Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 6 16
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Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P3 : t^11 - 6923/164*t^9 + 97479/164*t^7 - 566685/164*t^5 + 1313235/164*t^3 - 418635/82*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^27 - 18602579712383878626727500047181374637/74704257323725979223251765529020284*t^25 + 192929105341891780923534882307275370184011/7395721475048871943101924787373008116*t^23 - 55950380084413613458467937165969594423074041/36978607375244359715509623936865040580*t^21 + 663864826594708668963424528982895827637682549/12326202458414786571836541312288346860*t^19 - 3801287791192870507782550586682542459572035613/3081550614603696642959135328072086715*t^17 + 2078590764950990084632582196395305710554955567/112056385985588968834877648293530426*t^15 - 1839187122969481435753377901357387069479940493/10021302811719338676289870985600282*t^13 + 44010590698246551975681326315142359919699322615/37352128661862989611625882764510142*t^11 - 354948968306563035285879570862895401610640869861/74704257323725979223251765529020284*t^9 + 847268809082663823603602552646224294888980760013/74704257323725979223251765529020284*t^7 - 1075909353398307023974063851904183537025616991035/74704257323725979223251765529020284*t^5 + 585959156894788828875873698514534545937251754645/74704257323725979223251765529020284*t^3 - 38989004364594468641511334375185435705024746445/37352128661862989611625882764510142*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:   27 out of 27
Indefinite weights: 0 out of 27
Negative weights:   0 out of 27
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (3.8404632782027033067 - 3.4199566705258766545e-462j)  +/-  (1.76e-121, 1.76e-121j)
| (-2.9853708046841508504 - 4.2694639107913207965e-466j)  +/-  (1.15e-121, 1.15e-121j)
| (6.1173505205908588426 + 2.3852677575746616656e-467j)  +/-  (1.05e-121, 1.05e-121j)
| (-6.1173505205908588426 + 7.5431580236486525899e-473j)  +/-  (1.06e-121, 1.06e-121j)
| (-4.5448979391212497356 - 2.0016430741196791889e-473j)  +/-  (1.88e-121, 1.88e-121j)
| (5.3014763477984764883 - 3.675476560843028001e-473j)  +/-  (1.75e-121, 1.75e-121j)
| (8.1055899232799438761 - 3.367158419676267045e-477j)  +/-  (7.75e-123, 7.75e-123j)
| (-8.1055899232799438761 + 5.6644694543255444645e-477j)  +/-  (7.35e-123, 7.35e-123j)
| (-3.2728782272458314193 - 3.2227301022610795777e-474j)  +/-  (1.87e-121, 1.87e-121j)
| (1.5479164821821879085 - 1.5531319588888285312e-476j)  +/-  (7.94e-124, 7.94e-124j)
| (1 + 1.364916817583783907e-479j)  +/-  (4.03e-125, 4.03e-125j)
| (7.0232901629029016395 + 6.6530909347312556458e-480j)  +/-  (4.21e-122, 4.21e-122j)
| (-3.8404632782027033067 - 1.4735057199095792797e-480j)  +/-  (1.8e-121, 1.8e-121j)
| (-7.0232901629029016395 - 2.2676499232659270321e-481j)  +/-  (4.07e-122, 4.07e-122j)
| (3.2728782272458314193 - 2.9825048998026709627e-479j)  +/-  (1.77e-121, 1.77e-121j)
| (2.4494897427831780982 - 1.0819412252754646417e-488j)  +/-  (2.25e-122, 2.25e-122j)
| (-5.3014763477984764883 - 4.8101236390215336609e-497j)  +/-  (1.6e-121, 1.6e-121j)
| (-1.961016437141193946 + 2.1951934745246253507e-499j)  +/-  (4.45e-123, 4.45e-123j)
