Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 4 18
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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 18 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^27 - 8054880965040595537504108712022329/1308210241253142446361111433731*t^25 + 38318532686490862474726678493408987389/54944830132631982747166680216702*t^23 - 3709235259758805845518111914465376906699/109889660265263965494333360433404*t^21 + 65453924789021995893651495904258813923893/73259773510175976996222240288936*t^19 - 43255743556930569928321216757676028801511/3052490562923999041509260012039*t^17 + 6823477816157005987362812950159827283444729/48839849006783984664148160192624*t^15 - 12043632963166837691018952653624243452039725/13954242573366852761185188626464*t^13 + 46042208177338761495372292691268263221146285/13954242573366852761185188626464*t^11 - 844353751622751312357970658347724980970739555/111633940586934822089481509011712*t^9 + 2195390217545643743067297557248776952554001455/223267881173869644178963018023424*t^7 - 2933303286161246373455525132291856194622316065/446535762347739288357926036046848*t^5 + 1644110385427518271189164617717505558924272025/893071524695478576715852072093696*t^3 - 111889442686943409393747161516766198799180725/893071524695478576715852072093696*t
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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:
| (3.1942607017580172752 - 8.0868520538223975946e-457j)  +/-  (4.13e-122, 4.13e-122j)
| (-4.9564015102711848824 - 6.0259656286222360364e-465j)  +/-  (2.51e-122, 2.51e-122j)
| (4.3141071506541870836 + 1.0390048921334583715e-468j)  +/-  (5.22e-122, 5.22e-122j)
| (-4.3141071506541870836 - 2.5513683013257169337e-478j)  +/-  (4.46e-122, 4.46e-122j)
| (5.7228818520919899332 - 4.7815137613927290899e-482j)  +/-  (5.11e-123, 5.11e-123j)
| (37.691837088994312727 + 7.697799143464899674e-490j)  +/-  (4.4e-125, 4.4e-125j)
| (-37.691837088994312727 - 3.3215668027928478518e-491j)  +/-  (9.04e-125, 9.04e-125j)
| (-1.3414449210883628469 - 1.2133137244664536632e-488j)  +/-  (1.02e-123, 1.02e-123j)
| (-3.1942607017580172752 - 4.2897997543501028956e-488j)  +/-  (4.51e-122, 4.51e-122j)
| (3.7344565011010099084 - 2.9708213148030792486e-493j)  +/-  (5.76e-122, 5.76e-122j)
| (1.0672470719421885588 + 4.4593885924105652194e-503j)  +/-  (3.31e-124, 3.31e-124j)
| (4.9564015102711848824 - 7.6844999066873804563e-507j)  +/-  (2.24e-122, 2.24e-122j)
| (-2.1934331704733237894 + 4.8860344295231792193e-512j)  +/-  (8.93e-123, 8.93e-123j)
| (-0.3118182585570957074 + 4.1496978330028247712e-516j)  +/-  (1.47e-126, 1.47e-126j)
| (-3.7344565011010099084 + 1.8885735915532855848e-511j)  +/-  (4.68e-122, 4.68e-122j)
| (-2.6822224032999497583 + 7.3940255063794919569e-513j)  +/-  (2.17e-122, 2.17e-122j)
| (-3.8607677108198710726e-525 + 2.7379934275712350974e-525j)  +/-  (1.28e-523, 1.28e-523j)
| (-5.7228818520919899332 + 6.7058440170262161603e-514j)  +/-  (4.97e-123, 4.97e-123j)
| (-0.7071067811865475244 - 1.1664415672278582372e-516j)  +/-  (2.37e-125, 2.37e-125j)
