Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 12 23
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 23 Kronrod extension for:
P2 : 4*t^14 - 248498/1555*t^12 + 3530769/1555*t^10 - 8883963/622*t^8 + 50229333/1244*t^6 - 114812775/2488*t^4 + 78937551/4976*t^2 - 6151761/9952
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^37 - 5206884703785885069401677643109785203839199881736405351984973/5533163732601681780572327747967800058999238948871169643830*t^35 + 2156429944282243047560762390617286453826152091146369834371071307/22132654930406727122289310991871200235996955795484678575320*t^33 - 86671141549637352704475679652555623951611997891451497886174682427/14755103286937818081526207327914133490664637196989785716880*t^31 + 123518601412956111184936671657539022617506177131307392658484794715885/537085759644536578167553946736074459060192793970428200094432*t^29 - 6634894636616140976129239001203571630003689171698638172481741732529783/1074171519289073156335107893472148918120385587940856400188864*t^27 + 27984193286268544860406840523333155528054351995643712525407140010370871/238704782064238479185579531882699759582307908431301422264192*t^25 - 762319826189697387389954799944129656121308992952344429367894845400093273/477409564128476958371159063765399519164615816862602844528384*t^23 + 2141154568056680646228102431828154896676041637403169249211150215822469967/136402732608136273820331161075828434047033090532172241293824*t^21 - 2332727986225237200396896324418045137505390260409204757726171557292053045/20985035785867119049281717088588989853389706235718806352896*t^19 + 306647904980060519990721883441138932051996577804641660311663146649331107295/545610930432545095281324644303313736188132362128688965175296*t^17 - 2177945703339572817190900580135097263659178954192712199266029099102007723105/1091221860865090190562649288606627472376264724257377930350592*t^15 + 10594131628712078808649316189348036060554190415129309632821986435893666840505/2182443721730180381125298577213254944752529448514755860701184*t^13 - 2615777001630548106955338323855385492351061247026664881831433485591159869255/335760572573873904788507473417423837654235299771500901646336*t^11 + 5243227607723868206507210155028908789967102821968911098249588328935428433575/671521145147747809577014946834847675308470599543001803292672*t^9 - 6025327761610584106536736008289786718370542873480159816510125947967967444025/1343042290295495619154029893669695350616941199086003606585344*t^7 + 3440106866321040850522941439207881228368189838811425201201348807406843590225/2686084580590991238308059787339390701233882398172007213170688*t^5 - 754916267618211034491302104174238743065302564319660875949733949124139476225/5372169161181982476616119574678781402467764796344014426341376*t^3 + 10968860114584057416273968979414201488964692856321689645227909669688919075/2686084580590991238308059787339390701233882398172007213170688*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:
| (-5.0776054814676829901 - 3.4071588119365450165e-426j)  +/-  (8.32e-120, 8.32e-120j)
| (-4.5839247596140329024 - 4.5623326649699614723e-428j)  +/-  (1.13e-119, 1.13e-119j)
