Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 16
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^18 - 7811386810220820717618/53494522845766424537*t^17 + 7081468365842334724098991/374461659920364971759*t^16 - 538156784553621105373148416/374461659920364971759*t^15 + 26766658166278070252872238400/374461659920364971759*t^14 - 131471565464141593054409230080/53494522845766424537*t^13 + 3218160708389185026861696051840/53494522845766424537*t^12 - 56923797768860943401977150986240/53494522845766424537*t^11 + 731192189178316641663930516714240/53494522845766424537*t^10 - 6799632903621963992689400428416000/53494522845766424537*t^9 + 45296708192730190979032587677683200/53494522845766424537*t^8 - 212167808268947465684358278556057600/53494522845766424537*t^7 + 679132351957015877557332011181465600/53494522845766424537*t^6 - 1424717670555778624014174859299225600/53494522845766424537*t^5 + 1841533373056721018676047974287360000/53494522845766424537*t^4 - 1333899543785493377786962732351488000/53494522845766424537*t^3 + 462678627088542195699514892089344000/53494522845766424537*t^2 - 56941276461562146656158552940544000/53494522845766424537*t + 1154037738544193565655469420544000/53494522845766424537
-------------------------------------------------
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:   18 out of 18
Indefinite weights: 0 out of 18
Negative weights:   0 out of 18
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (55.577855192661022459 - 1.3874809817139517602e-276j)  +/-  (2.2e-120, 2.2e-120j)
| (37.983934196702733123 - 3.6519429761888999605e-287j)  +/-  (5.83e-119, 5.83e-119j)
| (45.563694987854120615 + 1.075694156304438451e-302j)  +/-  (1.75e-119, 1.75e-119j)
| (31.769450041511783414 + 8.791339873565181645e-318j)  +/-  (1.18e-118, 1.18e-118j)
| (4.956055934182182698 - 7.096625516296592501e-325j)  +/-  (3.19e-121, 3.19e-121j)
| (1.2423283460789458566 + 5.4696784919582838497e-327j)  +/-  (6.03e-124, 6.03e-124j)
| (14.594348173191627689 + 1.1701467518686448284e-337j)  +/-  (5.63e-119, 5.63e-119j)
| (18.025213499530744628 + 2.3524953932548063115e-353j)  +/-  (1.05e-118, 1.05e-118j)
| (6.8219907034781249987 - 1.1218725995258070743e-361j)  +/-  (1.72e-120, 1.72e-120j)
| (11.611513743071886861 + 7.6814664589228391725e-365j)  +/-  (2.31e-119, 2.31e-119j)
| (2.1807093317272986572 - 1.1962105593561132305e-373j)  +/-  (7.1e-123, 7.1e-123j)
| (0.024987386679131379603 - 5.456001994816131609e-375j)  +/-  (7.28e-128, 7.28e-128j)
| (26.502799961440424828 - 1.5301191151268361409e-377j)  +/-  (1.62e-118, 1.62e-118j)
| (21.965506767443185052 - 9.3100706603977091348e-391j)  +/-  (1.67e-118, 1.67e-118j)
| (3.4142135623730950488 + 1.3932005343663936869e-398j)  +/-  (5.52e-122, 5.52e-122j)
| (0.19204847855920442536 - 4.6628621137457360937e-403j)  +/-  (2.76e-126, 2.76e-126j)
| (0.5857864376269049512 - 5.3959282088403661132e-402j)  +/-  (4.46e-125, 4.46e-125j)
| (9.0319219930369374106 - 6.5438089286328249741e-396j)  +/-  (6.67e-120, 6.67e-120j)
-------------------------------------------------
The weights are:
