Starting with polynomial:
P : t
Extension levels are: 1 2 4 22
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Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : t^3 - 3/5*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P3 : t^7 - 77/45*t^5 + 749/891*t^3 - 31/297*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^29 - 743669323805712117007731327878993851/101118245240258330221759722752299185*t^27 + 2093043399568603222966332551841507719066536/86168822745693298423444543580876521190415*t^25 - 22132943513633149981940009626630315421354495/465311642826743811486600535336733214428241*t^23 + 1098833941924056513364715385309665660888790100/17893347719610239296257456949767104518467813*t^21 - 106022718058073173384810274439914911965506720/1928355769281303984308447741453597730060441*t^19 + 7741361942670806160233913306240929327000317/221463827844631550018617247617920187485933*t^17 - 73902727576746122749200976845259470123008158/4650740384737262550390962199976323937204593*t^15 + 294335008445275793053732842003993594199657735/57359131411759571454821867133041328558856647*t^13 - 463263595918369303494333342496043493173980475/401513919882317000183753069931289299911996529*t^11 + 209769159109345367116192160910198730071018550/1204541759646951000551259209793867899735989587*t^9 - 68884619114206275809935308325418209613772239/4148977172117275668565448389289989432423964133*t^7 + 1603943950950123049099376000379628182134554/1778133073764546715099477881124281185324556057*t^5 - 1739971014375660508570715921009942044763990/75443646129724339197792132956273073148770449847*t^3 + 143417554162634120678420206473856774015/811222001394885367718194978024441646760972579*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:
| (-0.99685672297465999108 + 6.7542980887071991274e-433j)  +/-  (2.51e-118, 2.51e-118j)
| (-0.96049126870802028342 - 2.6404651889392124438e-447j)  +/-  (9.17e-118, 9.17e-118j)
| (-0.92826055731734907496 + 5.8950205266337114557e-459j)  +/-  (6.85e-118, 6.85e-118j)
| (-5.9585289417284599639e-480 - 6.3668678700019534233e-481j)  +/-  (1.74e-478, 1.74e-478j)
| (0.88704611060711153723 - 6.1195843356196306275e-464j)  +/-  (3.56e-118, 3.56e-118j)
| (0.83605336860264937262 - 1.6539295134430341103e-465j)  +/-  (1.3e-118, 1.3e-118j)
| (0.96049126870802028342 - 6.6528833775789247846e-464j)  +/-  (8.84e-118, 8.84e-118j)
| (-0.88704611060711153723 + 2.5508217306485671723e-467j)  +/-  (3.8e-118, 3.8e-118j)
| (-0.98361965975013195204 - 2.8066155730050139332e-476j)  +/-  (8.16e-118, 8.16e-118j)
| (0.98361965975013195204 - 3.6774830480391243285e-483j)  +/-  (7.02e-118, 7.02e-118j)
| (0.92826055731734907496 + 8.1123285582099258065e-487j)  +/-  (6.79e-118, 6.79e-118j)
| (0.99685672297465999108 - 4.3432559843664965342e-489j)  +/-  (2.57e-118, 2.57e-118j)
| (-0.70280056519364656738 + 1.0926443806326000523e-489j)  +/-  (5.77e-120, 5.77e-120j)
| (-0.83605336860264937262 + 6.6812089770594956128e-490j)  +/-  (1.25e-118, 1.25e-118j)
| (-0.22325031359655868096 - 4.9609977183984492971e-500j)  +/-  (2.16e-125, 2.16e-125j)
| (0.77459666924148337704 + 6.7875887643070131788e-495j)  +/-  (2.98e-119, 2.98e-119j)
| (0.53148341425790366185 + 7.0214860491668667106e-498j)  +/-  (8.6e-122, 8.6e-122j)
| (-0.11239938358974068919 - 3.772020607524890604e-502j)  +/-  (9.38e-127, 9.38e-127j)
| (-0.77459666924148337704 - 1.0221337449368652338e-497j)  +/-  (3e-119, 3e-119j)