| (-4.1204787410992218738 + 1.0570103115528366283e-431j)  +/-  (1.29e-119, 1.29e-119j)
| (4.5839247596140329024 - 8.9851545157744794932e-434j)  +/-  (1.25e-119, 1.25e-119j)
| (6.2083813402075341455 - 4.0611887665899800371e-436j)  +/-  (1.16e-120, 1.16e-120j)
| (5.0776054814676829901 - 7.2311853854768060017e-434j)  +/-  (8.7e-120, 8.7e-120j)
| (1.8942430499246252602 - 2.8377058003901701942e-438j)  +/-  (1.73e-121, 1.73e-121j)
| (-6.9254270254578488751 + 1.0973548170448135926e-438j)  +/-  (1.37e-121, 1.37e-121j)
| (-1.5637358162600049373 + 3.1707854065662854157e-436j)  +/-  (3.97e-122, 3.97e-122j)
| (6.9254270254578488751 + 1.0034692336978882295e-437j)  +/-  (1.47e-121, 1.47e-121j)
| (-1.2798739543845792198 + 9.3605569751484957519e-440j)  +/-  (8.25e-123, 8.25e-123j)
| (-5.6118576190765062063 + 1.7663475718248091403e-436j)  +/-  (3.88e-120, 3.88e-120j)
| (1.0186126004208848735 - 1.33153170201764386e-440j)  +/-  (1.49e-123, 1.49e-123j)
| (5.6118576190765062063 + 4.784289140587801749e-438j)  +/-  (3.98e-120, 3.98e-120j)
| (3.270676901126319117 + 1.0702500367342774671e-436j)  +/-  (7.14e-120, 7.14e-120j)
| (-6.2083813402075341455 + 5.3589493617243575588e-438j)  +/-  (1.03e-120, 1.03e-120j)
| (3.682647592387373731 - 1.7341579665655718058e-437j)  +/-  (1.02e-119, 1.02e-119j)
| (2.2280691880626410905 - 3.8134273800633577866e-440j)  +/-  (6.68e-121, 6.68e-121j)
| (-2.5504966051126501465 - 2.2426894422901052398e-437j)  +/-  (2.01e-120, 2.01e-120j)
| (0.21096799267853511108 + 3.0440652979466972465e-453j)  +/-  (1.65e-126, 1.65e-126j)
| (4.1204787410992218738 - 4.1372859531320462972e-451j)  +/-  (1.2e-119, 1.2e-119j)
| (2.8910047184865201405 + 8.1310926362502180874e-452j)  +/-  (4.2e-120, 4.2e-120j)
| (1.2798739543845792198 - 1.6634696627780195622e-454j)  +/-  (8.42e-123, 8.42e-123j)
| (-0.38303484182812560296 - 9.4371163115383235114e-454j)  +/-  (9.37e-126, 9.37e-126j)
| (-2.2280691880626410905 + 1.0038731133900730875e-450j)  +/-  (7.8e-121, 7.8e-121j)
| (-2.8910047184865201405 - 2.8388287477501688337e-466j)  +/-  (4e-120, 4e-120j)
| (-7.1302839588809073559e-486 - 6.1278448928467985457e-485j)  +/-  (2.28e-483, 2.28e-483j)
| (-0.21096799267853511108 + 1.4603014588777044019e-483j)  +/-  (1.65e-126, 1.65e-126j)
| (-3.270676901126319117 + 2.2133980269165924988e-480j)  +/-  (8.41e-120, 8.41e-120j)
| (-0.7071067811865475244 + 1.3969272455274121395e-492j)  +/-  (1.13e-124, 1.13e-124j)
| (2.5504966051126501465 + 3.2704795430878318016e-489j)  +/-  (2.06e-120, 2.06e-120j)
| (1.5637358162600049373 + 1.8583374255685361673e-491j)  +/-  (3.89e-122, 3.89e-122j)
| (0.38303484182812560296 + 7.2350033825103273637e-494j)  +/-  (9.37e-126, 9.37e-126j)
| (-3.682647592387373731 + 1.1731985916124476042e-489j)  +/-  (1.06e-119, 1.06e-119j)
| (-1.8942430499246252602 + 5.1279852705294057163e-493j)  +/-  (1.77e-121, 1.77e-121j)
| (-1.0186126004208848735 - 7.8584535392247270247e-497j)  +/-  (1.27e-123, 1.27e-123j)
| (0.7071067811865475244 + 9.5485867749295393281e-498j)  +/-  (1.2e-124, 1.2e-124j)
-------------------------------------------------
The weights are:
| (1.8337971102649639799e-12 - 4.1827815009316241095e-437j)  +/-  (7.19e-31, 6.54e-90j)
