Starting with polynomial:
P : -t+1
Extension levels are: 1 3 18
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : -t^4 + 49/4*t^3 - 153/4*t^2 + 57/2*t - 3/2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^22 + 135595138927459374882635564209839292268037472324641394710211/332039463404475229927595034298271053249034681825839655227*t^21 - 10022569269274085312736997941445429054325663734958826187136281323/132815785361790091971038013719308421299613872730335862090800*t^20 + 2223623677858527732699620540205651471191943788086039355146517614269/265631570723580183942076027438616842599227745460671724181600*t^19 - 33133816142929517779395045598167011696136059073523436290774785939531/53126314144716036788415205487723368519845549092134344836320*t^18 + 4394336570338173213579947431374701550680555009582601346132497130821081/132815785361790091971038013719308421299613872730335862090800*t^17 - 171734420610949170825346187726942967149770479732292599618794882856932241/132815785361790091971038013719308421299613872730335862090800*t^16 + 315447910966628140649994221651226221600689276949437775432764897870631676/8300986585111880748189875857456776331225867045645991380675*t^15 - 1411355535270306041483349235715512892097438735602103328919463800731477812/1660197317022376149637975171491355266245173409129198276135*t^14 + 4836189394910435557572245216364063704038913382586112056233055884480814056/332039463404475229927595034298271053249034681825839655227*t^13 - 317776063575179038123397602804608997826649641420428348388248630293844997256/1660197317022376149637975171491355266245173409129198276135*t^12 + 3195268468832187690605085964667778499921555717918591175238814438598618297136/1660197317022376149637975171491355266245173409129198276135*t^11 - 24430911297459959383882976768295071433059021937605681611600712389113284910096/1660197317022376149637975171491355266245173409129198276135*t^10 + 28125221044460794041571246942411314926601627364971874917305598670588769635296/332039463404475229927595034298271053249034681825839655227*t^9 - 120147750202952678063807694546127555921927512038554163670820977886968485307360/332039463404475229927595034298271053249034681825839655227*t^8 + 373598695347422093628974478517494295479624937763773232547717964166340400485888/332039463404475229927595034298271053249034681825839655227*t^7 - 823889079986629677282188168710203636593635776472454705881887882686374169983488/332039463404475229927595034298271053249034681825839655227*t^6 + 1244034509533016547124027423828904488116872883994100788158890105693742995371008/332039463404475229927595034298271053249034681825839655227*t^5 - 1224960723277155160732317072001279106076575998023114671654661279574204488944640/332039463404475229927595034298271053249034681825839655227*t^4 + 732921866139544361579899671342793216942442039955766232167750282795633740979200/332039463404475229927595034298271053249034681825839655227*t^3 - 238544658750475285667765539984885106104076563410754208325638260557834069611520/332039463404475229927595034298271053249034681825839655227*t^2 + 34480526275424085094841634314910585666719796283681091126527618389319079761920/332039463404475229927595034298271053249034681825839655227*t - 1312488461864242772447069520840875622006260503882222451514296804273033041920/332039463404475229927595034298271053249034681825839655227
-------------------------------------------------
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:   22 out of 22
Indefinite weights: 0 out of 22
Negative weights:   0 out of 22
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (66.801161582063704921 - 1.075537522299034971e-344j)  +/-  (2.1e-119, 2.1e-119j)
| (30.220116408070489661 - 2.5860544858674209033e-343j)  +/-  (7.61e-117, 7.61e-117j)
