Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 3 34
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P2 : 3/2*t^5 - 25/14*t^3 + 3/7*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^39 - 228761697464588906376122370873957/16189849123139034364162472845472*t^37 + 211436862599813779228659835794152477/3448437863228614319566606716085536*t^35 - 120091670840912356726543209812694095/738950970691845925621415724875472*t^33 + 27915894059883076438416613405798975975/94893620486344547615216802669425196*t^31 - 41319520074568678217966647989844017151/107271049245432966869375516061089352*t^29 + 8370249481036642629772741043957157688073/22205107193804624141960731824645495864*t^27 - 135521143880474532235519341131621881877/482375904138918117044018746902911413*t^25 + 128315819226041805938317704649681054456675/796884993637492729356718969883609654276*t^23 - 29590136946543733248991039147250066975375/415766083636952728360027288634926776144*t^21 + 478801590964097837549756473052877842935/19798384935092987064763204220710798864*t^19 - 3285572463984235364479301495234405269535/524657200779964157216224911848836169896*t^17 + 957893821782295391782631745094684364405/786985801169946235824337367773254254844*t^15 - 91059384190469003893332573651879566275/524657200779964157216224911848836169896*t^13 + 3031845190204268938999362244958832096875/172612219056608207724137995998267099895784*t^11 - 3268453465890139135368133307282550701005/2718642450141579271655173436972706823358598*t^9 + 31282309233918088788583146395729311885/604142766698128727034482985993934849635244*t^7 - 1522124737959478569222988279492478744215/1217261368787201080870621147779779588465068768*t^5 + 11077752209152915567373756896161002975/804630396316963426338207199379854304239621728*t^3 - 340610804504599380234456134011646125/7912198897116807025659037460568567325022946992*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
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.92582009977255146157 + 5.5015690346549848988e-941j)  +/-  (1.37e-242, 1.37e-242j)
| (-0.95349741828540402373 + 8.413681163354250175e-940j)  +/-  (2.06e-242, 2.06e-242j)
| (-0.89202324259832778113 + 1.1542123288847164801e-955j)  +/-  (6.73e-243, 6.73e-243j)
| (-0.98974112479186593392 - 4.5419348886557713332e-968j)  +/-  (1.79e-242, 1.79e-242j)
| (0.95349741828540402373 + 1.8980921788965192261e-981j)  +/-  (1.97e-242, 1.97e-242j)
| (0.80709049477970182315 + 1.0743688074597950729e-984j)  +/-  (9.03e-244, 9.03e-244j)
| (0.9748556138175737231 + 5.204673297953900004e-983j)  +/-  (2.48e-242, 2.48e-242j)
| (-0.92582009977255146157 + 1.3329144008843373507e-988j)  +/-  (1.27e-242, 1.27e-242j)
| (-0.070250653320290839211 - 3.0775614125237058262e-1009j)  +/-  (1.63e-254, 1.63e-254j)
| (0.99805002478633812881 - 2.5992562559470531575e-999j)  +/-  (6.33e-243, 6.33e-243j)
| (0.89202324259832778113 + 2.4378283567396202428e-1004j)  +/-  (6.48e-243, 6.48e-243j)
