Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 4 16
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Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
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Trying to find an order 4 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P3 : t^9 - 71/3*t^7 + 1399/9*t^5 - 2965/9*t^3 + 590/3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^25 - 174007375964576309435136638373/733464270055645672977186689*t^23 + 153951172651106060050334095501747/6601178430500811056794680201*t^21 - 24632777273882457889865235837261211/19803535291502433170384040603*t^19 + 2354053015318629102743582121494602924/59410605874507299511152121809*t^17 - 46538604634608219310868929659510737410/59410605874507299511152121809*t^15 + 14767899455653971947839679012960762410/1523348868577110243875695431*t^13 - 113035766929709626151596261583095747070/1523348868577110243875695431*t^11 + 518594847574714663638285824411403957695/1523348868577110243875695431*t^9 - 149887996532323417856644169086966276615/169260985397456693763966159*t^7 + 200323274179145436469215778597849666625/169260985397456693763966159*t^5 - 112297857423043112018826691186454021075/169260985397456693763966159*t^3 + 5095223509927489689014550324111477250/56420328465818897921322053*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:
| (6.1010844584444323701 - 2.3491036261616885859e-325j)  +/-  (5.62e-122, 5.62e-122j)
| (8.093426170168748208 + 6.8217198380884769847e-340j)  +/-  (5.32e-123, 5.32e-123j)
| (-8.093426170168748208 + 7.5854913258069918641e-352j)  +/-  (5.73e-123, 5.73e-123j)
| (-6.1010844584444323701 - 2.8139883042942315354e-351j)  +/-  (5.35e-122, 5.35e-122j)
| (7.0094384241067441424 + 4.028416108152659168e-356j)  +/-  (2.57e-122, 2.57e-122j)
| (-7.0094384241067441424 - 1.3249531031800802609e-366j)  +/-  (2.74e-122, 2.74e-122j)
| (5.281326655926636035 - 1.448558960423804886e-369j)  +/-  (7.19e-122, 7.19e-122j)
| (-1.5093152835436173382 + 4.5715309906027121267e-375j)  +/-  (3.89e-124, 3.89e-124j)
| (-5.281326655926636035 - 1.8607227267533577793e-373j)  +/-  (7e-122, 7e-122j)
| (-1 + 1.0786056678727220563e-375j)  +/-  (4.33e-125, 4.33e-125j)
| (1.5093152835436173382 - 3.4354184933612482667e-374j)  +/-  (4.1e-124, 4.1e-124j)
| (2.4494897427831780982 - 1.1224430392723838181e-372j)  +/-  (3.96e-123, 3.96e-123j)
| (-3.7932353000477464006 - 1.5112166091995918966e-379j)  +/-  (2.72e-122, 2.72e-122j)
| (-1.8970921999035365153 + 2.4916380617174260925e-380j)  +/-  (1.48e-123, 1.48e-123j)
| (-2.4494897427831780982 - 1.0010826170967348664e-379j)  +/-  (4.54e-123, 4.54e-123j)
| (0.44098051603272466819 + 1.2990092313371329271e-382j)  +/-  (2.49e-126, 2.49e-126j)
| (1 - 1.2398236036371570481e-381j)  +/-  (4.33e-125, 4.33e-125j)
| (-3.1019820501215273233 + 3.2152707544689233842e-379j)  +/-  (1.1e-122, 1.1e-122j)
| (3.1019820501215273233 - 4.2830914120340701749e-384j)  +/-  (1.13e-122, 1.13e-122j)
| (3.7932353000477464006 - 2.2624586222555452204e-404j)  +/-  (2.73e-122, 2.73e-122j)
| (-1.0478032489827437913e-423 - 4.4029795473043296999e-423j)  +/-  (1.13e-421, 1.13e-421j)
| (1.8970921999035365153 + 3.346702106824128838e-419j)  +/-  (1.5e-123, 1.5e-123j)
| (4.5173694961524419313 - 4.4062898512305964051e-431j)  +/-  (5.31e-122, 5.31e-122j)
| (-4.5173694961524419313 + 1.2834514507784358051e-440j)  +/-  (5.19e-122, 5.19e-122j)
| (-0.44098051603272466819 + 1.328366324764673194e-447j)  +/-  (2.16e-126, 2.16e-126j)
-------------------------------------------------
The weights are:
| (2.8224051156123765114e-09 + 2.3661822307223668162e-333j)  +/-  (3.26e-45, 1.14e-105j)
| (2.9648891649656180409e-15 - 1.4084002448644929687e-337j)  +/-  (3.01e-48, 1.05e-108j)
| (2.9648891649656180409e-15 + 1.976830782027756334e-338j)  +/-  (2.13e-49, 7.42e-110j)
| (2.8224051156123765114e-09 + 5.4335603258250809691e-335j)  +/-  (5.92e-47, 2.06e-107j)
| (8.315495083621511987e-12 + 2.5607932327226826114e-335j)  +/-  (8.85e-48, 3.08e-108j)
| (8.315495083621511987e-12 - 1.7742287695334260343e-336j)  +/-  (2.95e-48, 1.03e-108j)
| (2.7594171590299776598e-07 - 1.2664221352621599138e-332j)  +/-  (6.45e-46, 2.25e-106j)
| (0.053004441932920119316 - 4.1682778694211013817e-329j)  +/-  (9.01e-38, 3.14e-98j)
| (2.7594171590299776598e-07 - 9.1207338781820728321e-334j)  +/-  (2.51e-46, 8.74e-107j)
| (0.13739459664090088616 + 6.2841768136863235546e-329j)  +/-  (1.57e-38, 5.46e-99j)
| (0.053004441932920119316 - 6.9085051128821316217e-329j)  +/-  (8.18e-39, 2.85e-99j)
| (0.012369450855440736234 - 9.2670911556145624938e-330j)  +/-  (5.24e-42, 1.83e-102j)
| (0.00021184779334027693017 - 8.6834061964908260707e-332j)  +/-  (6.13e-45, 2.14e-105j)
| (0.029618061245413510546 + 1.9909958160639262375e-329j)  +/-  (4.39e-41, 1.53e-101j)
| (0.012369450855440736234 - 3.9575893147076490468e-330j)  +/-  (8e-43, 2.79e-103j)
| (0.18866904339664570246 - 1.2494671940227625393e-328j)  +/-  (2.77e-40, 9.66e-101j)
| (0.13739459664090088616 + 8.7480359655509344515e-329j)  +/-  (1.98e-40, 6.89e-101j)
| (0.002190694902967108127 + 6.1275208343706029177e-331j)  +/-  (2.86e-44, 9.97e-105j)
| (0.002190694902967108127 + 1.8802953048499126956e-330j)  +/-  (7.18e-46, 2.5e-106j)
| (0.00021184779334027693017 - 3.7227908586816231607e-331j)  +/-  (2.85e-47, 9.95e-108j)
| (0.15306122941795454186 + 1.4682850657036842542e-328j)  +/-  (6.54e-43, 2.29e-103j)
| (0.029618061245413510546 + 3.7879080844068712116e-329j)  +/-  (1.34e-44, 4.71e-105j)
| (1.0969750954910715367e-05 + 6.8680490419940288738e-332j)  +/-  (2.51e-48, 8.73e-109j)
| (1.0969750954910715367e-05 + 1.0243517630786822943e-332j)  +/-  (1.8e-48, 6.09e-109j)
| (0.18866904339664570246 - 1.0810216985604819583e-328j)  +/-  (4.6e-44, 1.68e-104j)
