Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 5 24
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P2 : 4*t^7 - 106/3*t^5 + 215/3*t^3 - 55/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^31 - 193315083164302897574735353502/245453218400091920776940445*t^29 + 16525784320411178110137554287243/245453218400091920776940445*t^27 - 540039099972192259946823127602279/163635478933394613851293630*t^25 + 6756917853779025669084479334295455/65454191573357845540517452*t^23 - 40595088809386224908564905755364635/18701197592387955868719272*t^21 + 1178205960512932611330713531009743215/37402395184775911737438544*t^19 - 23852244649500030519836924678879492745/74804790369551823474877088*t^17 + 336467457528962278004654997588483422655/149609580739103646949754176*t^15 - 3267362881668834906997293857098828883925/299219161478207293899508352*t^13 + 21302598534616197849725834520688607676825/598438322956414587799016704*t^11 - 89362716720645198654683411072553147547575/1196876645912829175598033408*t^9 + 32138068803752257768465039917519303629925/341964755975094050170866688*t^7 - 43202649335807960445596863464308613916575/683929511950188100341733376*t^5 + 25031976048061962234911105259205584205875/1367859023900376200683466752*t^3 - 3822577331156843962680063363436679359125/2735718047800752401366933504*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:
| (-4.707887344096240087 - 1.0186222435504353219e-425j)  +/-  (2.07e-120, 2.07e-120j)
| (-5.2584719332290285449 + 2.5490723776142666592e-432j)  +/-  (9.39e-121, 9.39e-121j)
| (-6.6035501200484715517 + 2.7775357595956366537e-434j)  +/-  (5.24e-122, 5.24e-122j)
| (3.7117796631060002312 + 9.894436288303144117e-432j)  +/-  (2.13e-120, 2.13e-120j)
| (4.707887344096240087 + 1.3069151511106782566e-433j)  +/-  (1.7e-120, 1.7e-120j)
| (1.9191783517640334728 - 1.3265190915420168338e-436j)  +/-  (5.34e-122, 5.34e-122j)
| (-5.8705233892553708824 + 6.236837990993513655e-435j)  +/-  (3e-121, 3e-121j)
| (-2.4631197782145911371 - 5.6574407212197992323e-434j)  +/-  (1.47e-120, 1.47e-120j)
| (6.6035501200484715517 + 9.5168269471853603082e-441j)  +/-  (4.09e-122, 4.09e-122j)
| (-2.3162044632845871765 - 1.8496395147533235861e-437j)  +/-  (7.19e-121, 7.19e-121j)
| (2.3162044632845871765 + 8.0715856116755223986e-439j)  +/-  (7.48e-121, 7.48e-121j)
| (-3.7117796631060002312 + 2.8501486253879389135e-444j)  +/-  (1.95e-120, 1.95e-120j)
| (5.2584719332290285449 - 7.7294657204081933315e-451j)  +/-  (9.22e-121, 9.22e-121j)
| (3.2484237652943742172 - 1.5167477278897063255e-449j)  +/-  (1.7e-120, 1.7e-120j)
| (4.1961509788512259878 - 5.3501418874535333654e-451j)  +/-  (2.39e-120, 2.39e-120j)
| (5.8705233892553708824 + 3.8777056748362407955e-453j)  +/-  (3.16e-121, 3.16e-121j)
| (1.0994828390412916779 + 3.8014789691412037655e-455j)  +/-  (4.24e-124, 4.24e-124j)
| (-1.0994828390412916779 - 2.4075750243767547764e-455j)  +/-  (4.53e-124, 4.53e-124j)
| (-1.5054482028623358456 + 1.2747105004660296632e-454j)  +/-  (5.13e-123, 5.13e-123j)
| (2.805040489583001551 + 7.7939774132921857192e-452j)  +/-  (1.37e-120, 1.37e-120j)
| (1.5054482028623358456 - 1.4682511530344211236e-455j)  +/-  (4.56e-123, 4.56e-123j)
| (0.7071067811865475244 + 5.2416700668713438603e-460j)  +/-  (2.91e-125, 2.91e-125j)
| (2.2208933643669000591e-460 + 1.9047063976948950667e-460j)  +/-  (9.07e-459, 9.07e-459j)
| (-3.2484237652943742172 + 1.2783237747879503089e-454j)  +/-  (1.63e-120, 1.63e-120j)
