Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 5 8 18
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : 16*t^9 - 168*t^7 + 432*t^5 - 270*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P3 : 16*t^17 - 7832664/11003*t^15 + 652667928/55015*t^13 - 5229229734/55015*t^11 + 107801282178/275075*t^9 - 454972876533/550150*t^7 + 461002317867/550150*t^5 - 157900293621/440120*t^3 + 44369803107/880240*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^35 - 36890036899075169605030571972955213602296542390122951635364996693759358799981325652117008/11615349195169249864339020252241967790286614071155670645859947248410514583036436453807*t^33 + 5349773236554237678242719479008062357970804649472711680587651761241512524748297321028463084/19358915325282083107231700420403279650477690118592784409766578747350857638394060756345*t^31 - 2969987286618827114640689214129513459352493950185647222025420776323964826290552602261821957786/212948068578102914179548704624436076155254591304520628507432366220859434022334668319795*t^29 + 484859858783784729722036735381749238605173306663164609299911354741665683957780635248902666863639/1064740342890514570897743523122180380776272956522603142537161831104297170111673341598975*t^27 - 1966826001421326146543763277013887878503646153808590188203791605158701169615328568084876820696137/193589153252820831072317004204032796504776901185927844097665787473508576383940607563450*t^25 + 679344208665675067461488098512686296467354970819941658290246094071562642581712352951301726827749761/4258961371562058283590974092488721523105091826090412570148647324417188680446693366395900*t^23 - 609327259271967798440820667946764178863360449399765893656842635822017686491767890019584125831490837/340716909724964662687277927399097721848407346087233005611891785953375094435735469311672*t^21 + 1225075220972547914067455178664035586754131245884640616347468148666848018134420622442149105452070690333/85179227431241165671819481849774430462101836521808251402972946488343773608933867327918000*t^19 - 14078483908471315022170044053866508483779753460892215762733881044109361036702530666900527739033595320343/170358454862482331343638963699548860924203673043616502805945892976687547217867734655836000*t^17 + 114241815754912778470127735766425102961378283441391449282919974790408608222074768410325516669881231707299/340716909724964662687277927399097721848407346087233005611891785953375094435735469311672000*t^15 - 9873815573056117224285258718987195268345579079388596716123625552950884865547147993142236104688813007551/10483597222306605005762397766126083749181764494991784788058208798565387521099552901897600*t^13 + 3394518967459127572896589739891854511517497160978959130214009128123840984095814772445400422954449616307/1906108585873928182865890502932015227123957180907597234192401599739161367472645982163200*t^11 - 8327003471487652011939800015761518235262405973667930602776925124257973165138608137863931965275421809927/3812217171747856365731781005864030454247914361815194468384803199478322734945291964326400*t^9 + 12622462720716675192626879293623510252506256956924117314511829305133167144754828914915929817494251164037/7624434343495712731463562011728060908495828723630388936769606398956645469890583928652800*t^7 - 11037162954748057744100226216261469925345729811602134229162966491436372904192636394656248545968119455761/15248868686991425462927124023456121816991657447260777873539212797913290939781167857305600*t^5 + 249610307466812188902665616211245219538161165270983346479861967963286531628014947859721269464927787191/1524886868699142546292712402345612181699165744726077787353921279791329093978116785730560*t^3 - 178673726219503798365779220983697533486024342516968460230689457975035601491132623980437401698229039253/12199094949593140370341699218764897453593325957808622298831370238330632751824934285844480*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:
| (5.1633563093721985152 - 1.134799300243306073e-424j)  +/-  (2.14e-120, 2.14e-120j)
| (-5.1633563093721985152 + 8.8589244286603426268e-423j)  +/-  (2.13e-120, 2.13e-120j)
| (-4.1544036857737054549 - 8.1173731305238812596e-424j)  +/-  (8.44e-120, 8.44e-120j)
| (5.7656361323801143559 + 3.6483554040269758305e-428j)  +/-  (5.62e-121, 5.62e-121j)
| (4.6314718414279548435 + 1.0231191376340115506e-427j)  +/-  (4.73e-120, 4.73e-120j)
| (-4.6314718414279548435 - 2.3900689119725977771e-425j)  +/-  (5e-120, 5e-120j)
| (-5.7656361323801143559 - 1.0109115288581870445e-430j)  +/-  (6e-121, 6e-121j)
| (-6.493862879079753279 + 2.3853799609026653119e-432j)  +/-  (6.74e-122, 6.74e-122j)
| (-1.1670342301499899901 - 7.4759934726209420325e-430j)  +/-  (2.71e-121, 2.71e-121j)
| (4.1544036857737054549 + 3.0207920680686702063e-431j)  +/-  (8.18e-120, 8.18e-120j)
| (2.084674834989165342 + 5.7146671615659368802e-432j)  +/-  (2.8e-121, 2.8e-121j)
| (-2.9015447083136790504 - 1.0484940092864190654e-428j)  +/-  (9.35e-120, 9.35e-120j)
| (3.7255702905007693368 - 4.4007754519203803938e-443j)  +/-  (9.46e-120, 9.46e-120j)
| (3.3216152725800202064 + 1.2905344518353753014e-442j)  +/-  (9.19e-120, 9.19e-120j)
| (6.493862879079753279 - 1.2737264028185716822e-443j)  +/-  (8.02e-122, 8.02e-122j)
| (1.1670342301499899901 + 1.7998902421705689211e-442j)  +/-  (2.72e-121, 2.72e-121j)
| (1.6506801238857845559 - 2.8021557468051045989e-444j)  +/-  (3.23e-122, 3.23e-122j)
| (-3.7255702905007693368 - 1.9029109772135182774e-440j)  +/-  (9.69e-120, 9.69e-120j)
| (-0.73395630342256598469 + 8.8046807222868302645e-453j)  +/-  (6.56e-124, 6.56e-124j)
| (-2.5436805829732772969 + 1.0814554091519853141e-451j)  +/-  (8.28e-120, 8.28e-120j)
| (-2.084674834989165342 - 5.1588698724348903328e-466j)  +/-  (2.95e-121, 2.95e-121j)
| (2.5436805829732772969 + 7.070652397638856366e-467j)  +/-  (8.17e-120, 8.17e-120j)
| (-0.52464762327529031788 - 4.09011183847121578e-473j)  +/-  (1.72e-124, 1.72e-124j)
| (-2.6384291054842239697 + 8.817210408309288097e-468j)  +/-  (1.37e-119, 1.37e-119j)
| (-1.16343090596824255 + 3.8298525697029182405e-477j)  +/-  (2.66e-121, 2.66e-121j)
| (2.6384291054842239697 - 1.2492006598115092232e-475j)  +/-  (1.4e-119, 1.4e-119j)
| (0.73395630342256598469 - 1.1995515575492140526e-481j)  +/-  (6.02e-124, 6.02e-124j)
| (2.9015447083136790504 + 1.9364685967202021795e-479j)  +/-  (8.64e-120, 8.64e-120j)
| (-3.3216152725800202064 + 1.2682122692524462007e-484j)  +/-  (9.73e-120, 9.73e-120j)
| (-0.59327175793881913076 - 3.389129915497661224e-493j)  +/-  (4.27e-124, 4.27e-124j)
| (-1.6506801238857845559 - 1.0531779218783842337e-488j)  +/-  (3.31e-122, 3.31e-122j)
| (0.59327175793881913076 - 2.5638491580989311185e-490j)  +/-  (4.44e-124, 4.44e-124j)
