Starting with polynomial:
P : 8*t^3 - 12*t
Extension levels are: 3 8 26
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 8*t^3 - 12*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : 8*t^11 - 596/3*t^9 + 1596*t^7 - 4914*t^5 + 10605/2*t^3 - 5355/4*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^37 - 16818716006919620270534203439873/7906061752395205735712087219*t^35 + 178703928418642798214093198316599291/711545557715568516214087849710*t^33 - 7857518111436990743742589424289629534/450645519886526726935588971483*t^31 + 1791146387282077679919602060622132604409/2253227599432633634677944857415*t^29 - 14329882756963165527527952067865243780369/569236446172454812971270279768*t^27 + 6865736973134045560284981619404421741869969/12017213863640712718282372572880*t^25 - 22716819594914183031335062408514336374577595/2403442772728142543656474514576*t^23 + 551986468747729814171787768965889124751719815/4806885545456285087312949029152*t^21 - 259172849456568729127700156511114658469221905/252993976076646583542786791008*t^19 + 3371668037358119484036804042389619186335944275/505987952153293167085573582016*t^17 - 15765329333622269993043176884320324605677990755/505987952153293167085573582016*t^15 + 103610585354910028988727478957502659078441757625/1011975904306586334171147164032*t^13 - 3702672685663732146454581693531268299059123701275/16191614468905381346738354624512*t^11 + 10709821205191533477173530157596337825647795207725/32383228937810762693476709249024*t^9 - 9329870141149156706852741138743629491550190228125/32383228937810762693476709249024*t^7 + 4364419549004680001344365470494068057342120073425/32383228937810762693476709249024*t^5 - 14259268249997881297907747257575784666986435051375/518131663004972203095627347984384*t^3 + 1571565648912690099399168797165901199642315403625/1036263326009944406191254695968768*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
Positive weights:   37 out of 37
Indefinite weights: 0 out of 37
Negative weights:   0 out of 37
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-7.1607451129814005923 + 1.8117099656176173974e-437j)  +/-  (3.08e-121, 3.08e-121j)
| (-0.28992705156930772092 + 5.2521084380510481682e-441j)  +/-  (2.24e-126, 2.24e-126j)
| (-4.8327396613948970838 + 1.6447500537412634806e-434j)  +/-  (4.03e-119, 4.03e-119j)
| (4.8327396613948970838 - 7.1246576578042371486e-445j)  +/-  (4.03e-119, 4.03e-119j)
| (-4.3696420927707132222 - 1.6073529039992894905e-445j)  +/-  (5.3e-119, 5.3e-119j)
| (-6.4487380170617824996 + 6.120128117139932364e-449j)  +/-  (2.74e-120, 2.74e-120j)
| (-5.8560521089641104752 + 3.0366263327862743169e-449j)  +/-  (1.14e-119, 1.14e-119j)
| (-5.324662295632935465 - 5.1738155853637653024e-455j)  +/-  (2.39e-119, 2.39e-119j)
| (2.2652012185402619968 + 9.5171976421754034474e-464j)  +/-  (8.39e-121, 8.39e-121j)