| (-0.434243749346802558 + 2.1711820101370734659e-503j)  +/-  (6.21e-123, 6.21e-123j)
| (0.434243749346802558 + 9.0854035431856755337e-504j)  +/-  (6.06e-123, 6.06e-123j)
| (0.70280056519364656738 + 1.1330871238637767327e-500j)  +/-  (5.86e-120, 5.86e-120j)
| (0.11239938358974068919 + 9.1216025308436662604e-510j)  +/-  (8.36e-127, 8.36e-127j)
| (-0.53148341425790366185 + 1.0181421955317618478e-500j)  +/-  (7.92e-122, 7.92e-122j)
| (-0.62141026677071998722 - 1.2303908685643928351e-502j)  +/-  (7.88e-121, 7.88e-121j)
| (0.22325031359655868096 + 2.0954607642808191797e-509j)  +/-  (2.18e-125, 2.18e-125j)
| (0.62141026677071998722 + 8.8382396373533987804e-504j)  +/-  (7.52e-121, 7.52e-121j)
| (0.33102621368690377904 - 3.4824090420307579111e-507j)  +/-  (4.11e-124, 4.11e-124j)
| (-0.33102621368690377904 - 3.1657530861277178348e-507j)  +/-  (3.96e-124, 3.96e-124j)
-------------------------------------------------
The weights are:
| (0.0080457053059094172549 + 8.7534122998366502219e-433j)  +/-  (9.82e-28, 1.12e-83j)
| (0.02778592508196835853 + 1.0199575301688820989e-432j)  +/-  (5.45e-28, 6.23e-84j)
| (0.036647890621287933087 - 8.0354245790006327702e-433j)  +/-  (3.07e-28, 3.51e-84j)
| (0.11265819231011003316 + 5.1616849532130322374e-434j)  +/-  (3.88e-29, 4.44e-85j)
| (0.045937368776453318654 + 3.5987070165925440942e-434j)  +/-  (8.97e-30, 1.03e-85j)
| (0.056174851343592831352 - 3.9597431552297667112e-434j)  +/-  (6.98e-30, 7.98e-86j)
| (0.02778592508196835853 + 1.8949731511658737269e-434j)  +/-  (1.44e-30, 1.65e-86j)
| (0.045937368776453318654 + 6.1739154346004009238e-433j)  +/-  (1.31e-29, 1.5e-85j)
| (0.018322413329196253131 - 1.4457679022218226573e-432j)  +/-  (6.02e-29, 6.89e-85j)
| (0.018322413329196253131 - 9.6631907841149278739e-435j)  +/-  (3.2e-31, 3.66e-87j)
| (0.036647890621287933087 - 2.86319862790046976e-434j)  +/-  (3.25e-31, 3.71e-87j)
| (0.0080457053059094172549 + 2.7257222987794723884e-435j)  +/-  (1.12e-31, 1.28e-87j)
| (0.07675077998473403284 - 2.30451941742051616e-433j)  +/-  (9.13e-34, 1.04e-89j)
| (0.056174851343592831352 - 4.5134961379500373032e-433j)  +/-  (1.07e-32, 1.22e-88j)
| (0.10956494028087319235 + 6.8171065602437972139e-434j)  +/-  (3.66e-35, 4.19e-91j)
| (0.066711770528311653631 + 4.0342667659276486965e-434j)  +/-  (2.34e-34, 2.68e-90j)
| (0.093797582222480087741 - 3.9134176063531340259e-434j)  +/-  (9.73e-36, 1.11e-91j)
| (0.11188213336925912527 - 5.8536379871977116922e-434j)  +/-  (2.2e-35, 2.51e-91j)
| (0.066711770528311653631 + 3.2153846035629861397e-433j)  +/-  (1.86e-34, 2.13e-90j)
| (0.10045885562706650962 + 1.0082397854206148286e-433j)  +/-  (3.4e-36, 3.89e-92j)
| (0.10045885562706650962 + 3.9637243839717366934e-434j)  +/-  (7.36e-37, 8.42e-93j)
| (0.07675077998473403284 - 3.987028032861365275e-434j)  +/-  (2.92e-36, 3.34e-92j)
| (0.11188213336925912527 - 4.6673559417351754665e-434j)  +/-  (5.16e-37, 5.9e-93j)
| (0.093797582222480087741 - 1.28521191256853115e-433j)  +/-  (4.99e-37, 5.7e-93j)
| (0.085851391871002170182 + 1.6935689750866817999e-433j)  +/-  (7.98e-37, 9.14e-93j)
| (0.10956494028087319235 + 4.3223726856281183329e-434j)  +/-  (4.31e-38, 4.95e-94j)
| (0.085851391871002170182 + 3.9291691300783318628e-434j)  +/-  (4e-38, 4.62e-94j)
| (0.10573929550281009978 - 4.09492177504170784e-434j)  +/-  (2.42e-38, 2.78e-94j)
| (0.10573929550281009978 - 8.1666079823503160023e-434j)  +/-  (2.03e-38, 2.15e-94j)
