Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 5 22
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Trying to find an order 5 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : 16*t^9 - 168*t^7 + 432*t^5 - 270*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^31 - 1141095506714148484381618599808/394334649438902047439291999*t^29 + 88927831384329774079403741250856/394334649438902047439291999*t^27 - 3939055914409646359068550287760842/394334649438902047439291999*t^25 + 110202597553555404630830260160458875/394334649438902047439291999*t^23 - 2047816122068785856533145189035785000/394334649438902047439291999*t^21 + 2725584358776060213320359628104395525/41508910467252847098872842*t^19 - 94578798240134650855030604178268882575/166035641869011388395491368*t^17 + 1121582156113366272255712317195171533175/332071283738022776790982736*t^15 - 1119240266993390896154782462223483461875/83017820934505694197745684*t^13 + 23394531832116920082065031908230295524125/664142567476045553581965472*t^11 - 153086331990136240261409846974659930367125/2656570269904182214327861888*t^9 + 293927126963706132256150583662299207652875/5313140539808364428655723776*t^7 - 38026238313645153455146941321463075381125/1328285134952091107163930944*t^5 + 76932632729582873183696265897062685384375/10626281079616728857311447552*t^3 - 29620971981452253508004310914218154563125/42505124318466915429245790208*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: 0
  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:
| (-4.028001652082491739 - 8.9441976282345200869e-474j)  +/-  (1.08e-120, 1.08e-120j)
| (-5.0998483461663732281 - 2.1457578371259214684e-482j)  +/-  (5.96e-121, 5.96e-121j)
| (-5.7171246599997851654 + 1.3409510750599908606e-490j)  +/-  (2.01e-121, 2.01e-121j)
| (-6.4559581362565776528 - 1.2637901240205658996e-495j)  +/-  (3.18e-122, 3.18e-122j)
| (6.4559581362565776528 - 5.5199009573973792e-497j)  +/-  (3.15e-122, 3.15e-122j)
| (0.52464762327529031788 - 3.0276067251481913031e-500j)  +/-  (1.06e-124, 1.06e-124j)
| (5.7171246599997851654 - 1.0867377782930613289e-495j)  +/-  (1.97e-121, 1.97e-121j)
| (-3.074984294967197079 - 1.0276195396717300595e-495j)  +/-  (6.04e-121, 6.04e-121j)
| (5.0998483461663732281 - 3.8191072714111905209e-502j)  +/-  (5.7e-121, 5.7e-121j)
| (-4.544329839066371747 - 3.059725206377446247e-503j)  +/-  (1.02e-120, 1.02e-120j)
| (1.6506801238857845559 - 3.0145164767697584556e-513j)  +/-  (1.06e-122, 1.06e-122j)
| (-3.5398203594020123735 - 5.5823376516382954068e-514j)  +/-  (9.09e-121, 9.09e-121j)
| (4.028001652082491739 - 3.2865522235999436351e-515j)  +/-  (1.08e-120, 1.08e-120j)
| (-1.6506801238857845559 - 4.7593235013689937677e-517j)  +/-  (1.06e-122, 1.06e-122j)
| (2.6384291054842239697 + 1.589998390896128211e-514j)  +/-  (3.52e-121, 3.52e-121j)
| (2.27988363000695857 - 2.8574117086579083924e-516j)  +/-  (1.95e-121, 1.95e-121j)
| (3.074984294967197079 + 2.3616899053453691111e-514j)  +/-  (7.02e-121, 7.02e-121j)
| (-2.0178606009310764997 - 3.2151169308834959252e-516j)  +/-  (6.95e-122, 6.95e-122j)
| (-1.2281017008770861897 - 1.6942286682062745324e-519j)  +/-  (8.88e-124, 8.88e-124j)
| (4.544329839066371747 - 1.9054313424308770487e-517j)  +/-  (9.88e-121, 9.88e-121j)
| (3.5398203594020123735 - 1.7845604213028202858e-518j)  +/-  (9.76e-121, 9.76e-121j)
| (2.0178606009310764997 - 1.4241112308831346086e-518j)  +/-  (6.94e-122, 6.94e-122j)
| (0.58729369237672209445 - 1.6103151814180801676e-521j)  +/-  (2.4e-124, 2.4e-124j)
