Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 10 21
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 21 Kronrod extension for:
P2 : 4*t^12 - 8477/76*t^10 + 155745/152*t^8 - 563535/152*t^6 + 1500975/304*t^4 - 2132865/1216*t^2 + 110565/2432
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^33 - 31255889025505114576925602116015509974806127/40906641498965061406846854974256577719876*t^31 + 36182422658665850746692801579293857889138994595/572692980985510859695855969639592088078264*t^29 - 14812532864373937847105282565806001936069270117345/4963339168541094117364085070209798096678288*t^27 + 888886057776682655826615639198944139635411234448975/9926678337082188234728170140419596193356576*t^25 - 392223878481509749723914107834604094071275330080211985/218386923415808141164019743089231116253844672*t^23 + 1540720682722150237127794712924517029389797141833125605/62396263833088040332577069454066033215384192*t^21 - 29323063113371624385771415245139659445495119653842050225/124792527666176080665154138908132066430768384*t^19 + 20299322106651281798566606915683452775931008060154164525/13136055543808008491068856727171796466396672*t^17 - 825587375276875315849369086548426664355222189654920375/118878330713194646977998703413319425035264*t^15 + 4963985839664602417474247732372263387770219692168208525/237756661426389293955997406826638850070528*t^13 - 19316072138179042610348108012325250190028650783328383025/475513322852778587911994813653277700141056*t^11 + 4214630895185077673758419603020321475255729986548642125/86456967791414288711271784300595945480192*t^9 - 5828434641971556415735180323895716522286423760959094625/172913935582828577422543568601191890960384*t^7 + 4195056102841788930918878514030228944135441678115751875/345827871165657154845087137202383781920768*t^5 - 1268220036935948964919899801044284149125123123119038375/691655742331314309690174274404767563841536*t^3 + 59008678452520381468152930706458000431784443150909625/1383311484662628619380348548809535127683072*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:
| (-3.2255769197430722411 + 4.0324612995536110654e-434j)  +/-  (9.49e-121, 9.49e-121j)
| (-5.2066848663894687722 - 2.6970817673717844408e-437j)  +/-  (9.47e-121, 9.47e-121j)
| (-3.6783246397895513046 + 1.3069201679746914605e-438j)  +/-  (1.45e-120, 1.45e-120j)
| (-4.6608050964540920849 - 1.1928647850766779764e-442j)  +/-  (1.39e-120, 1.39e-120j)
| (6.5445394730082436286 - 9.5413650799060734801e-450j)  +/-  (4.11e-122, 4.11e-122j)
| (5.2066848663894687722 + 1.7367906085081931408e-448j)  +/-  (8.76e-121, 8.76e-121j)
| (4.1549738654310590099 - 2.2125658618080885822e-448j)  +/-  (1.75e-120, 1.75e-120j)
| (5.8148586009777255145 - 7.8010373738883053636e-449j)  +/-  (2.74e-121, 2.74e-121j)
| (-4.1549738654310590099 + 1.1393997859244225901e-448j)  +/-  (1.78e-120, 1.78e-120j)
| (-6.5445394730082436286 + 6.8671329970047404633e-455j)  +/-  (4.07e-122, 4.07e-122j)
| (2.7962452403682858841 - 9.6317275639058025706e-453j)  +/-  (5.29e-121, 5.29e-121j)
| (1.7136426040733484694 - 1.0060936386980046095e-458j)  +/-  (2.13e-122, 2.13e-122j)
| (-2.3974926745732757714 - 9.1281112582177394703e-458j)  +/-  (2.26e-121, 2.26e-121j)
| (-1.7136426040733484694 + 5.5264451418781636808e-471j)  +/-  (2.33e-122, 2.33e-122j)
| (-2.7962452403682858841 + 1.4462882102489551644e-479j)  +/-  (4.89e-121, 4.89e-121j)
| (-1.7406365214184255402e-488 - 4.1866392866246426575e-489j)  +/-  (5.91e-487, 5.91e-487j)
| (0.7071067811865475244 + 7.8415619651322934391e-491j)  +/-  (3.52e-124, 3.52e-124j)
| (-5.8148586009777255145 - 1.4120939962866805992e-487j)  +/-  (2.6e-121, 2.6e-121j)
| (-0.7071067811865475244 - 8.3397937894013391719e-492j)  +/-  (3.56e-124, 3.56e-124j)
| (-2.0436541275856649452 - 9.9507958779343054533e-489j)  +/-  (8.78e-122, 8.78e-122j)
| (0.95119200455189710095 - 5.7499704927018918741e-497j)  +/-  (6.52e-124, 6.52e-124j)
| (1.3532153932168790075 + 2.6974830031219714926e-496j)  +/-  (3.6e-123, 3.6e-123j)
