Starting with polynomial:
P : t^3 - 3*t
Extension levels are: 3 10 22
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Trying to find an order 10 Kronrod extension for:
P1 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : t^13 - 629/8*t^11 + 17435/8*t^9 - 105435/4*t^7 + 557865/4*t^5 - 2248785/8*t^3 + 1133055/8*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^35 - 1957041419687385592031338609712681/4164678192223993000091454933360*t^33 + 9696925531202360372178218788670551037/99952276613375832002194918400640*t^31 - 1628711726900995036250757940878068631175/139933187258726164803072885760896*t^29 + 1645753115556151343311476511346938655560321/1819131434363440142439947514891648*t^27 - 1388943929942253011288467747493161262291763/28875102132753018133967420871296*t^25 + 364058719364688754622059593697669282458715983/202125714929271126937771946099072*t^23 - 9741581530050132770614861112085974602118495199/202125714929271126937771946099072*t^21 + 26734943282103985962448371008342813155030180035/28875102132753018133967420871296*t^19 - 367490989508181877492439611443021093684722990895/28875102132753018133967420871296*t^17 + 3574790272569616860466666857790935831422103074055/28875102132753018133967420871296*t^15 - 1856580885973061254279193935525200350848071389835/2221161702519462933382109297792*t^13 + 8443231975521404105849581423801946507307883011105/2221161702519462933382109297792*t^11 - 24729747304468654744069032643480689722775482051325/2221161702519462933382109297792*t^9 + 43562151113534219814435895926332963425659001577775/2221161702519462933382109297792*t^7 - 41264607072279405372992746846401841045937885148975/2221161702519462933382109297792*t^5 + 17063544790674883176058839445684896043546200760725/2221161702519462933382109297792*t^3 - 1868015204665759955430194668363779739204907275425/2221161702519462933382109297792*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:   35 out of 35
Indefinite weights: 0 out of 35
Negative weights:   0 out of 35
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (5.8238536767427603773 - 6.9000965405024992481e-450j)  +/-  (1.53e-119, 1.53e-119j)
| (-5.1981333225525097202 + 1.4462903977983804375e-459j)  +/-  (1.12e-119, 1.12e-119j)
| (-9.8373893164697228294 + 7.6600587373687780475e-465j)  +/-  (1.55e-121, 1.55e-121j)
| (6.4863744342511499648 + 5.1429609040185753105e-461j)  +/-  (1.25e-119, 1.25e-119j)
| (8.8100488272596913813 - 1.5720879941541228972e-469j)  +/-  (1.31e-120, 1.31e-120j)
| (7.9563776940339709852 - 8.6938102588090332398e-478j)  +/-  (4.67e-120, 4.67e-120j)
| (2.6308380841127442917 - 1.8186143145605488095e-486j)  +/-  (1.51e-121, 1.51e-121j)
| (-2.6308380841127442917 - 1.2711647532581806673e-487j)  +/-  (1.44e-121, 1.44e-121j)
| (9.8373893164697228294 + 2.8907050243112234383e-485j)  +/-  (1.64e-121, 1.64e-121j)
| (-7.9563776940339709852 + 6.6850339543482826014e-486j)  +/-  (4.22e-120, 4.22e-120j)
| (3.5773982809904283695 - 1.7402427312066004331e-485j)  +/-  (1.78e-120, 1.78e-120j)
| (-3.5773982809904283695 + 2.7108407559457596217e-486j)  +/-  (1.96e-120, 1.96e-120j)
| (1.7320508075688772935 + 1.1014341598644116067e-489j)  +/-  (5.1e-123, 5.1e-123j)
| (-3.1102702826533725825 + 3.2008284312106062554e-487j)  +/-  (5.79e-121, 5.79e-121j)
| (-6.4863744342511499648 + 4.3423162872803107959e-485j)  +/-  (1.33e-119, 1.33e-119j)
| (-4.6096758921816875609 - 4.1438041279447307414e-487j)  +/-  (7.19e-120, 7.19e-120j)
| (7.1922580330761744432 - 1.5359232135609932007e-486j)  +/-  (1e-119, 1e-119j)
| (-7.1922580330761744432 - 3.6083509393551401539e-490j)  +/-  (9.61e-120, 9.61e-120j)
| (3.1102702826533725825 + 1.3764539079430813439e-490j)  +/-  (5.82e-121, 5.82e-121j)
| (-1.7320508075688772935 + 3.9668464915293099854e-493j)  +/-  (5e-123, 5e-123j)
| (-0.85995874045067267595 - 9.2297801392063846988e-495j)  +/-  (5.65e-125, 5.65e-125j)
| (-2.1594125703844250991 + 6.7375338899278481486e-493j)  +/-  (2.71e-122, 2.71e-122j)
| (4.6096758921816875609 - 4.4712244720685008353e-489j)  +/-  (7.18e-120, 7.18e-120j)
| (-5.8238536767427603773 + 4.8405689954483738805e-493j)  +/-  (1.4e-119, 1.4e-119j)
