Starting with polynomial:
P : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Extension levels are: 3 20
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P1 : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -1/6*t^23 + 1860243641478816998822550668022740360689/23860479164592510634708576413418533526*t^22 - 594023836368589312474061968600627395391567/35790718746888765952062864620127800289*t^21 + 432833314532488286883549183120640067434766071/202814072899036340395022899514057534971*t^20 - 37628219860911014643178518922604724862915073100/202814072899036340395022899514057534971*t^19 + 2345905923634574732743732963385686036837644571420/202814072899036340395022899514057534971*t^18 - 108577323524074886332558880193996470923182858206280/202814072899036340395022899514057534971*t^17 + 224162817320293474472127699748258896945145635265080/11930239582296255317354288206709266763*t^16 - 6042766061739426796752193334551662105340302800444160/11930239582296255317354288206709266763*t^15 + 125976952949740021175321459555374961306985704082144000/11930239582296255317354288206709266763*t^14 - 2035728312277737925041761195982922780411919970064934400/11930239582296255317354288206709266763*t^13 + 25457116619328491705857967156099818921722072761019609600/11930239582296255317354288206709266763*t^12 - 245048073633884542462794308326234125390427267353833011200/11930239582296255317354288206709266763*t^11 + 1799324356221732434404190496814022223280791951958691174400/11930239582296255317354288206709266763*t^10 - 9946083076976929097154232127540597521474545772946434560000/11930239582296255317354288206709266763*t^9 + 40647518869347877862500105221817505075450577534310393344000/11930239582296255317354288206709266763*t^8 - 119888304176613853568169002995678121033209654794901764096000/11930239582296255317354288206709266763*t^7 + 247145329995084750275145754443375965452415469822943721472000/11930239582296255317354288206709266763*t^6 - 341110761957369947934149133121900426991200821067281936384000/11930239582296255317354288206709266763*t^5 + 297234700816728318886580114024295165522481290622791782400000/11930239582296255317354288206709266763*t^4 - 150495522512702985666533066567455482437975670374185451520000/11930239582296255317354288206709266763*t^3 + 39088032028556617712627980423937438590270018107615559680000/11930239582296255317354288206709266763*t^2 - 4202772455744016423823706944883602061605616556172738560000/11930239582296255317354288206709266763*t + 110799097885362448344528759862066277467732508330065920000/11930239582296255317354288206709266763
-------------------------------------------------
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:   23 out of 23
Indefinite weights: 0 out of 23
Negative weights:   0 out of 23
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (72.381168272049857441 - 2.9844782436428663815e-320j)  +/-  (6.83e-119, 6.83e-119j)
| (61.346183182431417211 - 2.0886560494661700007e-320j)  +/-  (6.78e-118, 6.78e-118j)
| (52.876143036460384907 - 5.5747373331556774402e-335j)  +/-  (3.69e-117, 3.69e-117j)
| (45.828924256123345695 - 1.4950889052199516433e-352j)  +/-  (1.05e-116, 1.05e-116j)
| (25.496319236220267749 - 1.9499871142962969827e-364j)  +/-  (2.66e-116, 2.66e-116j)
| (29.710668656833508293 + 4.8966532133180678656e-378j)  +/-  (3.11e-116, 3.11e-116j)
| (10.233208060942359183 + 1.3679311112888675655e-387j)  +/-  (4.45e-118, 4.45e-118j)
