679869752015589492701162368177920146912940310378131187074330257115771/19358915325282083107231700420403279650477690118592784409766578747350857638394060756345*t^31 - 1484993643309413557320344607064756729676246975092823611012710388161982413145276301130910978893/212948068578102914179548704624436076155254591304520628507432366220859434022334668319795*t^29 + 484859858783784729722036735381749238605173306663164609299911354741665683957780635248902666863639/1064740342890514570897743523122180380776272956522603142537161831104297170111673341598975*t^27 - 1966826001421326146543763277013887878503646153808590188203791605158701169615328568084876820696137/96794576626410415536158502102016398252388450592963922048832893736754288191970303781725*t^25 + 679344208665675067461488098512686296467354970819941658290246094071562642581712352951301726827749761/1064740342890514570897743523122180380776272956522603142537161831104297170111673341598975*t^23 - 609327259271967798440820667946764178863360449399765893656842635822017686491767890019584125831490837/42589613715620582835909740924887215231050918260904125701486473244171886804466933663959*t^21 + 1225075220972547914067455178664035586754131245884640616347468148666848018134420622442149105452070690333/5323701714452572854488717615610901903881364782613015712685809155521485850558366707994875*t^19 - 14078483908471315022170044053866508483779753460892215762733881044109361036702530666900527739033595320343/5323701714452572854488717615610901903881364782613015712685809155521485850558366707994875*t^17 + 114241815754912778470127735766425102961378283441391449282919974790408608222074768410325516669881231707299/5323701714452572854488717615610901903881364782613015712685809155521485850558366707994875*t^15 - 9873815573056117224285258718987195268345579079388596716123625552950884865547147993142236104688813007551/81903103299270351607518732547860029290482535117123318656704756238792090008590257046075*t^13 + 3394518967459127572896589739891854511517497160978959130214009128123840984095814772445400422954449616307/7445736663570031964319884777078184480952957737920301696064068748981099091690023367825*t^11 - 8327003471487652011939800015761518235262405973667930602776925124257973165138608137863931965275421809927/7445736663570031964319884777078184480952957737920301696064068748981099091690023367825*t^9 + 12622462720716675192626879293623510252506256956924117314511829305133167144754828914915929817494251164037/7445736663570031964319884777078184480952957737920301696064068748981099091690023367825*t^7 - 11037162954748057744100226216261469925345729811602134229162966491436372904192636394656248545968119455761/7445736663570031964319884777078184480952957737920301696064068748981099091690023367825*t^5 + 998441229867248755610662464844980878152644661083933385919447871853146126512059791438885077859711148764/1489147332714006392863976955415636896190591547584060339212813749796219818338004673565*t^3 - 178673726219503798365779220983697533486024342516968460230689457975035601491132623980437401698229039253/1489147332714006392863976955415636896190591547584060339212813749796219818338004673565*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:
