Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 5 18
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Trying to find an order 5 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : t^7 - 53/3*t^5 + 215/3*t^3 - 55*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^25 - 1242923240142407407/3917479702543341*t^23 + 32172829350933064699091/795248379616298223*t^21 - 727510583935616176487947/265082793205432741*t^19 + 29097112278728987208581862/265082793205432741*t^17 - 65066653631891050825905186/24098435745948431*t^15 + 1562920144916143931410675950/37868970457918963*t^13 - 14655353173121149933438272330/37868970457918963*t^11 + 7396791576953884479287819685/3442633677992633*t^9 - 22826622339241546445089698735/3442633677992633*t^7 + 35276920329102940997326533105/3442633677992633*t^5 - 22803484244302509213359763675/3442633677992633*t^3 + 4155542523529489788081714900/3442633677992633*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:
| (5.7775771356646072669 + 1.7480736500897200866e-306j)  +/-  (6.12e-122, 6.12e-122j)
| (-7.7318968855697839378 + 1.6975966327722178521e-312j)  +/-  (1.53e-122, 1.53e-122j)
| (-10.449962011456689747 - 7.3217247808993323319e-325j)  +/-  (1.13e-123, 1.13e-123j)
| (6.6730637311538100616 - 4.2405994535171689011e-329j)  +/-  (3.97e-122, 3.97e-122j)
| (10.449962011456689747 + 1.5725096172303520746e-330j)  +/-  (9.91e-124, 9.91e-124j)
| (3.4833773961004847262 - 4.7235566135010686926e-328j)  +/-  (1.41e-122, 1.41e-122j)
| (4.2056213016062727824 - 8.4837296467255644111e-331j)  +/-  (3.49e-122, 3.49e-122j)
| (-1.5143657800537612228 - 3.0968251129916770764e-342j)  +/-  (1.49e-124, 1.49e-124j)
| (-4.9652937523538005367 + 1.7564931155278913436e-361j)  +/-  (5.24e-122, 5.24e-122j)
| (-6.6730637311538100616 + 6.6052759293765495814e-378j)  +/-  (4.04e-122, 4.04e-122j)
| (1.5143657800537612228 - 2.6801648236316434107e-390j)  +/-  (1.54e-124, 1.54e-124j)
| (2.7911397600829831004 - 5.4977739971931146887e-391j)  +/-  (3.67e-123, 3.67e-123j)
| (-4.2056213016062727824 + 9.7405894499602810645e-387j)  +/-  (3.25e-122, 3.25e-122j)
| (-2.7911397600829831004 + 8.7468653682556471488e-393j)  +/-  (3.63e-123, 3.63e-123j)
| (-2.1290252659381178426 + 7.0956428618761843478e-395j)  +/-  (8.71e-124, 8.71e-124j)
| (0.53880031698647339027 + 3.9201539164418153777e-400j)  +/-  (4.3e-126, 4.3e-126j)
| (7.7318968855697839378 + 1.3735792639792644423e-396j)  +/-  (1.41e-122, 1.41e-122j)
| (4.9652937523538005367 + 2.3348116713762844895e-397j)  +/-  (5.51e-122, 5.51e-122j)
| (-1 + 2.858778910493623187e-399j)  +/-  (3.36e-125, 3.36e-125j)
| (-3.4833773961004847262 - 3.8988197454679823689e-399j)  +/-  (1.48e-122, 1.48e-122j)
| (2.1290252659381178426 + 2.5295714308564690317e-408j)  +/-  (8.24e-124, 8.24e-124j)
| (1 - 2.1495235416250016102e-412j)  +/-  (3.5e-125, 3.5e-125j)
| (-5.7775771356646072669 + 4.9549984756542987439e-418j)  +/-  (5.55e-122, 5.55e-122j)
| (-3.2581594139015404636e-435 - 2.2690753061100013943e-435j)  +/-  (9.93e-434, 9.93e-434j)
| (-0.53880031698647339027 + 2.6181638147423093011e-435j)  +/-  (4.3e-126, 4.3e-126j)
-------------------------------------------------
The weights are:
| (1.9062269455788019053e-08 - 1.0554486849068816353e-313j)  +/-  (1.11e-43, 7.72e-105j)
| (5.0237764582012856781e-14 - 2.7158203771452926151e-318j)  +/-  (3.52e-47, 2.44e-108j)
| (4.2507598271756792681e-22 + 4.1180374042630041996e-322j)  +/-  (2.53e-50, 1.76e-111j)
| (8.1586684735675977154e-11 - 1.9605323254332146845e-315j)  +/-  (7.98e-46, 5.54e-107j)
| (4.2507598271756792681e-22 - 1.4302249081779684897e-321j)  +/-  (5.34e-51, 3.7e-112j)
| (0.0006534294454865725315 + 6.7282055542550661546e-312j)  +/-  (4.77e-41, 3.31e-102j)
| (4.2552200572767041804e-05 - 1.74881338558889753e-312j)  +/-  (2.29e-42, 1.59e-103j)
| (0.072924849260167711552 - 1.2183674759806214938e-310j)  +/-  (1.09e-36, 7.58e-98j)
| (1.3831431377728153432e-06 + 3.4131033460228343982e-314j)  +/-  (4.79e-46, 3.33e-107j)
| (8.1586684735675977154e-11 + 1.4100722910472725671e-316j)  +/-  (3.2e-48, 2.22e-109j)
| (0.072924849260167711552 - 2.0839375200631402667e-310j)  +/-  (1.79e-38, 1.24e-99j)
| (0.005501569358053536854 - 2.3293059879083346303e-311j)  +/-  (1.24e-41, 8.63e-103j)
| (4.2552200572767041804e-05 - 2.753684006363148829e-313j)  +/-  (2.4e-45, 1.66e-106j)
| (0.005501569358053536854 - 8.1182824950764256813e-312j)  +/-  (1.88e-43, 1.3e-104j)
| (0.026632764296295897338 + 3.3762629285185871885e-311j)  +/-  (4.13e-42, 2.87e-103j)
| (0.17213165699513021684 - 5.4225191400866194538e-310j)  +/-  (4.06e-41, 2.81e-102j)
| (5.0237764582012856781e-14 + 1.8773442489041577434e-317j)  +/-  (9.04e-51, 6.27e-112j)
| (1.3831431377728153432e-06 + 4.5140070143795254442e-313j)  +/-  (1.3e-46, 9.03e-108j)
| (0.11049493902123724926 + 3.020784472762245671e-310j)  +/-  (3.64e-42, 2.52e-103j)
| (0.0006534294454865725315 + 1.6667663475172520091e-312j)  +/-  (2.57e-45, 1.79e-106j)
| (0.026632764296295897338 + 7.3165380668342827158e-311j)  +/-  (9.54e-44, 6.61e-105j)
| (0.11049493902123724926 + 4.2853520131372350426e-310j)  +/-  (8.74e-43, 6.07e-104j)
| (1.9062269455788019053e-08 - 2.8837564351070463097e-315j)  +/-  (1.96e-48, 1.36e-109j)
| (0.22323367427202379496 + 5.093474578567281083e-310j)  +/-  (4.64e-43, 3.26e-104j)
| (0.17213165699513021684 - 4.4974145017003383896e-310j)  +/-  (3.35e-43, 2.2e-104j)