| (56.089184325299899704 - 3.7097719828340777947e-347j)  +/-  (2.28e-118, 2.28e-118j)
| (47.900160122818609296 - 2.254275105901105649e-353j)  +/-  (1.04e-117, 1.04e-117j)
| (35.29806029027207554 - 2.6152710668262447325e-361j)  +/-  (6.08e-117, 6.08e-117j)
| (0.57648541335337756846 + 8.2691570965576545739e-375j)  +/-  (2.89e-124, 2.89e-124j)
| (15.124303808388169673 - 3.458750674265010419e-375j)  +/-  (1.54e-117, 1.54e-117j)
| (6.0235675584843785045 - 2.478821056042719354e-383j)  +/-  (2.07e-119, 2.07e-119j)
| (41.115264317259796417 + 1.4018131345210401469e-387j)  +/-  (2.89e-117, 2.89e-117j)
| (18.250772387279925947 + 1.8343060435329959704e-397j)  +/-  (2.98e-117, 2.98e-117j)
| (1.6486442894169069674 + 1.5331300756011492174e-413j)  +/-  (2.44e-122, 2.44e-122j)
| (2.4483840343353324317 + 4.1317507771009452833e-411j)  +/-  (2.17e-121, 2.17e-121j)
| (25.742908336456338158 - 1.0088763581477307024e-412j)  +/-  (7.11e-117, 7.11e-117j)
| (12.36019292133930932 + 1.0988031551985086011e-417j)  +/-  (6.04e-118, 6.04e-118j)
| (4.5370885081649107564 - 6.0587251442139172759e-424j)  +/-  (4.89e-120, 4.89e-120j)
| (7.8232631436879996743 - 1.930099953166429412e-425j)  +/-  (6.64e-119, 6.64e-119j)
| (3.369839231310923141 - 1.6004330387318401765e-432j)  +/-  (1.14e-120, 1.14e-120j)
| (9.9324997747973989558 - 3.8116146340378704665e-438j)  +/-  (2.14e-118, 2.14e-118j)
| (0.056897625001077184683 + 1.0647845021837425376e-449j)  +/-  (4.09e-127, 4.09e-127j)
| (21.774623854796283311 - 4.0638087516448374755e-451j)  +/-  (5.66e-117, 5.66e-117j)
| (1 + 5.4930658056493875056e-467j)  +/-  (2.65e-123, 2.65e-123j)
| (0.27713398063637623161 + 1.0928211326786548388e-467j)  +/-  (2.27e-125, 2.27e-125j)
-------------------------------------------------
The weights are:
| (1.2558438851713064744e-28 + 1.3587078983240453093e-365j)  +/-  (1.03e-48, 1.14e-105j)
| (3.5736351746771222539e-13 + 5.1127989755606745792e-356j)  +/-  (3.54e-42, 3.89e-99j)
| (4.0011147534279490877e-24 - 4.4984970144329277873e-363j)  +/-  (2.03e-47, 2.23e-104j)
| (1.163054772356833822e-20 + 4.5410450251292178877e-361j)  +/-  (2.48e-46, 2.73e-103j)
| (2.5361351122813565668e-15 + 1.195730604780356544e-357j)  +/-  (2.36e-44, 2.6e-101j)
| (0.18458153430487404543 + 2.6146548413292631515e-349j)  +/-  (1.28e-30, 1.41e-87j)
| (7.9430329395523134091e-07 + 2.8805254810143820712e-353j)  +/-  (4.21e-40, 4.64e-97j)
| (0.0039823821001326554769 + 7.1870278769189159185e-351j)  +/-  (4.43e-35, 4.88e-92j)
| (8.7070861782064298953e-18 - 2.5638357513729197894e-359j)  +/-  (1.17e-45, 1.29e-102j)
| (3.9330161641829687079e-08 - 5.8675713321128988424e-354j)  +/-  (1.62e-41, 1.78e-98j)
| (0.14234054865018689389 + 1.7596744106871252712e-349j)  +/-  (1.26e-30, 1.39e-87j)
| (0.073506688790329183402 - 1.1474104461795381163e-349j)  +/-  (1.71e-32, 1.89e-89j)
| (2.7816029049127152205e-11 - 2.3607101047170861708e-355j)  +/-  (2.14e-43, 2.36e-100j)
| (1.1109981658316429037e-05 - 1.2971320623769565961e-352j)  +/-  (2.85e-40, 3.14e-97j)
| (0.014189551224624335743 - 2.308155041755288953e-350j)  +/-  (5.41e-37, 5.95e-94j)
| (0.00078216603901829773228 - 2.0342446720465085147e-351j)  +/-  (4.04e-39, 4.44e-96j)
| (0.035083767613818956484 + 6.0212713419239132461e-350j)  +/-  (8.41e-37, 9.26e-94j)
| (0.00011006714267702794593 + 5.3480847879337369643e-352j)  +/-  (4.21e-40, 4.63e-97j)
| (0.13592918945823027618 + 3.9725290628853091769e-350j)  +/-  (5.47e-37, 5.89e-94j)
| (1.3059451544985225511e-09 + 1.128599107168489768e-354j)  +/-  (1.64e-43, 1.81e-100j)
| (0.19889988026109935582 - 2.4833382419273473464e-349j)  +/-  (7.36e-37, 8.1e-94j)
| (0.21058227946577396648 - 1.5679627100902406631e-349j)  +/-  (6.61e-37, 7.01e-94j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 3 18
