Starting with polynomial:
P : 32*t^5 - 160*t^3 + 120*t
Extension levels are: 5 8 16
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 32*t^5 - 160*t^3 + 120*t
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P2 : 32*t^13 - 2720/3*t^11 + 26008/3*t^9 - 34608*t^7 + 59262*t^5 - 41790*t^3 + 19215/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 32*t^29 - 673430294314984484021216/139527960992289822237*t^27 + 7166986303859563706545748648/23022113563727820669105*t^25 - 781390966601757299291415962224/69066340691183462007315*t^23 + 17753475156494011623736773002102/69066340691183462007315*t^21 - 88217550694764034042247326662266/23022113563727820669105*t^19 + 352601232147804563918755868779777/9208845425491128267642*t^17 - 5930990134724161925062995899902598/23022113563727820669105*t^15 + 14202892543910658710228117364411877/12278460567321504356856*t^13 - 3783230591099896361804617757150177/1116223687938318577896*t^11 + 27837716764475429834380073083743739/4464894751753274311584*t^9 - 219024916593385168364279599608645/32354309795313581968*t^7 + 23393352488929388152056163419837621/5953193002337699082112*t^5 - 6111560775481539139195129854709005/5953193002337699082112*t^3 + 1939616588277833633824116159509265/23812772009350796328448*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
Positive weights:   29 out of 29
Indefinite weights: 0 out of 29
Negative weights:   0 out of 29
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-4.1553186931104200515 + 1.2763199463060489243e-465j)  +/-  (4.38e-121, 4.38e-121j)
| (3.6658316928775966507 + 1.2027400077403724953e-464j)  +/-  (4.35e-121, 4.35e-121j)
| (-6.0251202340753439513 + 4.7344183397779645027e-475j)  +/-  (1.6e-122, 1.6e-122j)
| (-4.6902511223036155377 + 6.8189258259544667508e-474j)  +/-  (2.79e-121, 2.79e-121j)
| (4.1553186931104200515 + 2.3607006977246525692e-472j)  +/-  (4.84e-121, 4.84e-121j)
| (6.0251202340753439513 + 8.1650982732130489741e-478j)  +/-  (1.69e-122, 1.69e-122j)
| (1.6740644038474549634 - 2.0987433296180319183e-476j)  +/-  (1.15e-122, 1.15e-122j)
| (-5.2936998635635066251 + 1.7523027659066229684e-484j)  +/-  (9.47e-122, 9.47e-122j)
| (-2.7796084806380178827 - 1.3009160939047035039e-482j)  +/-  (2.57e-121, 2.57e-121j)
| (5.2936998635635066251 + 2.7518550648185388063e-482j)  +/-  (1.07e-121, 1.07e-121j)
| (-0.66944416045059213743 + 7.7926893662616087913e-486j)  +/-  (4.21e-125, 4.21e-125j)
| (2.7796084806380178827 + 1.1806113325402861918e-487j)  +/-  (2.7e-121, 2.7e-121j)
| (-1.3117288375389628728 - 1.5564289409759775332e-499j)  +/-  (1.9e-123, 1.9e-123j)
| (3.2091772284106072603 + 8.2857474427924366737e-507j)  +/-  (4.09e-121, 4.09e-121j)
| (-2.0201828704560856329 + 1.319385004816551798e-516j)  +/-  (4.61e-122, 4.61e-122j)
| (2.3808826662414136717 - 9.8743032852205977561e-516j)  +/-  (1.14e-121, 1.14e-121j)
| (0.95857246461381850711 + 1.4723398024542235596e-518j)  +/-  (2.57e-124, 2.57e-124j)
| (-2.3808826662414136717 + 2.4232384306083122206e-521j)  +/-  (1.11e-121, 1.11e-121j)
| (-0.95857246461381850711 + 1.9548485161080900254e-523j)  +/-  (2.58e-124, 2.58e-124j)
| (0.36620009120789904326 - 1.7076018002600746086e-523j)  +/-  (3.07e-126, 3.07e-126j)
| (4.6902511223036155377 - 1.125074985639573531e-521j)  +/-  (2.8e-121, 2.8e-121j)
