Starting with polynomial:
P : 1/720*t^6 - 1/20*t^5 + 5/8*t^4 - 10/3*t^3 + 15/2*t^2 - 6*t + 1
Extension levels are: 6 12
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Trying to find an order 12 Kronrod extension for:
P1 : 1/720*t^6 - 1/20*t^5 + 5/8*t^4 - 10/3*t^3 + 15/2*t^2 - 6*t + 1
Solvable: 1
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Ending with final polynomial:
P : 1/720*t^18 - 33255221371886127/34757756461623743*t^17 + 30206384193517003044/173788782308118715*t^16 - 2720969863800472808106/173788782308118715*t^15 + 1647820089272647841418825/1946434361850929608*t^14 - 14591505802007837764750035/486608590462732402*t^13 + 709035899712122762576965375/973217180925464804*t^12 - 432627251105229480605887380/34757756461623743*t^11 + 36809819304179340538843285815/243304295231366201*t^10 - 319018397664033381317200167300/243304295231366201*t^9 + 1959762976637263014431268926190/243304295231366201*t^8 - 8415003011924259306782280489600/243304295231366201*t^7 + 3524939371049709342680351177040/34757756461623743*t^6 - 6812221008259057617687822989760/34757756461623743*t^5 + 8226488246661538240805174988000/34757756461623743*t^4 - 5712070601711490893770079577600/34757756461623743*t^3 + 1975871799779310464027424912000/34757756461623743*t^2 - 251705839963395060009627379200/34757756461623743*t + 4237901511990657331621996800/34757756461623743
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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
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The nodes are:
| (467.06028332685210525 + 2.1391772176970773289e-331j)  +/-  (2.3e-123, 2.3e-123j)
| (46.581690638240083777 + 7.4520437028552318287e-327j)  +/-  (6.93e-121, 6.93e-121j)
| (30.285940892429514958 + 1.382899697546314816e-328j)  +/-  (1.08e-119, 1.08e-119j)
| (37.257512856364665704 - 1.364050679196356551e-334j)  +/-  (3.93e-120, 3.93e-120j)
| (12.63425763893757949 + 4.4312622407852065292e-343j)  +/-  (1.47e-119, 1.47e-119j)
| (5.7751435691045105018 - 3.3595591379903579789e-357j)  +/-  (1.4e-120, 1.4e-120j)
| (24.648277558608535686 - 1.3723692890215150078e-364j)  +/-  (1.91e-119, 1.91e-119j)
| (9.8374674183825899177 - 1.4581749211721651538e-373j)  +/-  (7.96e-120, 7.96e-120j)
| (0.22284660417926068946 - 1.461055108313984499e-382j)  +/-  (3.09e-126, 3.09e-126j)
| (4.2964025075309456817 - 1.7958808628271140718e-385j)  +/-  (3.72e-121, 3.72e-121j)
| (0.64556582620629415676 + 8.4658918924876396598e-390j)  +/-  (1.12e-124, 1.12e-124j)
| (0.0197203113963623768 - 3.0776040141923317309e-393j)  +/-  (6.75e-128, 6.75e-128j)
| (19.948522004631981224 - 7.5288168227460313175e-403j)  +/-  (2.76e-119, 2.76e-119j)
| (15.982873980601701783 + 1.8966546465042393087e-418j)  +/-  (2.2e-119, 2.2e-119j)
| (2.9927363260593140777 - 3.9311234131407190913e-423j)  +/-  (5.77e-122, 5.77e-122j)
| (1.9321629075466997921 + 2.8918125620985637492e-426j)  +/-  (8.51e-123, 8.51e-123j)
| (1.1889321016726230307 - 7.494649404524107523e-433j)  +/-  (1.08e-123, 1.08e-123j)
| (7.5649485110112301746 - 1.0125769222288454536e-441j)  +/-  (3.89e-120, 3.89e-120j)
-------------------------------------------------
The weights are:
| (7.1388888631515963959e-55 - 1.30393595089437635e-365j)  +/-  (9.47e-72, 6.32e-131j)
| (6.6724734511323574845e-20 + 3.0810728539670502199e-346j)  +/-  (5.8e-55, 3.87e-114j)
| (4.3674692309139487911e-13 - 3.474852840318250168e-341j)  +/-  (2.04e-52, 1.36e-111j)
| (5.1935099300626885791e-16 - 1.8357323431498775255e-343j)  +/-  (1.16e-53, 7.76e-113j)
| (9.988489004778814179e-06 - 1.3008713084762568715e-337j)  +/-  (1.63e-48, 1.09e-107j)
| (0.0049507866311809364369 + 1.4188456915916466558e-335j)  +/-  (4.56e-45, 3.04e-104j)
| (1.0116327204498375137e-10 + 2.6070769724935499197e-340j)  +/-  (6.42e-52, 4.29e-111j)
| (0.00013525522945065541113 + 7.9225089602149728377e-337j)  +/-  (5.53e-48, 3.69e-107j)
| (0.26118465503789362435 + 1.9146716501877482745e-334j)  +/-  (3.07e-43, 2.05e-102j)
| (0.018923764200942872553 - 3.7089166135290010755e-335j)  +/-  (2.08e-45, 1.39e-104j)
| (0.26037770977785120044 - 2.6995968977660998047e-334j)  +/-  (1.13e-43, 7.54e-103j)
| (0.077436621787612288636 - 7.2559631663558317011e-335j)  +/-  (1.9e-43, 1.27e-102j)
| (9.3479915667456158189e-09 - 2.2300174849212718103e-339j)  +/-  (2.17e-51, 1.45e-110j)
| (4.1699523195839107513e-07 + 1.8271694023707325626e-338j)  +/-  (2.18e-50, 1.46e-109j)
| (0.060242035325495616166 + 8.2144453754045489657e-335j)  +/-  (2.62e-46, 1.76e-105j)
| (0.13089533601424796711 - 1.6824992790393979413e-334j)  +/-  (5.04e-46, 3.4e-105j)
| (0.18479828888818753518 + 2.6331484711116840992e-334j)  +/-  (1.08e-45, 7.32e-105j)
| (0.0010451321733084613719 - 3.9349385381234680022e-336j)  +/-  (3.08e-48, 2.03e-107j)