| (-4.6974733674682695184 - 6.404783923297503025e-444j)  +/-  (1.2e-119, 1.2e-119j)
| (-4.1034038783290910277 + 3.3229079437768676611e-452j)  +/-  (1.29e-119, 1.29e-119j)
| (9.1837089557857812546 - 4.7817711808933075265e-459j)  +/-  (1.05e-121, 1.05e-121j)
| (-2.948175424779571609 + 3.657513566098717367e-455j)  +/-  (3.75e-121, 3.75e-121j)
| (-9.1837089557857812546 + 1.2180254485723498768e-458j)  +/-  (1.01e-121, 1.01e-121j)
| (-7.3020885200788535202 - 7.3639648544124247849e-456j)  +/-  (3.09e-120, 3.09e-120j)
| (2.948175424779571609 - 3.921493701160621451e-457j)  +/-  (3.58e-121, 3.58e-121j)
| (8.1538408141203153555 - 3.0145728905699464403e-459j)  +/-  (7.96e-121, 7.96e-121j)
| (-8.1538408141203153555 + 3.0341087397296133648e-457j)  +/-  (7.63e-121, 7.63e-121j)
| (6.5498902918965063982 + 3.4881287197858555851e-457j)  +/-  (6.38e-120, 6.38e-120j)
| (-5.2687520324004595969 - 1.4589697006591465666e-455j)  +/-  (1.2e-119, 1.2e-119j)
| (-1.0379709584894152952 - 5.8120777967937327233e-461j)  +/-  (9.72e-124, 9.72e-124j)
| (-0.83901296625000593646 - 1.9381879446794989847e-460j)  +/-  (6.74e-124, 6.74e-124j)
| (3.7313022243357029508 + 3.0695373418669236352e-455j)  +/-  (1.86e-119, 1.86e-119j)
| (1.6453397661043056661 + 2.1419812395835715093e-455j)  +/-  (4.01e-121, 4.01e-121j)
| (5.2687520324004595969 + 6.3435832225749096261e-468j)  +/-  (1.4e-119, 1.4e-119j)
| (-6.5498902918965063982 + 1.301531789785398396e-468j)  +/-  (7.29e-120, 7.29e-120j)
| (1.6504356360317598312 - 1.4143530164857716874e-466j)  +/-  (3.78e-121, 3.78e-121j)
| (-1.6453397661043056661 + 7.7759460355319975226e-468j)  +/-  (3.51e-121, 3.51e-121j)
| (-3.7313022243357029508 + 5.0997139479714023223e-481j)  +/-  (1.82e-119, 1.82e-119j)
| (5.8752140359939481631 - 1.8868289283796984969e-488j)  +/-  (1.16e-119, 1.16e-119j)
| (4.1034038783290910277 - 2.4203558357895407915e-488j)  +/-  (1.26e-119, 1.26e-119j)
| (7.3020885200788535202 + 1.40563475636067372e-491j)  +/-  (2.91e-120, 2.91e-120j)
| (-1.6504356360317598312 + 4.0405931354819446216e-489j)  +/-  (3.75e-121, 3.75e-121j)
| (-2.3344142183389772393 - 7.049682871708655149e-493j)  +/-  (4.09e-122, 4.09e-122j)
| (4.6974733674682695184 + 1.4743889342947443111e-492j)  +/-  (1.22e-119, 1.22e-119j)
| (0.74196378430272585765 - 1.9688111708177369171e-498j)  +/-  (2.5e-124, 2.5e-124j)
| (2.3344142183389772393 + 5.2851251772265421013e-496j)  +/-  (4.08e-122, 4.08e-122j)
| (-5.8752140359939481631 - 6.1709550691044036026e-495j)  +/-  (1.23e-119, 1.23e-119j)
| (-0.74196378430272585765 - 2.6237650895487978057e-501j)  +/-  (2.31e-124, 2.31e-124j)
| (-3.5973075787859096682 + 2.0281418384144708389e-500j)  +/-  (1.07e-119, 1.07e-119j)
| (1.0379709584894152952 + 6.0655023491742043714e-508j)  +/-  (8.39e-124, 8.39e-124j)
| (0.83901296625000593646 - 3.3093187427158683994e-508j)  +/-  (6.47e-124, 6.47e-124j)
| (3.5973075787859096682 - 1.6271201565931777388e-507j)  +/-  (1.1e-119, 1.1e-119j)
| (-1.2084214317712885518e-579 + 2.620137627429977276e-580j)  +/-  (4.33e-578, 4.33e-578j)