| (0.52464762327529031788 + 1.7754101207445655442e-490j)  +/-  (1.82e-124, 1.82e-124j)
| (1.16343090596824255 - 1.1600367185546620501e-487j)  +/-  (2.67e-121, 2.67e-121j)
| (-1.2849439301937317709e-560 + 5.7930331200211467778e-560j)  +/-  (2.08e-558, 2.08e-558j)
-------------------------------------------------
The weights are:
| (8.3807677755845717645e-13 + 6.4732963751126810486e-436j)  +/-  (8.07e-35, 9.08e-94j)
| (8.3807677755845717645e-13 + 5.950911819672602478e-434j)  +/-  (3.04e-35, 3.42e-94j)
| (8.1362585973048926084e-09 - 3.7092809326050030112e-431j)  +/-  (2.39e-32, 2.69e-91j)
| (1.3396090498618103476e-15 + 2.4443913325104838158e-438j)  +/-  (3.29e-37, 3.7e-96j)
| (1.3723429642011743726e-10 - 5.7550197489123269871e-435j)  +/-  (3.71e-34, 4.18e-93j)
| (1.3723429642011743726e-10 - 1.137190178304290844e-432j)  +/-  (3.46e-34, 3.89e-93j)
| (1.3396090498618103476e-15 + 1.0937155166855141005e-436j)  +/-  (6.83e-38, 7.69e-97j)
| (2.2986340510778042778e-19 - 1.5322603878796668147e-439j)  +/-  (3.66e-40, 4.12e-99j)
| (1.1117227027246997949 - 5.0835667342294036742e-425j)  +/-  (5.78e-22, 6.5e-81j)
| (8.1362585973048926084e-09 + 5.1941478012166521146e-434j)  +/-  (3.85e-35, 4.34e-94j)
| (0.0031790989662896125781 - 2.3304413030259547478e-429j)  +/-  (3.1e-29, 3.49e-88j)
| (5.6384989519529962878e-05 + 7.5449531201075183528e-429j)  +/-  (1.94e-32, 2.18e-91j)
| (2.1697091446952387413e-07 - 2.9094891319174274127e-433j)  +/-  (1.42e-34, 1.59e-93j)
| (3.6907267275888806183e-06 - 5.096730957588522346e-433j)  +/-  (6.6e-34, 7.43e-93j)
| (2.2986340510778042778e-19 - 5.1289314318799543482e-441j)  +/-  (1.4e-42, 1.58e-101j)
| (1.1117227027246997949 - 1.2188992047274090686e-425j)  +/-  (1.01e-26, 1.13e-85j)
| (0.016113485128614560154 + 1.4061225243360824398e-428j)  +/-  (3.99e-29, 4.49e-88j)
| (2.1697091446952387413e-07 + 1.6427832693963225809e-430j)  +/-  (3.04e-36, 3.42e-95j)
| (0.32731159374619452747 - 5.2867776752404548773e-426j)  +/-  (1.96e-29, 2.21e-88j)
| (0.00055112647096373122178 + 5.796886266789663017e-428j)  +/-  (8.31e-34, 9.35e-93j)
| (0.0031790989662896125781 - 3.7147969132690598214e-428j)  +/-  (3.44e-33, 3.87e-92j)
| (0.00055112647096373122178 + 1.4924326945270864673e-429j)  +/-  (3.35e-34, 3.77e-93j)
| (0.73025971412822718576 - 8.5143706449188729163e-426j)  +/-  (1.91e-30, 2.15e-89j)
| (-0.00014350530468733640191 - 5.216638172725273406e-428j)  +/-  (3.7e-34, 4.17e-93j)
| (-1.0611519142453967444 + 5.1521484082884488956e-425j)  +/-  (1.21e-29, 1.36e-88j)
| (-0.00014350530468733640191 - 1.076378710558587696e-429j)  +/-  (1.25e-34, 1.4e-93j)
| (0.32731159374619452747 - 2.198177993100952459e-426j)  +/-  (7.2e-33, 8.09e-92j)
| (5.6384989519529962878e-05 + 7.4315143383078269307e-431j)  +/-  (1.18e-35, 1.33e-94j)
| (3.6907267275888806183e-06 - 7.7430745770873756685e-430j)  +/-  (3.37e-37, 3.79e-96j)
| (-0.75551949755494542613 + 1.2711259653285189016e-425j)  +/-  (1.19e-31, 1.33e-90j)
| (0.016113485128614560154 + 1.1336867771275111398e-427j)  +/-  (3.41e-34, 3.84e-93j)
| (-0.75551949755494542613 + 6.2727177585319354375e-426j)  +/-  (2.3e-33, 2.59e-92j)
| (0.73025971412822718576 - 4.5643677023036102738e-426j)  +/-  (1.62e-33, 1.81e-92j)
| (-1.0611519142453967444 + 1.2412290785472550164e-425j)  +/-  (4.04e-33, 5e-92j)
| (0.25523378995709239228 + 5.694607825470747279e-427j)  +/-  (1.55e-34, 1.58e-93j)