| (-2.27988363000695857 + 2.0103777017192789156e-520j)  +/-  (1.97e-121, 1.97e-121j)
| (-0.73395630342256598469 + 1.6797347110583193624e-528j)  +/-  (2.04e-124, 2.04e-124j)
| (-1.4349918121605397115e-533 + 1.8062946250101587311e-533j)  +/-  (7.15e-532, 7.15e-532j)
| (0.73395630342256598469 - 4.6841473006635611966e-529j)  +/-  (1.79e-124, 1.79e-124j)
| (1.2281017008770861897 + 8.3545657163251636506e-530j)  +/-  (9.38e-124, 9.38e-124j)
| (-0.52464762327529031788 - 1.2183081053938001832e-528j)  +/-  (1.07e-124, 1.07e-124j)
| (-0.58729369237672209445 + 4.8868733531192703409e-531j)  +/-  (2.2e-124, 2.2e-124j)
| (-2.6384291054842239697 - 2.0455336324960090319e-539j)  +/-  (4.01e-121, 4.01e-121j)
-------------------------------------------------
The weights are:
| (2.5404372475504477687e-08 - 1.1876568747534184261e-480j)  +/-  (9.21e-28, 5.28e-89j)
| (1.6608396108941544357e-12 + 5.7595816319151145881e-484j)  +/-  (4.67e-31, 2.68e-92j)
| (2.3824678925785586536e-15 - 8.3705037329172007757e-486j)  +/-  (7.24e-33, 4.15e-94j)
| (3.7974519741110367212e-19 + 4.3555522085694003846e-488j)  +/-  (7.19e-35, 4.12e-96j)
| (3.7974519741110367212e-19 - 1.0086924635268054511e-488j)  +/-  (6.11e-38, 3.5e-99j)
| (0.76744979985187594386 - 1.4960493944755447588e-475j)  +/-  (6.2e-26, 3.56e-87j)
| (2.3824678925785586536e-15 + 1.4508596388432858376e-486j)  +/-  (1.39e-36, 7.97e-98j)
| (2.000140895134877191e-05 - 2.7621864546440664163e-479j)  +/-  (7.42e-29, 4.26e-90j)
| (1.6608396108941544357e-12 - 6.7632449429600012849e-485j)  +/-  (1.09e-35, 6.25e-97j)
| (3.235375594631108827e-10 - 2.8135330043893989536e-482j)  +/-  (4e-32, 2.3e-93j)
| (0.015081206121430788211 - 1.1155754725294078858e-477j)  +/-  (4.69e-26, 2.69e-87j)
| (9.7133028767598245222e-07 + 5.4877094151755650552e-480j)  +/-  (3.45e-30, 1.98e-91j)
| (2.5404372475504477687e-08 - 2.820526748496934292e-482j)  +/-  (2.64e-34, 1.52e-95j)
| (0.015081206121430788211 - 2.6647628561710440927e-477j)  +/-  (1.47e-26, 8.46e-88j)
| (0.00022129081360678740391 + 3.5244414692272211039e-479j)  +/-  (3.79e-31, 2.17e-92j)
| (0.00088195709269059023856 - 2.2328292032596314382e-478j)  +/-  (3.34e-30, 1.92e-91j)
| (2.000140895134877191e-05 - 3.706063414103295281e-480j)  +/-  (1e-32, 5.74e-94j)
| (0.0029125606212812493777 + 1.6461531681959734673e-477j)  +/-  (1.36e-30, 7.83e-92j)
| (0.054331110832471718862 + 5.8749374698843123184e-477j)  +/-  (2.04e-28, 1.17e-89j)
| (3.235375594631108827e-10 + 1.694645612839549824e-483j)  +/-  (1.8e-36, 1.03e-97j)
| (9.7133028767598245222e-07 + 3.539984254620178678e-481j)  +/-  (3.23e-34, 1.85e-95j)
| (0.0029125606212812493777 + 5.4731648215471304666e-478j)  +/-  (4.41e-31, 2.53e-92j)
| (-0.77362802918095569677 + 1.8749438740258343042e-475j)  +/-  (6.84e-29, 3.92e-90j)
| (0.00088195709269059023856 - 8.0569105121103950439e-478j)  +/-  (1.93e-32, 1.11e-93j)
| (0.30512501324891644 - 7.1068869804892067325e-476j)  +/-  (9.86e-31, 5.66e-92j)
| (0.25520818425973979327 + 1.8686702273533434267e-476j)  +/-  (1.84e-30, 1.06e-91j)
| (0.30512501324891644 - 4.9161307639333850136e-476j)  +/-  (1.68e-30, 9.65e-92j)
| (0.054331110832471718862 + 3.1295497882673454833e-477j)  +/-  (7.8e-32, 4.47e-93j)
| (0.76744979985187594386 - 1.9441335747504550542e-475j)  +/-  (1.85e-31, 1.07e-92j)
| (-0.77362802918095569677 + 2.515011397139687023e-475j)  +/-  (1.99e-31, 1.14e-92j)
| (0.00022129081360678740391 + 1.690839752902074286e-478j)  +/-  (2.88e-35, 1.6e-96j)