-------------------------------------------------
The weights are:
| (3.6907267275888806183e-06 - 1.0268057240258862737e-448j)  +/-  (5.03e-29, 1.87e-87j)
| (5.6384989519529962878e-05 + 7.4155644054294489523e-448j)  +/-  (3.98e-27, 1.48e-85j)
| (2.2986340510778042778e-19 - 5.5934939122313742708e-460j)  +/-  (1.2e-40, 4.45e-99j)
| (0.0031790989662896125781 - 2.994224006291267825e-447j)  +/-  (2.19e-23, 8.14e-82j)
| (2.2986340510778042778e-19 + 1.7307229466319986271e-459j)  +/-  (3.09e-40, 1.15e-98j)
| (8.3807677755845717645e-13 + 5.0819238478256598307e-455j)  +/-  (7.44e-37, 2.77e-95j)
| (0.0031790989662896125781 - 6.8506807296567441937e-448j)  +/-  (2.23e-27, 8.29e-86j)
| (1.3396090498618103476e-15 + 1.4029397658584218327e-457j)  +/-  (2.34e-40, 8.73e-99j)
| (1.3396090498618103476e-15 - 5.2163492372807927902e-457j)  +/-  (8.87e-39, 3.3e-97j)
| (1.3723429642011743726e-10 + 4.5696041897477028586e-454j)  +/-  (5.5e-38, 2.05e-96j)
| (2.1697091446952387413e-07 - 3.42069037045154197e-450j)  +/-  (2.56e-33, 9.55e-92j)
| (0.32731159374619452747 - 5.6015418915004485363e-445j)  +/-  (1.8e-19, 6.69e-78j)
| (-0.75551949755494542613 + 1.3970373620237061561e-444j)  +/-  (1.8e-19, 6.69e-78j)
| (-0.00014350530468733640191 - 4.9892460739506745167e-448j)  +/-  (8.97e-32, 3.34e-90j)
| (-1.0611519142453967444 + 2.3526300152572801098e-444j)  +/-  (5.49e-24, 2.05e-82j)
| (2.1697091446952387413e-07 + 1.9607899222522544926e-451j)  +/-  (2.87e-36, 1.07e-94j)
| (1.3723429642011743726e-10 - 2.774537381896731998e-453j)  +/-  (2.22e-37, 8.26e-96j)
| (1.1117227027246997949 - 2.3134884365469373934e-444j)  +/-  (4.3e-24, 1.6e-82j)
| (-1.0611519142453967444 + 4.889134797020645423e-444j)  +/-  (1.92e-26, 7.14e-85j)
| (-0.00014350530468733640191 - 4.3525659098897894746e-447j)  +/-  (1e-31, 3.72e-90j)
| (8.1362585973048926084e-09 - 1.1760591694444194145e-452j)  +/-  (1.41e-37, 5.24e-96j)
| (5.6384989519529962878e-05 + 5.0055924961929547081e-449j)  +/-  (2.08e-34, 7.73e-93j)
| (8.3807677755845717645e-13 - 1.1030782620028373725e-455j)  +/-  (1.1e-40, 4.11e-99j)
| (1.1117227027246997949 - 4.8197020865998517764e-444j)  +/-  (1.09e-27, 4.08e-86j)
| (0.016113485128614560154 + 9.7402371426447331332e-447j)  +/-  (2.54e-31, 9.5e-90j)
| (3.6907267275888806183e-06 - 2.5160661346852670987e-450j)  +/-  (6.7e-36, 2.5e-94j)
| (0.73025971412822718576 - 6.9296873999839154751e-445j)  +/-  (5.16e-30, 2.02e-88j)
| (0.016113485128614560154 + 3.2731974438786463174e-447j)  +/-  (1.79e-32, 6.79e-91j)
| (8.1362585973048926084e-09 + 1.0557592412401900369e-451j)  +/-  (2.32e-38, 8.95e-97j)
| (0.73025971412822718576 - 9.5293914246257710097e-445j)  +/-  (5.74e-30, 2.3e-88j)
| (0.00055112647096373122178 + 4.720563514172923084e-447j)  +/-  (8.01e-34, 3.06e-92j)
| (0.32731159374619452747 - 3.5740659092049399185e-445j)  +/-  (8.38e-31, 3.32e-89j)
| (-0.75551949755494542613 + 9.7361629996716754205e-445j)  +/-  (2.18e-30, 8.65e-89j)
| (0.00055112647096373122178 + 6.2610483511540507187e-448j)  +/-  (6.61e-34, 2.37e-92j)
| (0.25523378995709239228 + 7.3728108417474397253e-446j)  +/-  (6.35e-32, 2.89e-90j)
