Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 10 21
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 21 Kronrod extension for:
P2 : t^12 - 8477/152*t^10 + 155745/152*t^8 - 563535/76*t^6 + 1500975/76*t^4 - 2132865/152*t^2 + 110565/152
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^33 - 31255889025505114576925602116015509974806127/81813282997930122813693709948513155439752*t^31 + 36182422658665850746692801579293857889138994595/572692980985510859695855969639592088078264*t^29 - 14812532864373937847105282565806001936069270117345/2481669584270547058682042535104899048339144*t^27 + 888886057776682655826615639198944139635411234448975/2481669584270547058682042535104899048339144*t^25 - 392223878481509749723914107834604094071275330080211985/27298365426976017645502467886153889531730584*t^23 + 1540720682722150237127794712924517029389797141833125605/3899766489568002520786066840879127075961512*t^21 - 29323063113371624385771415245139659445495119653842050225/3899766489568002520786066840879127075961512*t^19 + 20299322106651281798566606915683452775931008060154164525/205250867872000132672950886362059319787448*t^17 - 825587375276875315849369086548426664355222189654920375/928736958696833179515614870416558008088*t^15 + 4963985839664602417474247732372263387770219692168208525/928736958696833179515614870416558008088*t^13 - 19316072138179042610348108012325250190028650783328383025/928736958696833179515614870416558008088*t^11 + 4214630895185077673758419603020321475255729986548642125/84430632608803016319601351856050728008*t^9 - 5828434641971556415735180323895716522286423760959094625/84430632608803016319601351856050728008*t^7 + 4195056102841788930918878514030228944135441678115751875/84430632608803016319601351856050728008*t^5 - 1268220036935948964919899801044284149125123123119038375/84430632608803016319601351856050728008*t^3 + 59008678452520381468152930706458000431784443150909625/84430632608803016319601351856050728008*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:
| (-6.5913737789830184418 - 8.6341206692904698114e-463j)  +/-  (2.09e-120, 2.09e-120j)
| (5.8760203917983668049 - 2.2562354826431673522e-462j)  +/-  (2.44e-120, 2.44e-120j)
| (-9.2553764822143263514 + 2.5080318462056183015e-466j)  +/-  (6.43e-122, 6.43e-122j)
| (-2.8901633840314029187 + 8.562420382922066758e-467j)  +/-  (1.16e-121, 1.16e-121j)
| (8.223451896784540836 - 5.6206472313825368508e-464j)  +/-  (4.29e-121, 4.29e-121j)
| (-5.2019365924015129919 + 1.601435357358249002e-466j)  +/-  (2.05e-120, 2.05e-120j)
| (7.3633643530507330559 - 8.2065699011596160991e-466j)  +/-  (1.16e-120, 1.16e-120j)
| (9.2553764822143263514 - 5.2308033442090703281e-471j)  +/-  (5.14e-122, 5.14e-122j)
| (4.5616546263782850971 + 7.3908562743389042753e-471j)  +/-  (1.43e-120, 1.43e-120j)
| (-7.3633643530507330559 - 3.14315907845443042e-474j)  +/-  (1.16e-120, 1.16e-120j)
| (1.3451886332581436404 - 3.0850774849510630448e-478j)  +/-  (8.9e-124, 8.9e-124j)
| (6.5913737789830184418 - 9.1593042454137105741e-475j)  +/-  (2.04e-120, 2.04e-120j)
| (-0.23704314987094039888 - 3.7248331267021943443e-484j)  +/-  (1.19e-126, 1.19e-126j)
| (-1.9137355618993510628 + 1.247805970657986794e-480j)  +/-  (5.54e-123, 5.54e-123j)
| (5.2019365924015129919 + 2.7630527023489684127e-477j)  +/-  (1.98e-120, 1.98e-120j)
| (-4.5616546263782850971 + 1.5847206660529976113e-482j)  +/-  (1.41e-120, 1.41e-120j)
| (1.9137355618993510628 - 1.9664442073940871673e-484j)  +/-  (5.15e-123, 5.15e-123j)
| (-3.9544879426500450264 - 8.0828124720235684327e-489j)  +/-  (6.89e-121, 6.89e-121j)
| (0.23704314987094039888 + 1.1933866515954266317e-496j)  +/-  (1.19e-126, 1.19e-126j)
| (-8.223451896784540836 - 8.04407002162064535e-491j)  +/-  (4.11e-121, 4.11e-121j)
| (2.8901633840314029187 + 2.0145732221482688422e-494j)  +/-  (1.1e-121, 1.1e-121j)
| (1 + 1.0780867942601403446e-507j)  +/-  (4.94e-124, 4.94e-124j)