| (8.1262968218011757271 - 3.3413894324947671202e-392j)  +/-  (1.16e-118, 1.16e-118j)
| (21.724096006263149728 + 4.4780533083483601296e-399j)  +/-  (1.72e-116, 1.72e-116j)
| (6.2899450829374791969 - 1.7932302797829609268e-409j)  +/-  (2.37e-119, 2.37e-119j)
| (3.3828058141300386996 - 3.3191422245950824564e-413j)  +/-  (5.92e-121, 5.92e-121j)
| (4.7120544948573747666 + 5.6649683174244211663e-412j)  +/-  (3.89e-120, 3.89e-120j)
| (39.759134637685809778 - 1.3864011757765448127e-415j)  +/-  (1.92e-116, 1.92e-116j)
| (0.037930013848796219938 + 1.221844388125571394e-432j)  +/-  (3.86e-127, 3.86e-127j)
| (15.321862026869285952 + 7.5790651592073304206e-421j)  +/-  (4.24e-117, 4.24e-117j)
| (2.2942803602790417198 - 5.0609707412579961642e-430j)  +/-  (7.81e-122, 7.81e-122j)
| (12.62558416676934855 + 8.9399577616141090668e-425j)  +/-  (1.77e-117, 1.77e-117j)
| (18.345028446333721402 - 1.5475775714641100226e-432j)  +/-  (9.81e-117, 9.81e-117j)
| (34.433577775247189846 + 2.1352268901951676043e-433j)  +/-  (2.84e-116, 2.84e-116j)
| (0.18260105307921594075 + 2.619619513306050167e-449j)  +/-  (7.36e-126, 7.36e-126j)
| (0.41577455678347908331 - 3.7372163672405105608e-448j)  +/-  (8.58e-125, 8.58e-125j)
| (0.81643142121551964623 + 1.1390669497019313872e-447j)  +/-  (7.31e-124, 7.31e-124j)
| (1.4402720223950810929 + 1.6059458319091974649e-446j)  +/-  (7.35e-123, 7.35e-123j)
-------------------------------------------------
The weights are:
| (4.8713033713752354418e-31 + 1.7178335043736234805e-349j)  +/-  (1.56e-45, 7.84e-104j)
| (2.1523289439780236584e-26 + 2.3175970033346950053e-346j)  +/-  (4.16e-44, 2.08e-102j)
| (8.3200996970592136016e-23 - 3.8138766038497467538e-345j)  +/-  (3.74e-43, 1.87e-101j)
| (8.1323277761586261784e-20 + 7.4974363797360856926e-344j)  +/-  (2.24e-42, 1.12e-100j)
| (3.3682096344555989855e-11 + 1.1827730434531134248e-339j)  +/-  (4.22e-39, 2.11e-97j)
| (5.5684760280802654859e-13 - 1.4802490983331562192e-340j)  +/-  (3.8e-40, 1.9e-98j)
| (8.0789823657300867425e-05 - 3.176806659437913624e-336j)  +/-  (3.32e-34, 1.66e-92j)
| (0.00058227534850194868229 + 1.0283518193422936417e-335j)  +/-  (5.99e-33, 3e-91j)
| (1.3117265711755747533e-09 - 7.8302626563631669387e-339j)  +/-  (8.27e-39, 4.14e-97j)
| (0.0031631137552615881203 - 2.9809398212583697833e-335j)  +/-  (4.12e-32, 2.07e-90j)
| (0.041004299144000617666 - 1.8681689983566486635e-334j)  +/-  (4.74e-30, 2.38e-88j)
| (0.013049016216425350482 + 7.810932277817419844e-335j)  +/-  (2.71e-31, 1.36e-89j)
| (3.0640824758844589002e-17 - 1.204547264384788504e-342j)  +/-  (1.51e-43, 7.58e-102j)
| (0.091868947743804326961 - 6.9653356754621867073e-334j)  +/-  (1.75e-31, 8.76e-90j)
| (6.3310259345528195175e-07 - 2.0943566807654000834e-337j)  +/-  (4.05e-38, 2.03e-96j)
| (0.097846871516390718763 + 4.1201928219178707347e-334j)  +/-  (2.51e-32, 1.26e-90j)
| (8.3515795103022246293e-06 + 8.7049151130119720481e-337j)  +/-  (3.18e-37, 1.59e-95j)
| (3.4468254992598576454e-08 + 4.3745973786202220358e-338j)  +/-  (3.66e-39, 1.83e-97j)
| (5.5607642012014529631e-15 + 1.5015889382721392153e-341j)  +/-  (4.44e-43, 2.23e-101j)
| (0.15454351179926016431 + 2.013727709760508268e-333j)  +/-  (5.6e-33, 2.82e-91j)
| (0.19760014331711435595 - 2.3396641494491606177e-333j)  +/-  (1.58e-33, 7.95e-92j)
| (0.22536012371720105216 + 1.5859327805515171048e-333j)  +/-  (2.66e-34, 1.35e-92j)
| (0.17489188712205271933 - 8.4476981195756646799e-334j)  +/-  (1.08e-34, 5.33e-93j)