| (2.3974926745732757714 + 4.7580808615940505523e-494j)  +/-  (2.1e-121, 2.1e-121j)
| (0.16761481870756104368 + 9.7584474997005475105e-499j)  +/-  (8.02e-127, 8.02e-127j)
| (-0.95119200455189710095 - 2.2702144925119374624e-497j)  +/-  (6.5e-124, 6.5e-124j)
| (-1.3532153932168790075 - 1.5287834100895855214e-495j)  +/-  (3.81e-123, 3.81e-123j)
| (0.63329927056795754969 - 3.2807121708006617744e-498j)  +/-  (2.13e-124, 2.13e-124j)
| (3.6783246397895513046 - 1.1674486780238546245e-492j)  +/-  (1.43e-120, 1.43e-120j)
| (3.2255769197430722411 + 3.3082648265050091585e-494j)  +/-  (9.82e-121, 9.82e-121j)
| (-0.63329927056795754969 + 2.0038784483342795199e-500j)  +/-  (1.73e-124, 1.73e-124j)
| (-0.16761481870756104368 - 2.7431286156602128514e-501j)  +/-  (8.02e-127, 8.02e-127j)
| (2.0436541275856649452 - 1.2453748073208342651e-496j)  +/-  (7.61e-122, 7.61e-122j)
| (4.6608050964540920849 - 1.56527888320964339e-501j)  +/-  (1.39e-120, 1.39e-120j)
-------------------------------------------------
The weights are:
| (7.5464201316087125622e-06 + 1.5702072713515926162e-438j)  +/-  (6.77e-29, 1.66e-88j)
| (5.433854505758620757e-13 - 2.3030592753964434962e-444j)  +/-  (5.61e-36, 1.37e-95j)
| (3.4840400912558727459e-07 + 6.4310202298664735882e-440j)  +/-  (2.81e-31, 6.87e-91j)
| (1.0865479401021200442e-10 + 8.657187393884414768e-443j)  +/-  (1.81e-34, 4.42e-94j)
| (1.1869214202238018785e-19 + 5.6736664150834298811e-449j)  +/-  (3.26e-42, 7.98e-102j)
| (5.433854505758620757e-13 + 5.4106928364200771837e-445j)  +/-  (1.34e-39, 3.28e-99j)
| (8.7907423195942438735e-09 + 3.0031658625079475984e-442j)  +/-  (1.74e-37, 4.26e-97j)
| (7.6140000839893234517e-16 - 9.8495080671081374809e-447j)  +/-  (6.45e-41, 1.58e-100j)
| (8.7907423195942438735e-09 - 2.3848569775015420273e-441j)  +/-  (4.73e-36, 1.16e-95j)
| (1.1869214202238018785e-19 - 1.6701578079448207467e-448j)  +/-  (2.66e-43, 6.52e-103j)
| (9.4388886284983316071e-05 - 4.4177734791155648937e-439j)  +/-  (7.58e-35, 1.85e-94j)
| (0.010174915879990275018 + 7.2304445877902147562e-437j)  +/-  (1.62e-30, 3.97e-90j)
| (0.00068065151493777469939 + 2.3240389698172784711e-437j)  +/-  (7.94e-33, 1.94e-92j)
| (0.010174915879990275018 + 2.3620647230373881084e-436j)  +/-  (5.48e-31, 1.34e-90j)
| (9.4388886284983316071e-05 - 6.1964399665906741251e-438j)  +/-  (5.56e-34, 1.36e-93j)
| (-0.13099704525708264651 + 2.6553309041608912812e-434j)  +/-  (3.21e-29, 7.85e-89j)
| (-0.14382827271089891501 - 1.5574658744276213605e-434j)  +/-  (1.63e-29, 3.99e-89j)
| (7.6140000839893234517e-16 + 3.4388880356671820187e-446j)  +/-  (3.81e-42, 9.31e-102j)
| (-0.14382827271089891501 - 2.4320429072898805897e-434j)  +/-  (2.85e-30, 6.98e-90j)
| (0.002876207902820953571 - 8.3949377263740657573e-437j)  +/-  (2.44e-32, 5.98e-92j)
| (0.10198915617307023335 + 2.2201266272450773048e-435j)  +/-  (6.93e-30, 1.69e-89j)
| (0.034342918683344827069 - 2.7603374179785561428e-436j)  +/-  (8.07e-32, 1.97e-91j)
| (0.00068065151493777469939 + 3.4224881599566216729e-438j)  +/-  (4.4e-36, 1.08e-95j)
| (0.27920982125864395058 - 1.5609805745473359768e-434j)  +/-  (2.55e-30, 6.25e-90j)
| (0.10198915617307023335 + 4.0771331273431136097e-435j)  +/-  (2.77e-31, 6.78e-91j)
| (0.034342918683344827069 - 6.7503208574389804654e-436j)  +/-  (3.25e-32, 7.95e-92j)
| (0.27995083131626524579 + 1.635413463466307826e-434j)  +/-  (2.86e-30, 7e-90j)
| (3.4840400912558727459e-07 - 4.2171328849188961728e-441j)  +/-  (3.93e-40, 9.61e-100j)
| (7.5464201316087125622e-06 + 4.7170054238409181483e-440j)  +/-  (4.6e-39, 1.12e-98j)
| (0.27995083131626524579 + 2.434486249154820255e-434j)  +/-  (4.09e-32, 9.97e-92j)
| (0.27920982125864395058 - 1.7321037876951791962e-434j)  +/-  (2.19e-32, 5.33e-92j)
| (0.002876207902820953571 - 1.8830311661902912419e-437j)  +/-  (1.91e-36, 4.59e-96j)
| (1.0865479401021200442e-10 - 1.5755009746015951722e-443j)  +/-  (1.02e-42, 2.53e-102j)