| (-5.8760203917983668049 - 9.1628364476573055099e-506j)  +/-  (2.5e-120, 2.5e-120j)
| (-0.89562041747819383167 + 7.6144628697571099023e-514j)  +/-  (2.21e-124, 2.21e-124j)
| (-3.1894721366810702115e-516 + 4.7358267891551733006e-516j)  +/-  (1.88e-514, 1.88e-514j)
| (-2.4234566117408774191 + 7.5728335748641700049e-511j)  +/-  (3.07e-122, 3.07e-122j)
| (-1 - 5.8168526851364366966e-514j)  +/-  (4.38e-124, 4.38e-124j)
| (3.390566656071671805 - 7.2871218452796408371e-511j)  +/-  (3.31e-121, 3.31e-121j)
| (-1.3451886332581436404 - 3.4179612917421634108e-524j)  +/-  (8.66e-124, 8.66e-124j)
| (3.9544879426500450264 + 1.73911827136880825e-523j)  +/-  (6.52e-121, 6.52e-121j)
| (-3.390566656071671805 + 8.7113207382073295181e-528j)  +/-  (3.35e-121, 3.35e-121j)
| (0.89562041747819383167 + 1.0294333796254417593e-531j)  +/-  (2.41e-124, 2.41e-124j)
| (2.4234566117408774191 + 2.0701379276409431e-531j)  +/-  (3.04e-122, 3.04e-122j)
-------------------------------------------------
The weights are:
| (1.0865479401021200442e-10 - 4.8307652332884114076e-472j)  +/-  (6.91e-40, 1.37e-98j)
| (8.7907423195942438735e-09 + 7.8628307559160321121e-470j)  +/-  (7.17e-39, 1.42e-97j)
| (1.1869214202238018785e-19 + 1.7117124016302354694e-478j)  +/-  (6.19e-45, 1.23e-103j)
| (0.002876207902820953571 - 1.206687700230463715e-466j)  +/-  (5.2e-30, 1.03e-88j)
| (7.6140000839893234517e-16 + 3.351433219947930105e-475j)  +/-  (5.72e-44, 1.14e-102j)
| (3.4840400912558727459e-07 - 3.9159029593663157066e-470j)  +/-  (4.83e-38, 9.58e-97j)
| (5.433854505758620757e-13 - 2.720455474311330138e-473j)  +/-  (1.28e-42, 2.54e-101j)
| (1.1869214202238018785e-19 - 1.4413616319343579813e-477j)  +/-  (3.97e-46, 7.87e-105j)
| (7.5464201316087125622e-06 + 2.0921218293734624124e-468j)  +/-  (1.72e-38, 3.42e-97j)
| (5.433854505758620757e-13 - 1.3721073898646394813e-474j)  +/-  (2.88e-44, 5.71e-103j)
| (0.10198915617307023335 + 1.9187467879480024115e-464j)  +/-  (4.54e-28, 9e-87j)
| (1.0865479401021200442e-10 + 1.5471960382007605714e-471j)  +/-  (9.46e-42, 1.88e-100j)
| (0.27920982125864395058 - 8.3754668835357408167e-464j)  +/-  (4.55e-29, 9.03e-88j)
| (0.034342918683344827069 - 1.6518966528141836205e-465j)  +/-  (1.97e-32, 3.91e-91j)
| (3.4840400912558727459e-07 - 3.8833779847814261723e-469j)  +/-  (9.85e-40, 1.95e-98j)
| (7.5464201316087125622e-06 + 3.7361061226884974619e-469j)  +/-  (4.59e-40, 9.11e-99j)
| (0.034342918683344827069 - 2.9654970404486321922e-465j)  +/-  (4.24e-34, 8.42e-93j)
| (9.4388886284983316071e-05 - 3.1853520788549610788e-468j)  +/-  (3.37e-39, 6.69e-98j)
| (0.27920982125864395058 - 8.9845332367065996081e-464j)  +/-  (4.85e-32, 9.6e-91j)
| (7.6140000839893234517e-16 - 1.5414221322662637116e-476j)  +/-  (5.87e-47, 1.16e-105j)
| (0.002876207902820953571 - 3.0518484438631439564e-466j)  +/-  (1.64e-38, 3.24e-97j)
| (-0.14382827271089891501 - 1.1843525388109892281e-463j)  +/-  (2.88e-33, 5.69e-92j)
| (8.7907423195942438735e-09 + 4.0352627133477498661e-471j)  +/-  (1.19e-42, 2.35e-101j)
| (0.27995083131626524579 + 9.1650803241765781017e-464j)  +/-  (1.26e-33, 2.49e-92j)
| (-0.13099704525708264651 + 1.4013411237760367558e-463j)  +/-  (5.13e-33, 1.01e-91j)
| (0.010174915879990275018 + 4.4758479701801385841e-466j)  +/-  (3.03e-37, 6.01e-96j)
| (-0.14382827271089891501 - 8.7869992751276416665e-464j)  +/-  (7.76e-34, 1.53e-92j)
| (0.00068065151493777469939 + 7.0729303262176891776e-467j)  +/-  (4.61e-40, 9.08e-99j)
| (0.10198915617307023335 + 1.2805499193386190076e-464j)  +/-  (4.87e-36, 9.73e-95j)
| (9.4388886284983316071e-05 - 1.2577411776853270998e-467j)  +/-  (5.57e-41, 1.1e-99j)
| (0.00068065151493777469939 + 2.3198083790312459523e-467j)  +/-  (8.49e-40, 1.74e-98j)
| (0.27995083131626524579 + 1.1968750913811335572e-463j)  +/-  (2.61e-36, 5.72e-95j)
| (0.010174915879990275018 + 9.5523195686194414864e-466j)  +/-  (8.21e-39, 1.58e-97j)