| (5.8560521089641104752 + 1.035199962711889263e-462j)  +/-  (9.51e-120, 9.51e-120j)
| (7.1607451129814005923 + 2.5013260336719715294e-466j)  +/-  (2.64e-121, 2.64e-121j)
| (1.5495888910389564541 - 5.6161914111833572939e-466j)  +/-  (2.47e-122, 2.47e-122j)
| (-1.5495888910389564541 - 4.8959417750606072111e-463j)  +/-  (2.57e-122, 2.57e-122j)
| (-3.9306785492919721851 + 4.3413808233042852861e-464j)  +/-  (5.62e-119, 5.62e-119j)
| (1.8979025739610826354 - 1.0681073086629472411e-474j)  +/-  (1.31e-121, 1.31e-121j)
| (0.59841605318147530927 + 1.8782458146257753404e-478j)  +/-  (3.22e-125, 3.22e-125j)
| (2.6414479718130762063 + 1.1379266256944288333e-471j)  +/-  (4.69e-120, 4.69e-120j)
| (-2.9905101912817771305 + 4.115164435614105071e-471j)  +/-  (2.8e-119, 2.8e-119j)
| (-1.2247448713915890491 - 7.0140773052228327717e-484j)  +/-  (3.61e-123, 3.61e-123j)
| (6.4487380170617824996 - 1.4833758627763781704e-481j)  +/-  (2.59e-120, 2.59e-120j)
| (5.324662295632935465 - 4.1419131976186374484e-482j)  +/-  (2.29e-119, 2.29e-119j)
| (3.5207882629582430588 - 1.3548140302967071015e-479j)  +/-  (5.71e-119, 5.71e-119j)
| (2.9905101912817771305 + 4.9008204366983848988e-479j)  +/-  (2.65e-119, 2.65e-119j)
| (-3.5207882629582430588 - 3.8779779483805519736e-480j)  +/-  (5.37e-119, 5.37e-119j)
| (-1.8979025739610826354 - 4.0374572061781059066e-486j)  +/-  (1.31e-121, 1.31e-121j)
| (3.9306785492919721851 + 7.1325252116822523804e-486j)  +/-  (5.6e-119, 5.6e-119j)
| (3.206558810099933527 + 1.9326286249994385621e-485j)  +/-  (5.58e-119, 5.58e-119j)
| (0.28992705156930772092 - 6.6338125837947223859e-492j)  +/-  (3.32e-126, 3.32e-126j)
| (4.3696420927707132222 + 2.5936884952135381189e-486j)  +/-  (5.32e-119, 5.32e-119j)
| (-0.59841605318147530927 - 6.3786102534289322844e-491j)  +/-  (3.13e-125, 3.13e-125j)
| (-2.6414479718130762063 + 7.7951893057180623303e-485j)  +/-  (4.48e-120, 4.48e-120j)
| (6.8916997882315767495e-503 - 1.2809190983283699811e-502j)  +/-  (5.38e-501, 5.38e-501j)
| (0.91253219429574698166 + 2.2730499830976783443e-492j)  +/-  (4.15e-124, 4.15e-124j)
| (1.2247448713915890491 - 1.719187047698802643e-491j)  +/-  (3.35e-123, 3.35e-123j)
| (-2.2652012185402619968 + 1.5632349094210482072e-491j)  +/-  (7.87e-121, 7.87e-121j)
| (-0.91253219429574698166 + 1.0677030143051439553e-496j)  +/-  (3.93e-124, 3.93e-124j)
| (-3.206558810099933527 - 9.703826035756795239e-499j)  +/-  (5.34e-119, 5.34e-119j)
-------------------------------------------------
The weights are:
| (2.4907710528739964531e-23 - 1.5334538799749286114e-452j)  +/-  (2.22e-31, 1.07e-90j)
| (0.15538166841428428759 - 9.5608715797139073892e-439j)  +/-  (4.95e-18, 2.38e-77j)
| (1.93278130276958879e-11 + 1.9635560660218002451e-444j)  +/-  (1.29e-25, 6.2e-85j)
| (1.93278130276958879e-11 + 3.2877997993282869411e-446j)  +/-  (1.54e-27, 7.39e-87j)