Starting with polynomial:
P : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Extension levels are: 3 20
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P1 : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -1/6*t^23 + 1860243641478816998822550668022740360689/23860479164592510634708576413418533526*t^22 - 594023836368589312474061968600627395391567/35790718746888765952062864620127800289*t^21 + 432833314532488286883549183120640067434766071/202814072899036340395022899514057534971*t^20 - 37628219860911014643178518922604724862915073100/202814072899036340395022899514057534971*t^19 + 2345905923634574732743732963385686036837644571420/202814072899036340395022899514057534971*t^18 - 108577323524074886332558880193996470923182858206280/202814072899036340395022899514057534971*t^17 + 224162817320293474472127699748258896945145635265080/11930239582296255317354288206709266763*t^16 - 6042766061739426796752193334551662105340302800444160/11930239582296255317354288206709266763*t^15 + 125976952949740021175321459555374961306985704082144000/11930239582296255317354288206709266763*t^14 - 2035728312277737925041761195982922780411919970064934400/11930239582296255317354288206709266763*t^13 + 25457116619328491705857967156099818921722072761019609600/11930239582296255317354288206709266763*t^12 - 245048073633884542462794308326234125390427267353833011200/11930239582296255317354288206709266763*t^11 + 1799324356221732434404190496814022223280791951958691174400/11930239582296255317354288206709266763*t^10 - 9946083076976929097154232127540597521474545772946434560000/11930239582296255317354288206709266763*t^9 + 40647518869347877862500105221817505075450577534310393344000/11930239582296255317354288206709266763*t^8 - 119888304176613853568169002995678121033209654794901764096000/11930239582296255317354288206709266763*t^7 + 247145329995084750275145754443375965452415469822943721472000/11930239582296255317354288206709266763*t^6 - 341110761957369947934149133121900426991200821067281936384000/11930239582296255317354288206709266763*t^5 + 297234700816728318886580114024295165522481290622791782400000/11930239582296255317354288206709266763*t^4 - 150495522512702985666533066567455482437975670374185451520000/11930239582296255317354288206709266763*t^3 + 39088032028556617712627980423937438590270018107615559680000/11930239582296255317354288206709266763*t^2 - 4202772455744016423823706944883602061605616556172738560000/11930239582296255317354288206709266763*t + 110799097885362448344528759862066277467732508330065920000/11930239582296255317354288206709266763
-------------------------------------------------
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:   23 out of 23
Indefinite weights: 0 out of 23
Negative weights:   0 out of 23
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (72.381168272049857441 - 2.9844782436428663815e-320j)  +/-  (6.83e-119, 6.83e-119j)
| (61.346183182431417211 - 2.0886560494661700007e-320j)  +/-  (6.78e-118, 6.78e-118j)
| (52.876143036460384907 - 5.5747373331556774402e-335j)  +/-  (3.69e-117, 3.69e-117j)
| (45.828924256123345695 - 1.4950889052199516433e-352j)  +/-  (1.05e-116, 1.05e-116j)
| (25.496319236220267749 - 1.9499871142962969827e-364j)  +/-  (2.66e-116, 2.66e-116j)
| (29.710668656833508293 + 4.8966532133180678656e-378j)  +/-  (3.11e-116, 3.11e-116j)
| (10.233208060942359183 + 1.3679311112888675655e-387j)  +/-  (4.45e-118, 4.45e-118j)