| (0.66944416045059213743 + 5.5632874801136623815e-523j)  +/-  (4.07e-125, 4.07e-125j)
| (-1.6740644038474549634 + 3.4022030561877965901e-522j)  +/-  (1.19e-122, 1.19e-122j)
| (-3.6658316928775966507 + 7.5766857204240023292e-522j)  +/-  (5.06e-121, 5.06e-121j)
| (-0.36620009120789904326 + 7.1142893523279113395e-527j)  +/-  (3.07e-126, 3.07e-126j)
| (8.973172522245193711e-528 - 1.0765017788223305709e-528j)  +/-  (2.62e-526, 2.62e-526j)
| (1.3117288375389628728 + 6.0418060005164538507e-524j)  +/-  (1.78e-123, 1.78e-123j)
| (-3.2091772284106072603 - 2.856925594165182193e-528j)  +/-  (4e-121, 4e-121j)
| (2.0201828704560856329 - 2.1247279532101316721e-529j)  +/-  (4.45e-122, 4.45e-122j)
-------------------------------------------------
The weights are:
| (9.1154030040601388754e-09 + 1.095030760277627554e-472j)  +/-  (2.14e-44, 5.61e-104j)
| (3.8790073469446402676e-07 - 2.4169810694707295713e-470j)  +/-  (7.54e-44, 1.97e-103j)
| (8.1780676637025954844e-17 - 2.8194571406590541768e-478j)  +/-  (1.8e-49, 4.72e-109j)
| (8.8880800933677487779e-11 - 9.5336439048134777565e-475j)  +/-  (3.86e-46, 1.01e-105j)
| (9.1154030040601388754e-09 - 7.1216619473646099606e-472j)  +/-  (4.95e-46, 1.3e-105j)
| (8.1780676637025954844e-17 + 1.3889568330901780905e-477j)  +/-  (3.95e-51, 1.03e-110j)
| (0.012090363742594227662 + 1.0101372949854046767e-467j)  +/-  (2.02e-38, 5.28e-98j)
| (2.4822237682499410358e-13 + 3.3976459640300711872e-476j)  +/-  (1.16e-48, 3.03e-108j)
| (0.0001034520120717422609 - 5.7757840995485253873e-470j)  +/-  (1.38e-43, 3.61e-103j)
| (2.4822237682499410358e-13 - 2.5198781458221529744e-475j)  +/-  (1.28e-49, 3.36e-109j)
| (0.097163868810179192561 - 4.6061890111405013837e-467j)  +/-  (1.66e-39, 4.33e-99j)
| (0.0001034520120717422609 - 3.6490979790525420733e-469j)  +/-  (6.01e-44, 1.57e-103j)
| (0.037023840575093941127 - 1.0537157279287119678e-467j)  +/-  (9.44e-40, 2.47e-99j)
| (8.412807290520406759e-06 + 9.726883460651862136e-470j)  +/-  (6.19e-45, 1.62e-104j)
| (0.0032945517119965995279 - 1.3457544352217156963e-468j)  +/-  (4.33e-43, 1.13e-102j)
| (0.00073977416063591983754 + 1.4064813919523261032e-468j)  +/-  (1.27e-43, 3.32e-103j)
| (0.073523678154449134012 + 4.4512062578062569249e-467j)  +/-  (7.56e-41, 1.93e-100j)
| (0.00073977416063591983754 + 3.3064234039774496921e-469j)  +/-  (3.06e-44, 8.02e-104j)
| (0.073523678154449134012 + 2.6840965464485282601e-467j)  +/-  (8.84e-41, 2.26e-100j)
| (0.16986664164669874815 + 6.3061987368867170408e-467j)  +/-  (3.28e-41, 8.3e-101j)
| (8.8880800933677487779e-11 + 1.6149031383379419771e-473j)  +/-  (2.8e-49, 7.31e-109j)
| (0.097163868810179192561 - 6.5316767158815480721e-467j)  +/-  (2.03e-41, 5.14e-101j)
| (0.012090363742594227662 + 3.9924377861644017795e-468j)  +/-  (9.41e-43, 2.46e-102j)
| (3.8790073469446402676e-07 - 9.5381716517204315034e-472j)  +/-  (6.22e-48, 1.61e-107j)
| (0.16986664164669874815 + 5.2168158698324231495e-467j)  +/-  (7.26e-42, 1.79e-101j)
| (0.21237003854744634167 - 5.3146111194151168497e-467j)  +/-  (5.47e-42, 1.34e-101j)
| (0.037023840575093941127 - 2.1354443133770458151e-467j)  +/-  (8.23e-44, 2.04e-103j)
| (8.412807290520406759e-06 + 8.0080309023242766111e-471j)  +/-  (3.34e-47, 9.1e-107j)
| (0.0032945517119965995279 - 4.3088831798489812655e-468j)  +/-  (6.24e-45, 1.49e-104j)