| (-0.99805002478633812881 + 1.9724030906894632276e-1001j)  +/-  (5.9e-243, 5.9e-243j)
| (-0.85235096843230253005 + 1.9937097930211722511e-1016j)  +/-  (2.82e-243, 2.82e-243j)
| (-0.80709049477970182315 - 3.9944855156701245515e-1030j)  +/-  (9.01e-244, 9.01e-244j)
| (0.98974112479186593392 - 3.6582001658346923765e-1034j)  +/-  (1.78e-242, 1.78e-242j)
| (0.85235096843230253005 + 1.2298787883869587976e-1039j)  +/-  (2.79e-243, 2.79e-243j)
| (0.43945480667863374259 + 2.6804855077442881753e-1047j)  +/-  (1.13e-248, 1.13e-248j)
| (-0.9748556138175737231 + 4.8856404530325448537e-1049j)  +/-  (2.39e-242, 2.39e-242j)
| (-0.75657071273159740107 + 1.4739371662850372618e-1062j)  +/-  (2.37e-244, 2.37e-244j)
| (-0.70116100578483626398 + 2.8990785547116793564e-1068j)  +/-  (5.04e-245, 5.04e-245j)
| (0.64127074523328724542 + 2.1378530581066442979e-1065j)  +/-  (8.44e-246, 8.44e-246j)
| (0.70116100578483626398 - 6.8857825557658652229e-1065j)  +/-  (5.02e-245, 5.02e-245j)
| (4.6309563690332206968e-1077 - 1.6336004516912117006e-1078j)  +/-  (1.81e-1075, 1.81e-1075j)
| (-0.57735026918962576451 + 9.6589394162628684664e-1068j)  +/-  (1.07e-246, 1.07e-246j)
| (-0.50989487463118129875 - 3.9050725220187878295e-1069j)  +/-  (1.32e-247, 1.32e-247j)
| (0.21718907274290636799 + 4.8614190093076465516e-1073j)  +/-  (4.78e-252, 4.78e-252j)
| (0.75657071273159740107 + 8.9927496823713124221e-1069j)  +/-  (2.47e-244, 2.47e-244j)
| (0.29225074053553326977 - 5.2443226335666584286e-1075j)  +/-  (7.05e-251, 7.05e-251j)
| (-0.29225074053553326977 - 2.8598044953251646303e-1074j)  +/-  (7.46e-251, 7.46e-251j)
| (-0.64127074523328724542 - 2.6913645973340527867e-1071j)  +/-  (8.4e-246, 8.4e-246j)
| (-0.21718907274290636799 + 1.0070369622098784425e-1077j)  +/-  (4.87e-252, 4.87e-252j)
| (0.36665714971506803423 + 6.0137420565995680059e-1075j)  +/-  (1.01e-249, 1.01e-249j)
| (0.57735026918962576451 - 2.1473750259605151701e-1072j)  +/-  (1.2e-246, 1.2e-246j)
| (-0.14272850180710537402 - 7.9952564330390850762e-1081j)  +/-  (3.21e-253, 3.21e-253j)
| (-0.43945480667863374259 - 2.9262514192291259205e-1077j)  +/-  (1.27e-248, 1.27e-248j)
| (-0.36665714971506803423 + 4.317365239576745325e-1077j)  +/-  (1.02e-249, 1.02e-249j)
| (0.070250653320290839211 - 2.5704023043392823558e-1083j)  +/-  (1.63e-254, 1.63e-254j)
| (0.50989487463118129875 + 2.6603416497832068294e-1075j)  +/-  (1.19e-247, 1.19e-247j)
| (0.14272850180710537402 - 1.6299707330094790499e-1081j)  +/-  (2.96e-253, 2.96e-253j)
-------------------------------------------------
The weights are:
| (0.030774110625146033173 - 2.9199435605403225466e-941j)  +/-  (2.91e-78, 5.69e-196j)
| (0.024547239003810385414 + 2.4408679943621895612e-940j)  +/-  (1.04e-78, 2.02e-196j)
| (0.036778892637152583559 + 6.7009719698165748455e-940j)  +/-  (8.34e-79, 1.63e-196j)
| (0.011609909139755284517 - 1.7717802526756171104e-940j)  +/-  (1.6e-79, 3.13e-197j)
| (0.024547239003810385414 - 3.1191306829249095755e-941j)  +/-  (5.21e-79, 1.02e-196j)