| (0.3118182585570957074 - 9.7357685206631640035e-518j)  +/-  (1.3e-126, 1.3e-126j)
| (1.3414449210883628469 + 6.3129551946721872462e-514j)  +/-  (1.02e-123, 1.02e-123j)
| (0.7071067811865475244 + 2.4888669342436666919e-516j)  +/-  (2.39e-125, 2.39e-125j)
| (2.1934331704733237894 + 1.3029425145395144585e-512j)  +/-  (7.53e-123, 7.53e-123j)
| (-1.7320508075688772935 + 1.8781507011755904163e-516j)  +/-  (2.99e-123, 2.99e-123j)
| (-1.0672470719421885588 + 1.1421186696338049829e-517j)  +/-  (3.56e-124, 3.56e-124j)
| (2.6822224032999497583 - 3.5769464705272055316e-515j)  +/-  (2.12e-122, 2.12e-122j)
| (1.7320508075688772935 + 1.5765799507432916778e-522j)  +/-  (2.87e-123, 2.87e-123j)
-------------------------------------------------
The weights are:
| (1.0969829399561777188e-05 + 3.7441775971132280638e-461j)  +/-  (1.87e-40, 8.06e-101j)
| (8.3170036595688753649e-12 - 2.3517180924308515951e-466j)  +/-  (5.67e-46, 2.45e-106j)
| (2.822641293439896717e-09 - 4.8579035038755560821e-464j)  +/-  (2.83e-44, 1.22e-104j)
| (2.822641293439896717e-09 + 7.2453908712339058803e-465j)  +/-  (1.07e-44, 4.6e-105j)
| (2.9659995857988814657e-15 - 9.198737813318907375e-468j)  +/-  (6.51e-48, 2.81e-108j)
| (5.8660790842740262777e-56 + 3.72964005749943192e-490j)  +/-  (6.39e-70, 2.76e-130j)
| (5.8660790842740262777e-56 - 3.1468775386068801756e-490j)  +/-  (4.48e-70, 1.93e-130j)
| (0.029618303265473400068 + 2.8463981344469876464e-459j)  +/-  (9.52e-37, 4.11e-97j)
| (1.0969829399561777188e-05 + 1.3886059357883459457e-462j)  +/-  (1e-43, 4.31e-104j)
| (2.7595062565327185381e-07 + 1.5716098696104678154e-462j)  +/-  (1.79e-44, 7.71e-105j)
| (0.053003966905533439969 - 1.2085645823810767809e-458j)  +/-  (3.78e-37, 1.63e-97j)
| (8.3170036595688753649e-12 + 1.0877711743482944065e-465j)  +/-  (4.76e-47, 2.05e-107j)
| (0.0021906887213644710218 + 8.5038189541632842915e-461j)  +/-  (2.36e-42, 1.02e-102j)
| (0.18867004994440842309 - 1.6333749503040808003e-458j)  +/-  (5.38e-39, 2.32e-99j)
| (2.7595062565327185381e-07 - 1.2253019210344027552e-463j)  +/-  (7.93e-46, 3.42e-106j)
| (0.00021184727145440471032 - 1.1898575322956392405e-461j)  +/-  (8.36e-44, 3.61e-104j)
| (0.15305839319021698062 + 2.2707971123420795376e-458j)  +/-  (3.06e-39, 1.32e-99j)
| (2.9659995857988814657e-15 + 2.6084727079037387629e-468j)  +/-  (1.22e-50, 5.26e-111j)
| (0.13739520919768364555 + 9.2647557641149777955e-459j)  +/-  (7.92e-40, 3.41e-100j)
| (0.18867004994440842309 - 1.9867670076271503131e-458j)  +/-  (6.47e-40, 2.79e-100j)
| (0.029618303265473400068 + 6.9680019771206757957e-459j)  +/-  (2.79e-42, 1.2e-102j)
| (0.13739520919768364555 + 1.4532762357861581711e-458j)  +/-  (6.02e-41, 2.6e-101j)
| (0.0021906887213644710218 + 4.577809046572897641e-460j)  +/-  (4.84e-45, 2.09e-105j)
| (0.012369489487987247135 - 5.5737330825976177928e-460j)  +/-  (2.19e-43, 9.49e-104j)
| (0.053003966905533439969 - 6.0322155344916269365e-459j)  +/-  (3.07e-42, 1.33e-102j)
| (0.00021184727145440471032 - 1.3655575582055689192e-460j)  +/-  (4.15e-46, 1.83e-106j)
| (0.012369489487987247135 - 1.8778388480953201211e-459j)  +/-  (2.01e-44, 8.31e-105j)