| (4.0671618472579156455 - 2.022395049885476889e-493j)  +/-  (4.45e-120, 4.45e-120j)
| (-8.8100488272596913813 + 7.0187837006087557842e-501j)  +/-  (1.24e-120, 1.24e-120j)
| (-0.40575512453257556375 + 1.1774050522709673505e-504j)  +/-  (3.24e-126, 3.24e-126j)
| (0.85995874045067267595 + 4.4484005807818940051e-503j)  +/-  (5.65e-125, 5.65e-125j)
| (0.40575512453257556375 - 1.5652375328219667106e-504j)  +/-  (3.24e-126, 3.24e-126j)
| (-3.5984579873347089819e-506 - 2.0207083740588393167e-506j)  +/-  (1.44e-504, 1.44e-504j)
| (1.3147468329792055678 - 3.8125842295871857048e-502j)  +/-  (6.44e-124, 6.44e-124j)
| (5.1981333225525097202 + 5.5400136073645238596e-501j)  +/-  (1.14e-119, 1.14e-119j)
| (2.1594125703844250991 - 2.8340511517947502886e-514j)  +/-  (2.95e-122, 2.95e-122j)
| (-4.0671618472579156455 - 2.3472191031735157973e-515j)  +/-  (4.23e-120, 4.23e-120j)
| (-1.3147468329792055678 - 1.1042463802132336421e-520j)  +/-  (6.42e-124, 6.42e-124j)
-------------------------------------------------
The weights are:
| (1.1078361998241356542e-08 + 2.9829656520681370777e-457j)  +/-  (1.21e-32, 2.89e-91j)
| (3.2902944052028258171e-07 - 7.3946681380462362397e-458j)  +/-  (1.2e-31, 2.86e-90j)
| (4.5735526921276173753e-22 - 6.5303089510868058289e-467j)  +/-  (4.76e-41, 1.13e-99j)
| (1.990605388259805749e-10 + 8.4208669650456735793e-459j)  +/-  (1.26e-34, 3e-93j)
| (5.1199078722220798243e-18 - 6.1005655627884928929e-464j)  +/-  (7.15e-40, 1.7e-98j)
| (5.7346787621540178101e-15 + 4.7505539134694388963e-462j)  +/-  (2.22e-38, 5.29e-97j)
| (0.0060452072997491820322 + 7.1798182349633818739e-454j)  +/-  (3.54e-26, 8.42e-85j)
| (0.0060452072997491820322 + 2.7115443337641308253e-454j)  +/-  (2.72e-27, 6.47e-86j)
| (4.5735526921276173753e-22 + 2.5481960121595430023e-466j)  +/-  (4.76e-42, 1.13e-100j)
| (5.7346787621540178101e-15 - 7.3515966981346006213e-463j)  +/-  (2.84e-41, 6.76e-100j)
| (0.00031165920298949983544 + 9.8454442441405844896e-455j)  +/-  (1.06e-30, 2.52e-89j)
| (0.00031165920298949983544 + 2.3525963747882834124e-455j)  +/-  (8e-32, 1.9e-90j)
| (0.036370169937916793081 + 3.3067429292221282403e-453j)  +/-  (8.35e-25, 1.99e-83j)
| (0.0014937001783885241605 - 8.5752099491984210894e-455j)  +/-  (2.33e-30, 5.54e-89j)
| (1.990605388259805749e-10 - 4.5320030963169187414e-460j)  +/-  (2.92e-39, 6.95e-98j)
| (5.5051000870902684479e-06 + 6.6976364110585938869e-457j)  +/-  (2.38e-35, 5.66e-94j)
| (1.7079298063876292677e-12 - 2.1594352528377086524e-460j)  +/-  (6.12e-40, 1.46e-98j)
| (1.7079298063876292677e-12 + 2.2702483538455683063e-461j)  +/-  (1.19e-40, 2.83e-99j)
| (0.0014937001783885241605 - 2.8232774790573454169e-454j)  +/-  (7.04e-33, 1.68e-91j)
| (0.036370169937916793081 + 1.7907240914637443344e-453j)  +/-  (7.84e-30, 1.87e-88j)
| (0.12807203158896278002 + 4.554103187935079326e-453j)  +/-  (9.4e-30, 2.24e-88j)
| (0.017542010785325942435 - 7.8810917273776439001e-454j)  +/-  (8e-31, 1.91e-89j)
| (5.5051000870902684479e-06 + 5.7553341152804608047e-456j)  +/-  (4.28e-37, 1.02e-95j)
| (1.1078361998241356542e-08 + 6.5628166822519829733e-459j)  +/-  (9.41e-39, 2.24e-97j)
| (5.260810344469944737e-05 - 2.6590570458126067866e-455j)  +/-  (3.78e-36, 9e-95j)
| (5.1199078722220798243e-18 + 1.2448818307244534056e-464j)  +/-  (1.09e-44, 2.59e-103j)
| (0.15927752721138376309 - 6.8173231030375446468e-453j)  +/-  (1.94e-31, 4.62e-90j)
| (0.12807203158896278002 + 6.1320337839896866569e-453j)  +/-  (7.2e-32, 1.71e-90j)
| (0.15927752721138376309 - 7.8384059652723588149e-453j)  +/-  (8.92e-32, 2.12e-90j)
| (0.15485588496170529248 + 8.4923844888801714817e-453j)  +/-  (7.03e-32, 1.67e-90j)
| (0.073401297802322352439 - 4.8002158289977130875e-453j)  +/-  (1.26e-32, 3.01e-91j)
| (3.2902944052028258171e-07 - 1.3025617195551205827e-456j)  +/-  (2.16e-38, 5.14e-97j)
| (0.017542010785325942435 - 1.7169563333061029073e-453j)  +/-  (4.67e-34, 1.11e-92j)
| (5.260810344469944737e-05 - 4.7226129125421615267e-456j)  +/-  (7.3e-37, 1.76e-95j)
| (0.073401297802322352439 - 3.0320629375629595541e-453j)  +/-  (5.79e-34, 1.3e-92j)