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : -t^4 + 49/4*t^3 - 153/4*t^2 + 57/2*t - 3/2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^22 + 135595138927459374882635564209839292268037472324641394710211/332039463404475229927595034298271053249034681825839655227*t^21 - 10022569269274085312736997941445429054325663734958826187136281323/132815785361790091971038013719308421299613872730335862090800*t^20 + 2223623677858527732699620540205651471191943788086039355146517614269/265631570723580183942076027438616842599227745460671724181600*t^19 - 33133816142929517779395045598167011696136059073523436290774785939531/53126314144716036788415205487723368519845549092134344836320*t^18 + 4394336570338173213579947431374701550680555009582601346132497130821081/132815785361790091971038013719308421299613872730335862090800*t^17 - 171734420610949170825346187726942967149770479732292599618794882856932241/132815785361790091971038013719308421299613872730335862090800*t^16 + 315447910966628140649994221651226221600689276949437775432764897870631676/8300986585111880748189875857456776331225867045645991380675*t^15 - 1411355535270306041483349235715512892097438735602103328919463800731477812/1660197317022376149637975171491355266245173409129198276135*t^14 + 4836189394910435557572245216364063704038913382586112056233055884480814056/332039463404475229927595034298271053249034681825839655227*t^13 - 317776063575179038123397602804608997826649641420428348388248630293844997256/1660197317022376149637975171491355266245173409129198276135*t^12 + 3195268468832187690605085964667778499921555717918591175238814438598618297136/1660197317022376149637975171491355266245173409129198276135*t^11 - 24430911297459959383882976768295071433059021937605681611600712389113284910096/1660197317022376149637975171491355266245173409129198276135*t^10 + 28125221044460794041571246942411314926601627364971874917305598670588769635296/332039463404475229927595034298271053249034681825839655227*t^9 - 120147750202952678063807694546127555921927512038554163670820977886968485307360/332039463404475229927595034298271053249034681825839655227*t^8 + 373598695347422093628974478517494295479624937763773232547717964166340400485888/332039463404475229927595034298271053249034681825839655227*t^7 - 823889079986629677282188168710203636593635776472454705881887882686374169983488/332039463404475229927595034298271053249034681825839655227*t^6 + 1244034509533016547124027423828904488116872883994100788158890105693742995371008/332039463404475229927595034298271053249034681825839655227*t^5 - 1224960723277155160732317072001279106076575998023114671654661279574204488944640/332039463404475229927595034298271053249034681825839655227*t^4 + 732921866139544361579899671342793216942442039955766232167750282795633740979200/332039463404475229927595034298271053249034681825839655227*t^3 - 238544658750475285667765539984885106104076563410754208325638260557834069611520/332039463404475229927595034298271053249034681825839655227*t^2 + 34480526275424085094841634314910585666719796283681091126527618389319079761920/332039463404475229927595034298271053249034681825839655227*t - 1312488461864242772447069520840875622006260503882222451514296804273033041920/332039463404475229927595034298271053249034681825839655227
-------------------------------------------------
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:   22 out of 22
Indefinite weights: 0 out of 22
Negative weights:   0 out of 22
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (66.801161582063704921 - 1.075537522299034971e-344j)  +/-  (2.1e-119, 2.1e-119j)
| (30.220116408070489661 - 2.5860544858674209033e-343j)  +/-  (7.61e-117, 7.61e-117j)