| (8.8291137898982157481e-24 + 6.2342464676713318779e-300j)  +/-  (7.96e-52, 7.6e-110j)
| (2.1691881037981910724e-16 + 4.1652756958961011438e-297j)  +/-  (2.07e-49, 1.98e-107j)
| (1.3862700652249841093e-19 - 1.6911076523631058378e-298j)  +/-  (1.15e-50, 1.1e-108j)
| (9.0798595194794286564e-14 - 6.8763633386752642459e-296j)  +/-  (1.06e-48, 1.02e-106j)
| (0.011975893798179165902 - 2.8454034808803756579e-290j)  +/-  (9.85e-40, 9.41e-98j)
| (0.22953569186008560362 + 2.0279281652683223832e-289j)  +/-  (2.95e-33, 2.82e-91j)
| (1.4677930687715767309e-06 - 2.3463346990325895172e-292j)  +/-  (1.33e-45, 1.27e-103j)
| (5.4555582362826871614e-08 + 4.4576059894272090607e-293j)  +/-  (9.06e-47, 8.65e-105j)
| (0.0022163567557375102374 + 1.0984525785966584708e-290j)  +/-  (5.02e-43, 4.79e-101j)
| (2.5143058811773069175e-05 + 1.0101553669783881635e-291j)  +/-  (3.25e-45, 3.11e-103j)
| (0.1224335245096283263 - 1.2236672719249850409e-289j)  +/-  (7.83e-41, 7.48e-99j)
| (0.073353944335723876115 - 1.3294190941589155703e-289j)  +/-  (5.14e-40, 4.92e-98j)
| (1.5063656511585505659e-11 + 7.9272499674233854277e-295j)  +/-  (2.63e-49, 2.51e-107j)
| (1.2188472099232674893e-09 - 6.7611663982968268839e-294j)  +/-  (2.47e-48, 2.36e-106j)
| (0.045580157683956622228 + 6.3473778618283428998e-290j)  +/-  (1.76e-43, 1.73e-101j)
| (0.22454711671716917951 + 2.8981077585616150782e-289j)  +/-  (2.91e-42, 2.93e-100j)
| (0.29004497568521946485 - 2.8048988353803756356e-289j)  +/-  (1.63e-42, 1.64e-100j)
| (0.00028567201283546168141 - 3.6234065863460157714e-291j)  +/-  (1.86e-45, 1.74e-103j)
Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 16
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^18 - 7811386810220820717618/53494522845766424537*t^17 + 7081468365842334724098991/374461659920364971759*t^16 - 538156784553621105373148416/374461659920364971759*t^15 + 26766658166278070252872238400/374461659920364971759*t^14 - 131471565464141593054409230080/53494522845766424537*t^13 + 3218160708389185026861696051840/53494522845766424537*t^12 - 56923797768860943401977150986240/53494522845766424537*t^11 + 731192189178316641663930516714240/53494522845766424537*t^10 - 6799632903621963992689400428416000/53494522845766424537*t^9 + 45296708192730190979032587677683200/53494522845766424537*t^8 - 212167808268947465684358278556057600/53494522845766424537*t^7 + 679132351957015877557332011181465600/53494522845766424537*t^6 - 1424717670555778624014174859299225600/53494522845766424537*t^5 + 1841533373056721018676047974287360000/53494522845766424537*t^4 - 1333899543785493377786962732351488000/53494522845766424537*t^3 + 462678627088542195699514892089344000/53494522845766424537*t^2 - 56941276461562146656158552940544000/53494522845766424537*t + 1154037738544193565655469420544000/53494522845766424537
-------------------------------------------------
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:   18 out of 18
Indefinite weights: 0 out of 18
Negative weights:   0 out of 18
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (55.577855192661022459 - 1.3874809817139517602e-276j)  +/-  (2.2e-120, 2.2e-120j)
