Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 4 20
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Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P3 : 4*t^9 - 142/3*t^7 + 1399/9*t^5 - 2965/18*t^3 + 295/6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^29 - 829139585937614978979402714277093090301/1378881628977837424165594577148926709*t^27 + 632302510632936902241048484301798821150373/16546579547734049089987134925787120508*t^25 - 133941471496856391029749088686875193827092575/99279477286404294539922809554722723048*t^23 + 5812003766304564296473156866518750037270263725/198558954572808589079845619109445446096*t^21 - 54025956642797691258910571666516932068374861975/132372636381872392719897079406296964064*t^19 + 603877569919164942461387778098031792605245475/162221368115039696960658185546932554*t^17 - 115443679327911227297664718666850498609700896675/5191083779681270302741061937501841728*t^15 + 298176834579103849366196347179886330112983716125/3460722519787513535160707958334561152*t^13 - 736090568044381600330446179331731487076992773875/3460722519787513535160707958334561152*t^11 + 9054463555436496086999528587909127093970502364125/27685780158300108281285663666676489216*t^9 - 5608227679638681641085999055889470249698464710875/18457186772200072187523775777784326144*t^7 + 5953200369555895740825743048514448396557188872625/36914373544400144375047551555568652288*t^5 - 3207017432282282361822130466316155679429127248125/73828747088800288750095103111137304576*t^3 + 325090183839808317978679153730322922234122320625/73828747088800288750095103111137304576*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:
| (-3.1695749797433954244 - 1.8462185731355831336e-465j)  +/-  (1.13e-121, 1.13e-121j)
| (-5.403367990235555017 + 1.6111445856697140604e-465j)  +/-  (5.57e-122, 5.57e-122j)
| (-4.2051169778104238937 + 1.4551292493639947271e-465j)  +/-  (1.81e-121, 1.81e-121j)
| (-6.1553279759282458668 + 1.3616412197390506884e-467j)  +/-  (1.11e-122, 1.11e-122j)
| (5.403367990235555017 + 8.4180029532144425851e-466j)  +/-  (6.42e-122, 6.42e-122j)
| (6.1553279759282458668 + 6.8041006963230265937e-470j)  +/-  (1.16e-122, 1.16e-122j)
| (3.6745625916955208506 - 4.670932869044402476e-472j)  +/-  (1.72e-121, 1.72e-121j)
| (4.5782887878301473153e-485 + 6.4690180295599551666e-484j)  +/-  (1.88e-482, 1.88e-482j)
| (-4.7735853814474776058 + 2.8910709355219760008e-477j)  +/-  (1.45e-121, 1.45e-121j)
| (-2.2060595696653970513 + 4.6106355938978488312e-481j)  +/-  (1.8e-122, 1.8e-122j)
| (1.0672470719421885588 + 1.4818958818611273849e-481j)  +/-  (1.54e-122, 1.54e-122j)
| (4.7735853814474776058 - 3.943156479480186741e-481j)  +/-  (1.39e-121, 1.39e-121j)
| (2.6822224032999497583 - 1.5576116832233810016e-491j)  +/-  (4.81e-122, 4.81e-122j)
| (-0.97778890935543307184 - 7.7474727260233848617e-499j)  +/-  (6.2e-123, 6.2e-123j)
| (-2.6822224032999497583 - 2.6868878560006348994e-499j)  +/-  (4.9e-122, 4.9e-122j)
| (0.97778890935543307184 - 9.9462858027363264392e-500j)  +/-  (6.14e-123, 6.14e-123j)
| (-3.6745625916955208506 + 4.2806558511297692988e-499j)  +/-  (1.65e-121, 1.65e-121j)
| (-1.1530591875902305495 - 6.2314309252538831225e-500j)  +/-  (1.11e-122, 1.11e-122j)
| (-0.48932189980227080554 - 4.4329941094506883341e-506j)  +/-  (2.04e-125, 2.04e-125j)
| (-1.7320508075688772935 - 1.3445140324301691632e-502j)  +/-  (5.54e-123, 5.54e-123j)