| (-2.805040489583001551 + 1.9554937102380940467e-468j)  +/-  (1.38e-120, 1.38e-120j)
| (-4.1961509788512259878 - 2.4730858939402988845e-479j)  +/-  (2.41e-120, 2.41e-120j)
| (0.33861828754162769618 + 2.2593983030669518658e-492j)  +/-  (3.19e-126, 3.19e-126j)
| (2.4631197782145911371 - 1.2256237596578365097e-489j)  +/-  (1.26e-120, 1.26e-120j)
| (-1.9191783517640334728 + 8.4542958589041044372e-492j)  +/-  (5.42e-122, 5.42e-122j)
| (-0.7071067811865475244 + 5.3325412038719713429e-496j)  +/-  (2.73e-125, 2.73e-125j)
| (-0.33861828754162769618 - 1.1240865101194374827e-498j)  +/-  (3.19e-126, 3.19e-126j)
-------------------------------------------------
The weights are:
| (7.059904041318889451e-11 - 3.952170242124984531e-435j)  +/-  (1.64e-36, 2.86e-96j)
| (3.1838102561754028429e-13 - 5.8813052942811808045e-437j)  +/-  (4.31e-38, 7.51e-98j)
| (5.4842555550131140184e-20 - 3.2642318579177605787e-441j)  +/-  (1.24e-41, 2.16e-101j)
| (2.7732875752126613316e-07 - 1.3956204250139702124e-434j)  +/-  (1.7e-36, 2.97e-96j)
| (7.059904041318889451e-11 - 7.6358985413588724527e-437j)  +/-  (1.51e-39, 2.63e-99j)
| (0.0058891845520775767337 + 1.6998009203691460638e-431j)  +/-  (1.21e-29, 2.11e-89j)
| (3.9946778316436988942e-16 + 6.7380962184366796278e-439j)  +/-  (1.77e-40, 3.08e-100j)
| (0.00018435102875898057251 + 3.922445530424637838e-431j)  +/-  (8.47e-33, 1.48e-92j)
| (5.4842555550131140184e-20 + 5.4699877445773893855e-442j)  +/-  (6.89e-45, 1.2e-104j)
| (0.00086002575368211658016 - 5.2460950523968823787e-431j)  +/-  (1.92e-32, 3.34e-92j)
| (0.00086002575368211658016 - 1.7864767008433046663e-431j)  +/-  (1.4e-33, 2.45e-93j)
| (2.7732875752126613316e-07 - 1.1785214575793179108e-433j)  +/-  (2.1e-37, 3.67e-97j)
| (3.1838102561754028429e-13 + 3.2486006151427994005e-438j)  +/-  (5.86e-42, 1.02e-101j)
| (6.6934464076465601738e-06 + 1.3949251271515237503e-433j)  +/-  (1.76e-37, 3.08e-97j)
| (6.3177689136264169159e-09 + 1.1876879407745138556e-435j)  +/-  (1.28e-39, 2.23e-99j)
| (3.9946778316436988942e-16 - 7.4047761532618387287e-440j)  +/-  (8.51e-44, 1.48e-103j)
| (0.067435715679031119586 + 5.0539100177556175229e-431j)  +/-  (2.8e-33, 4.88e-93j)
| (0.067435715679031119586 + 8.1334868684530402245e-431j)  +/-  (1.85e-33, 3.22e-93j)
| (0.024027106625354611443 - 5.4304322152876951542e-431j)  +/-  (4.4e-35, 7.66e-95j)
| (9.2743858390955478085e-05 - 1.4756863828114137038e-432j)  +/-  (2.71e-37, 4.73e-97j)
| (0.024027106625354611443 - 2.7990649271859160011e-431j)  +/-  (2.06e-35, 3.59e-95j)
| (0.13093417475324305957 - 8.9273794217529269651e-431j)  +/-  (1.95e-34, 3.4e-94j)
| (0.18653202856361616987 - 1.7714324188475955121e-430j)  +/-  (8.4e-35, 1.46e-94j)
| (6.6934464076465601738e-06 + 7.6014667362055221033e-433j)  +/-  (8.76e-40, 1.53e-99j)
| (9.2743858390955478085e-05 - 5.8253050807228863029e-432j)  +/-  (9.15e-39, 1.59e-98j)
| (6.3177689136264169159e-09 + 2.0674279784942071774e-434j)  +/-  (5.7e-42, 9.95e-102j)
| (0.17730370630380159269 + 1.4181688603092118703e-430j)  +/-  (3.49e-36, 6.07e-96j)
| (0.00018435102875898057251 + 1.2280147254249232307e-431j)  +/-  (6.05e-38, 1.06e-97j)
| (0.0058891845520775767337 + 4.0390890624285152386e-431j)  +/-  (7.34e-38, 1.28e-97j)
| (0.13093417475324305957 - 1.208281443505922341e-430j)  +/-  (2.06e-37, 3.64e-97j)
| (0.17730370630380159269 + 1.6379689428665523809e-430j)  +/-  (3.55e-37, 5.96e-97j)