| (8.1262968218011757271 - 3.3413894324947671202e-392j)  +/-  (1.16e-118, 1.16e-118j)
| (21.724096006263149728 + 4.4780533083483601296e-399j)  +/-  (1.72e-116, 1.72e-116j)
| (6.2899450829374791969 - 1.7932302797829609268e-409j)  +/-  (2.37e-119, 2.37e-119j)
| (3.3828058141300386996 - 3.3191422245950824564e-413j)  +/-  (5.92e-121, 5.92e-121j)
| (4.7120544948573747666 + 5.6649683174244211663e-412j)  +/-  (3.89e-120, 3.89e-120j)
| (39.759134637685809778 - 1.3864011757765448127e-415j)  +/-  (1.92e-116, 1.92e-116j)
| (0.037930013848796219938 + 1.221844388125571394e-432j)  +/-  (3.86e-127, 3.86e-127j)
| (15.321862026869285952 + 7.5790651592073304206e-421j)  +/-  (4.24e-117, 4.24e-117j)
| (2.2942803602790417198 - 5.0609707412579961642e-430j)  +/-  (7.81e-122, 7.81e-122j)
| (12.62558416676934855 + 8.9399577616141090668e-425j)  +/-  (1.77e-117, 1.77e-117j)
| (18.345028446333721402 - 1.5475775714641100226e-432j)  +/-  (9.81e-117, 9.81e-117j)
| (34.433577775247189846 + 2.1352268901951676043e-433j)  +/-  (2.84e-116, 2.84e-116j)
| (0.18260105307921594075 + 2.619619513306050167e-449j)  +/-  (7.36e-126, 7.36e-126j)
| (0.41577455678347908331 - 3.7372163672405105608e-448j)  +/-  (8.58e-125, 8.58e-125j)
| (0.81643142121551964623 + 1.1390669497019313872e-447j)  +/-  (7.31e-124, 7.31e-124j)
| (1.4402720223950810929 + 1.6059458319091974649e-446j)  +/-  (7.35e-123, 7.35e-123j)
-------------------------------------------------
The weights are:
| (4.8713033713752354418e-31 + 1.7178335043736234805e-349j)  +/-  (1.56e-45, 7.84e-104j)
| (2.1523289439780236584e-26 + 2.3175970033346950053e-346j)  +/-  (4.16e-44, 2.08e-102j)
| (8.3200996970592136016e-23 - 3.8138766038497467538e-345j)  +/-  (3.74e-43, 1.87e-101j)
| (8.1323277761586261784e-20 + 7.4974363797360856926e-344j)  +/-  (2.24e-42, 1.12e-100j)
| (3.3682096344555989855e-11 + 1.1827730434531134248e-339j)  +/-  (4.22e-39, 2.11e-97j)
| (5.5684760280802654859e-13 - 1.4802490983331562192e-340j)  +/-  (3.8e-40, 1.9e-98j)
| (8.0789823657300867425e-05 - 3.176806659437913624e-336j)  +/-  (3.32e-34, 1.66e-92j)
| (0.00058227534850194868229 + 1.0283518193422936417e-335j)  +/-  (5.99e-33, 3e-91j)
| (1.3117265711755747533e-09 - 7.8302626563631669387e-339j)  +/-  (8.27e-39, 4.14e-97j)
| (0.0031631137552615881203 - 2.9809398212583697833e-335j)  +/-  (4.12e-32, 2.07e-90j)
| (0.041004299144000617666 - 1.8681689983566486635e-334j)  +/-  (4.74e-30, 2.38e-88j)
| (0.013049016216425350482 + 7.810932277817419844e-335j)  +/-  (2.71e-31, 1.36e-89j)
| (3.0640824758844589002e-17 - 1.204547264384788504e-342j)  +/-  (1.51e-43, 7.58e-102j)
| (0.091868947743804326961 - 6.9653356754621867073e-334j)  +/-  (1.75e-31, 8.76e-90j)
| (6.3310259345528195175e-07 - 2.0943566807654000834e-337j)  +/-  (4.05e-38, 2.03e-96j)
| (0.097846871516390718763 + 4.1201928219178707347e-334j)  +/-  (2.51e-32, 1.26e-90j)
| (8.3515795103022246293e-06 + 8.7049151130119720481e-337j)  +/-  (3.18e-37, 1.59e-95j)
| (3.4468254992598576454e-08 + 4.3745973786202220358e-338j)  +/-  (3.66e-39, 1.83e-97j)
| (5.5607642012014529631e-15 + 1.5015889382721392153e-341j)  +/-  (4.44e-43, 2.23e-101j)
| (0.15454351179926016431 + 2.013727709760508268e-333j)  +/-  (5.6e-33, 2.82e-91j)
| (0.19760014331711435595 - 2.3396641494491606177e-333j)  +/-  (1.58e-33, 7.95e-92j)
| (0.22536012371720105216 + 1.5859327805515171048e-333j)  +/-  (2.66e-34, 1.35e-92j)
| (0.17489188712205271933 - 8.4476981195756646799e-334j)  +/-  (1.08e-34, 5.33e-93j)