| (56.089184325299899704 - 3.7097719828340777947e-347j)  +/-  (2.28e-118, 2.28e-118j)
| (47.900160122818609296 - 2.254275105901105649e-353j)  +/-  (1.04e-117, 1.04e-117j)
| (35.29806029027207554 - 2.6152710668262447325e-361j)  +/-  (6.08e-117, 6.08e-117j)
| (0.57648541335337756846 + 8.2691570965576545739e-375j)  +/-  (2.89e-124, 2.89e-124j)
| (15.124303808388169673 - 3.458750674265010419e-375j)  +/-  (1.54e-117, 1.54e-117j)
| (6.0235675584843785045 - 2.478821056042719354e-383j)  +/-  (2.07e-119, 2.07e-119j)
| (41.115264317259796417 + 1.4018131345210401469e-387j)  +/-  (2.89e-117, 2.89e-117j)
| (18.250772387279925947 + 1.8343060435329959704e-397j)  +/-  (2.98e-117, 2.98e-117j)
| (1.6486442894169069674 + 1.5331300756011492174e-413j)  +/-  (2.44e-122, 2.44e-122j)
| (2.4483840343353324317 + 4.1317507771009452833e-411j)  +/-  (2.17e-121, 2.17e-121j)
| (25.742908336456338158 - 1.0088763581477307024e-412j)  +/-  (7.11e-117, 7.11e-117j)
| (12.36019292133930932 + 1.0988031551985086011e-417j)  +/-  (6.04e-118, 6.04e-118j)
| (4.5370885081649107564 - 6.0587251442139172759e-424j)  +/-  (4.89e-120, 4.89e-120j)
| (7.8232631436879996743 - 1.930099953166429412e-425j)  +/-  (6.64e-119, 6.64e-119j)
| (3.369839231310923141 - 1.6004330387318401765e-432j)  +/-  (1.14e-120, 1.14e-120j)
| (9.9324997747973989558 - 3.8116146340378704665e-438j)  +/-  (2.14e-118, 2.14e-118j)
| (0.056897625001077184683 + 1.0647845021837425376e-449j)  +/-  (4.09e-127, 4.09e-127j)
| (21.774623854796283311 - 4.0638087516448374755e-451j)  +/-  (5.66e-117, 5.66e-117j)
| (1 + 5.4930658056493875056e-467j)  +/-  (2.65e-123, 2.65e-123j)
| (0.27713398063637623161 + 1.0928211326786548388e-467j)  +/-  (2.27e-125, 2.27e-125j)
-------------------------------------------------
The weights are:
| (1.2558438851713064744e-28 + 1.3587078983240453093e-365j)  +/-  (1.03e-48, 1.14e-105j)
| (3.5736351746771222539e-13 + 5.1127989755606745792e-356j)  +/-  (3.54e-42, 3.89e-99j)
| (4.0011147534279490877e-24 - 4.4984970144329277873e-363j)  +/-  (2.03e-47, 2.23e-104j)
| (1.163054772356833822e-20 + 4.5410450251292178877e-361j)  +/-  (2.48e-46, 2.73e-103j)
| (2.5361351122813565668e-15 + 1.195730604780356544e-357j)  +/-  (2.36e-44, 2.6e-101j)
| (0.18458153430487404543 + 2.6146548413292631515e-349j)  +/-  (1.28e-30, 1.41e-87j)
| (7.9430329395523134091e-07 + 2.8805254810143820712e-353j)  +/-  (4.21e-40, 4.64e-97j)
| (0.0039823821001326554769 + 7.1870278769189159185e-351j)  +/-  (4.43e-35, 4.88e-92j)
| (8.7070861782064298953e-18 - 2.5638357513729197894e-359j)  +/-  (1.17e-45, 1.29e-102j)
| (3.9330161641829687079e-08 - 5.8675713321128988424e-354j)  +/-  (1.62e-41, 1.78e-98j)
| (0.14234054865018689389 + 1.7596744106871252712e-349j)  +/-  (1.26e-30, 1.39e-87j)
| (0.073506688790329183402 - 1.1474104461795381163e-349j)  +/-  (1.71e-32, 1.89e-89j)
| (2.7816029049127152205e-11 - 2.3607101047170861708e-355j)  +/-  (2.14e-43, 2.36e-100j)
| (1.1109981658316429037e-05 - 1.2971320623769565961e-352j)  +/-  (2.85e-40, 3.14e-97j)
| (0.014189551224624335743 - 2.308155041755288953e-350j)  +/-  (5.41e-37, 5.95e-94j)
| (0.00078216603901829773228 - 2.0342446720465085147e-351j)  +/-  (4.04e-39, 4.44e-96j)
| (0.035083767613818956484 + 6.0212713419239132461e-350j)  +/-  (8.41e-37, 9.26e-94j)
| (0.00011006714267702794593 + 5.3480847879337369643e-352j)  +/-  (4.21e-40, 4.63e-97j)
| (0.13592918945823027618 + 3.9725290628853091769e-350j)  +/-  (5.47e-37, 5.89e-94j)
| (1.3059451544985225511e-09 + 1.128599107168489768e-354j)  +/-  (1.64e-43, 1.81e-100j)
| (0.19889988026109935582 - 2.4833382419273473464e-349j)  +/-  (7.36e-37, 8.1e-94j)
| (0.21058227946577396648 - 1.5679627100902406631e-349j)  +/-  (6.61e-37, 7.01e-94j)