| (1.1530591875902305495 - 5.3162907140894581439e-502j)  +/-  (1.12e-122, 1.12e-122j)
| (0.48932189980227080554 + 6.0678310123916792483e-509j)  +/-  (2.35e-125, 2.35e-125j)
| (3.1695749797433954244 - 2.5003721898079958278e-506j)  +/-  (1.02e-121, 1.02e-121j)
| (4.2051169778104238937 + 4.4703370743296485405e-514j)  +/-  (1.77e-121, 1.77e-121j)
| (-1.0672470719421885588 - 4.8815163191054229901e-518j)  +/-  (1.52e-122, 1.52e-122j)
| (2.2060595696653970513 - 1.7289936050251275677e-523j)  +/-  (1.72e-122, 1.72e-122j)
| (0.7071067811865475244 - 5.1703549789296751229e-533j)  +/-  (2.38e-124, 2.38e-124j)
| (1.7320508075688772935 - 3.4429897191510127273e-532j)  +/-  (5.66e-123, 5.66e-123j)
| (-0.7071067811865475244 - 4.5568981576998697861e-534j)  +/-  (2.12e-124, 2.12e-124j)
-------------------------------------------------
The weights are:
| (1.2107784337657120707e-05 - 1.0029746915227721281e-469j)  +/-  (8.47e-35, 1.47e-95j)
| (7.9525695496406376606e-14 + 7.667989968805384639e-476j)  +/-  (1.3e-41, 2.26e-102j)
| (6.4517731824237476003e-09 + 1.9792257757605995776e-472j)  +/-  (8.11e-39, 1.41e-99j)
| (1.7108920079510052532e-17 - 4.976684317033284515e-478j)  +/-  (1.86e-43, 3.24e-104j)
| (7.9525695496406376606e-14 - 2.149585912422140991e-476j)  +/-  (1.17e-44, 2.04e-105j)
| (1.7108920079510052532e-17 + 1.6574059710909039781e-478j)  +/-  (2.62e-46, 4.55e-107j)
| (3.9831196902117147761e-07 + 2.9699481515609462521e-472j)  +/-  (2.46e-41, 4.27e-102j)
| (0.26514872236018446175 + 1.5141272064105127389e-466j)  +/-  (1.49e-31, 2.58e-92j)
| (4.2525581344758030859e-11 - 3.8185737788838839569e-474j)  +/-  (6.83e-42, 1.19e-102j)
| (0.0020541937978009921665 - 1.5339236624615503713e-468j)  +/-  (3.53e-36, 6.14e-97j)
| (-0.69546590977159670146 + 1.5942522980903186604e-465j)  +/-  (1.39e-31, 2.42e-92j)
| (4.2525581344758030859e-11 + 8.8269181591739254813e-475j)  +/-  (6.46e-44, 1.12e-104j)
| (0.00020362418288266500982 + 3.1182373675857453435e-470j)  +/-  (1.8e-39, 3.13e-100j)
| (0.53866471649222075269 - 2.6186452142732488885e-465j)  +/-  (7.98e-33, 1.39e-93j)
| (0.00020362418288266500982 + 3.8699205507716449405e-469j)  +/-  (2.92e-38, 5.08e-99j)
| (0.53866471649222075269 - 1.3734076935520542326e-465j)  +/-  (6.95e-34, 1.21e-94j)
| (3.9831196902117147761e-07 - 4.4924871983416185232e-471j)  +/-  (2.13e-40, 3.71e-101j)
| (0.34581096614247636542 - 1.1717218672898970092e-465j)  +/-  (1.03e-34, 1.8e-95j)
| (0.2531423427785982849 - 4.5460571007020796519e-466j)  +/-  (2.79e-34, 4.85e-95j)
| (0.013468653413458594536 + 9.178856900058602134e-468j)  +/-  (1.4e-36, 2.43e-97j)
| (0.34581096614247636542 - 5.4161967250478647796e-466j)  +/-  (1.76e-35, 3.06e-96j)
| (0.2531423427785982849 - 3.3179868615805084601e-466j)  +/-  (1.59e-35, 2.76e-96j)
| (1.2107784337657120707e-05 - 3.3436034122493321617e-471j)  +/-  (3.98e-42, 6.93e-103j)
| (6.4517731824237476003e-09 - 1.9839538899180954817e-473j)  +/-  (3.08e-44, 5.35e-105j)
| (-0.69546590977159670146 + 3.2399749735695381015e-465j)  +/-  (5.47e-36, 9.57e-97j)
| (0.0020541937978009921665 - 2.6886901119492290079e-469j)  +/-  (9.75e-41, 1.7e-101j)
| (-0.090465460806618169002 + 5.791557068134721465e-466j)  +/-  (3.42e-37, 6.06e-98j)
| (0.013468653413458594536 + 2.6509919167211372254e-468j)  +/-  (1.02e-39, 1.76e-100j)
| (-0.090465460806618169002 + 9.1666557552492783461e-466j)  +/-  (1.96e-37, 3.64e-98j)