| (0.047948349570230093576 + 7.1938467263265639589e-941j)  +/-  (1.56e-79, 3.05e-197j)
| (0.018143524708011654457 + 8.0447874730296270916e-942j)  +/-  (9.4e-80, 1.84e-197j)
| (0.030774110625146033173 - 1.0871909866150885198e-939j)  +/-  (3.71e-80, 7.24e-198j)
| (0.07120119212409358034 - 8.4157668392576562225e-940j)  +/-  (2.83e-82, 5.52e-200j)
| (0.005002504830780694169 + 4.8750688072626496003e-943j)  +/-  (1.21e-80, 2.36e-198j)
| (0.036778892637152583559 + 9.0785567342504411559e-941j)  +/-  (5.04e-80, 9.84e-198j)
| (0.005002504830780694169 + 4.0895229041424105988e-941j)  +/-  (4.26e-81, 8.32e-199j)
| (0.042517761889078183455 - 5.3560961644216804847e-940j)  +/-  (1.64e-81, 3.2e-199j)
| (0.047948349570230093576 + 4.7366741138862063694e-940j)  +/-  (3.05e-82, 5.95e-200j)
| (0.011609909139755284517 - 2.3551917176030177829e-942j)  +/-  (3.52e-81, 6.88e-199j)
| (0.042517761889078183455 - 7.129562562734339693e-941j)  +/-  (4.62e-82, 9.03e-200j)
| (0.071731495777500843261 + 2.0235494390207079175e-940j)  +/-  (4.05e-85, 7.91e-203j)
| (0.018143524708011654457 + 5.9765422129286179637e-940j)  +/-  (1.01e-81, 1.96e-199j)
| (0.053029640404521012449 - 4.4255588880709222398e-940j)  +/-  (1.1e-83, 2.16e-201j)
| (0.057721557879968038258 + 4.2874418614102834772e-940j)  +/-  (1.48e-84, 2.89e-202j)
| (0.061983966847210017803 - 1.0874444280508230686e-940j)  +/-  (5.15e-86, 1e-203j)
| (0.057721557879968038258 + 9.1701104208958367367e-941j)  +/-  (1.25e-85, 2.43e-203j)
| (0.06972738646163952987 + 8.4288121411807774887e-940j)  +/-  (1.05e-87, 2.05e-205j)
| (0.065774589187774705536 + 4.3512126572989168764e-940j)  +/-  (3.48e-87, 6.8e-205j)
| (0.069044831654816235476 - 4.531499938490851814e-940j)  +/-  (1.05e-87, 2.05e-205j)
| (0.074997799803918251263 - 4.4109705328178468155e-940j)  +/-  (5.31e-89, 1.04e-206j)
| (0.053029640404521012449 - 7.9436912708891189443e-941j)  +/-  (3.83e-87, 7.47e-205j)
| (0.074915594094811286473 + 3.3442402357802845264e-940j)  +/-  (4.29e-89, 8.37e-207j)
| (0.074915594094811286473 + 5.8456856480495751423e-940j)  +/-  (4.05e-90, 7.92e-208j)
| (0.061983966847210017803 - 4.269271456029561386e-940j)  +/-  (1.16e-88, 2.27e-206j)
| (0.074997799803918251263 - 6.649024099778575288e-940j)  +/-  (3.19e-90, 6.23e-208j)
| (0.07374038077776505812 - 2.5769838535639064532e-940j)  +/-  (1.9e-90, 3.71e-208j)
| (0.065774589187774705536 + 1.3151027548376241642e-940j)  +/-  (1.82e-90, 3.55e-208j)
| (0.073672965812836293766 + 7.611728927950070902e-940j)  +/-  (1.23e-90, 2.4e-208j)
| (0.071731495777500843261 + 4.821983587570980657e-940j)  +/-  (3.88e-91, 7.58e-209j)
| (0.07374038077776505812 - 5.2477099166782955335e-940j)  +/-  (3.3e-91, 6.44e-209j)
| (0.07120119212409358034 - 7.3814295274937840623e-940j)  +/-  (3.08e-92, 6.02e-210j)
| (0.069044831654816235476 - 1.6176635544055950488e-940j)  +/-  (5.85e-93, 1.19e-210j)
| (0.073672965812836293766 + 5.8245538765790059225e-940j)  +/-  (1.71e-92, 3.31e-210j)