| (2.0172067632092924306e-10 + 2.3171102211252996871e-436j)  +/-  (1.98e-29, 1.8e-88j)
| (1.0746824492606225642e-08 - 2.1652650151216468739e-435j)  +/-  (4.02e-28, 3.66e-87j)
| (2.0172067632092924306e-10 + 1.3779610473829625905e-437j)  +/-  (2.56e-32, 2.33e-91j)
| (6.5885990641427932204e-18 - 2.1932510059337892528e-442j)  +/-  (2.49e-37, 2.27e-96j)
| (1.8337971102649639799e-12 - 5.7355253007331536993e-439j)  +/-  (3.14e-34, 2.85e-93j)
| (0.0052721430068038914905 - 4.1545978425583388655e-431j)  +/-  (2.28e-22, 2.07e-81j)
| (6.9030027834980081943e-22 - 6.278771716902418087e-444j)  +/-  (6.34e-40, 5.77e-99j)
| (0.015399045901706882643 + 3.3697386178879365993e-430j)  +/-  (5.15e-21, 4.68e-80j)
| (6.9030027834980081943e-22 + 9.4992275882065219694e-445j)  +/-  (8.72e-40, 7.94e-99j)
| (0.027938046061644863218 - 9.8397741638244286126e-430j)  +/-  (1.44e-19, 1.31e-78j)
| (6.6462901066638945314e-15 - 3.2169458106315178474e-439j)  +/-  (2.59e-36, 2.35e-95j)
| (0.057119876345811745568 + 1.2988341622365066208e-429j)  +/-  (9.5e-19, 8.65e-78j)
| (6.6462901066638945314e-15 + 1.551081196986993703e-440j)  +/-  (3.98e-36, 3.62e-95j)
| (5.0690967691515691529e-06 - 3.7963230872831166568e-434j)  +/-  (3e-31, 2.73e-90j)
| (6.5885990641427932204e-18 + 2.2419719639984940908e-441j)  +/-  (6.63e-39, 6.03e-98j)
| (3.0929098959748808277e-07 + 3.3553325924290711029e-435j)  +/-  (1.79e-32, 1.63e-91j)
| (0.0012867390658984062125 + 9.8365049864619765325e-432j)  +/-  (1.04e-28, 9.43e-88j)
| (0.0002739702584504456345 - 6.3785178137404035002e-432j)  +/-  (2.47e-31, 2.25e-90j)
| (0.050327021021995919912 - 2.2704728864350783793e-428j)  +/-  (2.03e-24, 1.85e-83j)
| (1.0746824492606225642e-08 - 2.4226287115068665508e-436j)  +/-  (9.98e-34, 9.08e-93j)
| (4.764651408606486519e-05 + 3.396709018440664565e-433j)  +/-  (5.8e-31, 5.28e-90j)
| (0.027938046061644863218 - 5.9046588903531624213e-430j)  +/-  (7.03e-27, 6.4e-86j)
| (0.14566939899085658634 + 1.4001338726737219275e-428j)  +/-  (1.38e-26, 1.26e-85j)
| (0.0012867390658984062125 + 2.4979190094282673455e-431j)  +/-  (4.15e-31, 3.77e-90j)
| (4.764651408606486519e-05 + 1.2184997925252169188e-432j)  +/-  (2.1e-33, 1.92e-92j)
| (0.16868713436424372495 + 2.6062758985873161979e-428j)  +/-  (7.83e-27, 7.12e-86j)
| (0.050327021021995919912 - 2.4656189258512254992e-428j)  +/-  (5.84e-27, 5.31e-86j)
| (5.0690967691515691529e-06 - 1.7158847432956770199e-433j)  +/-  (8.91e-35, 8.1e-94j)
| (0.11231715631247896367 - 3.8899449947359310774e-429j)  +/-  (5.74e-29, 5.21e-88j)
| (0.0002739702584504456345 - 2.1388799926829459178e-432j)  +/-  (2.46e-32, 2.23e-91j)
| (0.015399045901706882643 + 1.7932426717717473547e-430j)  +/-  (2.19e-30, 1.99e-89j)
| (0.14566939899085658634 + 1.2052276211907059262e-428j)  +/-  (1.24e-28, 1.13e-87j)
| (3.0929098959748808277e-07 + 2.0357872522745444825e-434j)  +/-  (4.09e-36, 3.73e-95j)
| (0.0052721430068038914905 - 9.0311916805042902735e-431j)  +/-  (3.64e-32, 3.3e-91j)
| (0.057119876345811745568 + 1.9439060407787113501e-429j)  +/-  (1.49e-30, 1.36e-89j)
| (0.11231715631247896367 - 2.945916362977087309e-429j)  +/-  (2.59e-30, 2.24e-89j)