| (37.983934196702733123 - 3.6519429761888999605e-287j)  +/-  (5.83e-119, 5.83e-119j)
| (45.563694987854120615 + 1.075694156304438451e-302j)  +/-  (1.75e-119, 1.75e-119j)
| (31.769450041511783414 + 8.791339873565181645e-318j)  +/-  (1.18e-118, 1.18e-118j)
| (4.956055934182182698 - 7.096625516296592501e-325j)  +/-  (3.19e-121, 3.19e-121j)
| (1.2423283460789458566 + 5.4696784919582838497e-327j)  +/-  (6.03e-124, 6.03e-124j)
| (14.594348173191627689 + 1.1701467518686448284e-337j)  +/-  (5.63e-119, 5.63e-119j)
| (18.025213499530744628 + 2.3524953932548063115e-353j)  +/-  (1.05e-118, 1.05e-118j)
| (6.8219907034781249987 - 1.1218725995258070743e-361j)  +/-  (1.72e-120, 1.72e-120j)
| (11.611513743071886861 + 7.6814664589228391725e-365j)  +/-  (2.31e-119, 2.31e-119j)
| (2.1807093317272986572 - 1.1962105593561132305e-373j)  +/-  (7.1e-123, 7.1e-123j)
| (0.024987386679131379603 - 5.456001994816131609e-375j)  +/-  (7.28e-128, 7.28e-128j)
| (26.502799961440424828 - 1.5301191151268361409e-377j)  +/-  (1.62e-118, 1.62e-118j)
| (21.965506767443185052 - 9.3100706603977091348e-391j)  +/-  (1.67e-118, 1.67e-118j)
| (3.4142135623730950488 + 1.3932005343663936869e-398j)  +/-  (5.52e-122, 5.52e-122j)
| (0.19204847855920442536 - 4.6628621137457360937e-403j)  +/-  (2.76e-126, 2.76e-126j)
| (0.5857864376269049512 - 5.3959282088403661132e-402j)  +/-  (4.46e-125, 4.46e-125j)
| (9.0319219930369374106 - 6.5438089286328249741e-396j)  +/-  (6.67e-120, 6.67e-120j)
-------------------------------------------------
The weights are:
| (8.8291137898982157481e-24 + 6.2342464676713318779e-300j)  +/-  (7.96e-52, 7.6e-110j)
| (2.1691881037981910724e-16 + 4.1652756958961011438e-297j)  +/-  (2.07e-49, 1.98e-107j)
| (1.3862700652249841093e-19 - 1.6911076523631058378e-298j)  +/-  (1.15e-50, 1.1e-108j)
| (9.0798595194794286564e-14 - 6.8763633386752642459e-296j)  +/-  (1.06e-48, 1.02e-106j)
| (0.011975893798179165902 - 2.8454034808803756579e-290j)  +/-  (9.85e-40, 9.41e-98j)
| (0.22953569186008560362 + 2.0279281652683223832e-289j)  +/-  (2.95e-33, 2.82e-91j)
| (1.4677930687715767309e-06 - 2.3463346990325895172e-292j)  +/-  (1.33e-45, 1.27e-103j)
| (5.4555582362826871614e-08 + 4.4576059894272090607e-293j)  +/-  (9.06e-47, 8.65e-105j)
| (0.0022163567557375102374 + 1.0984525785966584708e-290j)  +/-  (5.02e-43, 4.79e-101j)
| (2.5143058811773069175e-05 + 1.0101553669783881635e-291j)  +/-  (3.25e-45, 3.11e-103j)
| (0.1224335245096283263 - 1.2236672719249850409e-289j)  +/-  (7.83e-41, 7.48e-99j)
| (0.073353944335723876115 - 1.3294190941589155703e-289j)  +/-  (5.14e-40, 4.92e-98j)
| (1.5063656511585505659e-11 + 7.9272499674233854277e-295j)  +/-  (2.63e-49, 2.51e-107j)
| (1.2188472099232674893e-09 - 6.7611663982968268839e-294j)  +/-  (2.47e-48, 2.36e-106j)
| (0.045580157683956622228 + 6.3473778618283428998e-290j)  +/-  (1.76e-43, 1.73e-101j)
| (0.22454711671716917951 + 2.8981077585616150782e-289j)  +/-  (2.91e-42, 2.93e-100j)
| (0.29004497568521946485 - 2.8048988353803756356e-289j)  +/-  (1.63e-42, 1.64e-100j)
| (0.00028567201283546168141 - 3.6234065863460157714e-291j)  +/-  (1.86e-45, 1.74e-103j)