| (-1 - 5.9369215169380874961e-502j)  +/-  (4.03e-125, 4.03e-125j)
| (4.5448979391212497356 + 6.7960126644798815335e-498j)  +/-  (1.71e-121, 1.71e-121j)
| (2.9853708046841508504 - 1.1617811680706802537e-509j)  +/-  (1.26e-121, 1.26e-121j)
| (1.961016437141193946 - 5.9150112976871298196e-521j)  +/-  (4.3e-123, 4.3e-123j)
| (-2.4494897427831780982 - 7.71759586275115044e-525j)  +/-  (2.22e-122, 2.22e-122j)
| (-0.43640296874272388689 + 1.2389604926582741552e-526j)  +/-  (2.45e-126, 2.45e-126j)
| (-1.5479164821821879085 - 2.486077103328085825e-527j)  +/-  (7.47e-124, 7.47e-124j)
| (1.4657027374433479531e-529 - 3.4084013211540173871e-530j)  +/-  (4.06e-528, 4.06e-528j)
| (0.43640296874272388689 - 3.1424986087519633428e-533j)  +/-  (2.45e-126, 2.45e-126j)
-------------------------------------------------
The weights are:
| (0.000167875563269929339 + 2.4757928479348808818e-465j)  +/-  (2.32e-38, 3.24e-98j)
| (0.0018700307591674720403 + 2.3720152254231387733e-465j)  +/-  (3.77e-36, 5.28e-96j)
| (2.5465529869010766443e-09 + 3.8269537745470405789e-470j)  +/-  (5.31e-44, 7.43e-104j)
| (2.5465529869010766443e-09 - 8.7517816797915658328e-471j)  +/-  (1.2e-44, 1.68e-104j)
| (9.543402580773294287e-06 - 4.2541572906818050291e-468j)  +/-  (2.11e-41, 2.96e-101j)
| (2.4643553511255249536e-07 - 1.4025758027086161421e-468j)  +/-  (5.46e-43, 7.65e-103j)
| (2.6835292923650413121e-15 + 4.2825202407654090391e-474j)  +/-  (3.23e-48, 4.52e-108j)
| (2.6835292923650413121e-15 - 1.5291434764601577935e-474j)  +/-  (8.17e-49, 1.14e-108j)
| (0.0006971013750211989649 - 9.9499284038987906177e-466j)  +/-  (1.52e-39, 2.13e-99j)
| (0.058400603298841288783 - 5.13393230726093589e-464j)  +/-  (1.09e-35, 1.52e-95j)
| (0.14030513762584780822 + 5.0661755437760249343e-464j)  +/-  (1.09e-35, 1.52e-95j)
| (7.5300734092034141422e-12 - 6.7236182224487584125e-472j)  +/-  (8.65e-47, 1.21e-106j)
| (0.000167875563269929339 + 7.4780265631837931978e-467j)  +/-  (2.51e-41, 3.51e-101j)
| (7.5300734092034141422e-12 + 1.970090356247472007e-472j)  +/-  (2.92e-47, 4.08e-107j)
| (0.0006971013750211989649 - 1.2454637886764315446e-464j)  +/-  (8.93e-42, 1.25e-101j)
| (0.011199772111725564284 - 2.4927584290646643527e-464j)  +/-  (1.05e-40, 1.47e-100j)
| (2.4643553511255249536e-07 + 2.2419380751233174377e-469j)  +/-  (4.66e-45, 6.52e-105j)
| (0.023332068581095853866 + 1.4004888043464789289e-464j)  +/-  (1.21e-40, 1.69e-100j)
| (0.14030513762584780822 + 2.9726622952427186511e-464j)  +/-  (4.5e-40, 6.3e-100j)
| (9.543402580773294287e-06 + 5.0626874300237665521e-467j)  +/-  (2.32e-44, 3.25e-104j)
| (0.0018700307591674720403 + 1.8937585625804981116e-464j)  +/-  (8.97e-42, 1.26e-101j)
| (0.023332068581095853866 + 4.324156898352537355e-464j)  +/-  (6.44e-41, 9.02e-101j)
| (0.011199772111725564284 - 5.5094195247594724372e-465j)  +/-  (4.61e-42, 6.46e-102j)
| (0.18916701354179256298 - 5.2507361430248142527e-464j)  +/-  (1.79e-41, 2.52e-101j)
| (0.058400603298841288783 - 2.1839403272554534991e-464j)  +/-  (6.93e-42, 9.7e-102j)
| (0.14970120950207338367 + 7.4005033080057417867e-464j)  +/-  (8.37e-42, 1.18e-101j)
| (0.18916701354179256298 - 6.5972543524228523772e-464j)  +/-  (5.61e-42, 7.64e-102j)