| (1.2971963533788100134e-09 - 1.1149473339345178889e-443j)  +/-  (1.96e-24, 9.41e-84j)
| (3.1233047790880202694e-19 + 4.4337033601238681773e-450j)  +/-  (1.95e-30, 9.36e-90j)
| (4.0158250719394416354e-16 - 4.3663449299929440617e-448j)  +/-  (3.71e-29, 1.78e-88j)
| (1.3971283600988779725e-13 + 2.9875929827669515274e-446j)  +/-  (8.66e-28, 4.16e-87j)
| (0.0012466046174997762851 - 1.0380179849163292595e-440j)  +/-  (2.75e-21, 1.32e-80j)
| (4.0158250719394416354e-16 + 4.17898539710957131e-449j)  +/-  (3.98e-34, 1.91e-93j)
| (2.4907710528739964531e-23 + 2.9758140294223771903e-453j)  +/-  (1.55e-37, 7.44e-97j)
| (0.017197000418961522298 - 8.1484052850045742328e-440j)  +/-  (2.26e-18, 1.09e-77j)
| (0.017197000418961522298 - 1.5858291600515497869e-439j)  +/-  (7.37e-19, 3.54e-78j)
| (4.6959581333746291364e-08 + 7.7941537880140374279e-443j)  +/-  (2.8e-27, 1.35e-86j)
| (0.0055259021546119642176 + 2.992296527300418818e-440j)  +/-  (5.7e-21, 2.74e-80j)
| (0.12395995385809593359 + 5.8064231183394348113e-439j)  +/-  (1.24e-18, 5.98e-78j)
| (0.00019728639521785036136 + 3.8632373628575450754e-441j)  +/-  (4.94e-25, 2.38e-84j)
| (2.147662883442546077e-05 - 7.8917019256124551266e-441j)  +/-  (2.58e-26, 1.24e-85j)
| (0.039685772651746155269 + 3.1688993832736773054e-439j)  +/-  (6.99e-19, 3.36e-78j)
| (3.1233047790880202694e-19 - 6.3493087527590943897e-451j)  +/-  (2.66e-36, 1.28e-95j)
| (1.3971283600988779725e-13 - 1.4464253912654313509e-447j)  +/-  (1.32e-33, 6.34e-93j)
| (8.9985393354514834234e-07 - 1.0767382001310401572e-442j)  +/-  (4.82e-30, 2.32e-89j)
| (2.147662883442546077e-05 - 1.8572787547613982066e-441j)  +/-  (2.28e-28, 1.1e-87j)
| (8.9985393354514834234e-07 - 6.8592112988728779978e-442j)  +/-  (1.79e-30, 8.59e-90j)
| (0.0055259021546119642176 + 6.8687361981963437552e-440j)  +/-  (7.83e-27, 3.76e-86j)
| (4.6959581333746291364e-08 + 8.0193998051870000522e-444j)  +/-  (9.7e-32, 4.66e-91j)
| (4.1441005031928805136e-06 + 8.0084224849143662786e-442j)  +/-  (1.26e-29, 6.04e-89j)
| (0.15538166841428428759 - 8.471328260387469267e-439j)  +/-  (4.25e-26, 2.04e-85j)
| (1.2971963533788100134e-09 - 5.6086236426878204039e-445j)  +/-  (5.85e-33, 2.81e-92j)
| (0.12395995385809593359 + 7.4753820543433597964e-439j)  +/-  (8.49e-27, 4.07e-86j)
| (0.00019728639521785036136 + 1.3185576201305725337e-440j)  +/-  (6.34e-31, 3.04e-90j)
| (0.1603198146031904401 + 1.0176815546715939968e-438j)  +/-  (8.95e-27, 4.3e-86j)
| (0.076619335328470511968 - 3.5598737677720888625e-439j)  +/-  (1.37e-27, 6.61e-87j)
| (0.039685772651746155269 + 1.8846957754477396182e-439j)  +/-  (4.75e-28, 2.29e-87j)
| (0.0012466046174997762851 - 2.8717909989848501407e-440j)  +/-  (1.05e-30, 4.97e-90j)
| (0.076619335328470511968 - 5.2280407350201222458e-439j)  +/-  (6.71e-29, 2.98e-88j)
| (4.1441005031928805136e-06 + 3.961222659716114249e-441j)  +/-  (5.93e-32, 2.9e-91j)
