Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 36
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^41 - 300485341728498038566567469904881468758/201055517588041462530306433067873447*t^39 + 50543970073899062469657084528036329598177/201055517588041462530306433067873447*t^37 - 10149808554700615983939299074490427271306035/402111035176082925060612866135746894*t^35 + 40008287883114330640418466174753765009109665/23653590304475466180036050949161582*t^33 - 1895491345607474818141305392225889332881601595/23653590304475466180036050949161582*t^31 + 131266943451154149928549714612306924867698414885/47307180608950932360072101898323164*t^29 - 6775154378010846941806504216426646845273178133855/94614361217901864720144203796646328*t^27 + 526960562196274658483589386430665441052531523191525/378457444871607458880576815186585312*t^25 - 15513513509070585469385323227900587841786050279815125/756914889743214917761153630373170624*t^23 + 345643814840630251973900713604183984495984827414014375/1513829779486429835522307260746341248*t^21 - 5800947917589203542224405725272662748422356238006805125/3027659558972859671044614521492682496*t^19 + 4542104526503841887323086953653797825463020147788404125/378457444871607458880576815186585312*t^17 - 335089994690656135852498939288513422546926870586916359375/6055319117945719342089229042985364992*t^15 + 2229345663790954390638664594220329373215450029886719875625/12110638235891438684178458085970729984*t^13 - 10397692150840660519443347589807063886481874369944967076875/24221276471782877368356916171941459968*t^11 + 130402165991881882485947088812746057603452820701762376314375/193770211774263018946855329375531679744*t^9 - 257717460101339943447813946260953656259052327844145734861875/387540423548526037893710658751063359488*t^7 + 288716657539005346582007637954959922577755326291048840915625/775080847097052075787421317502126718976*t^5 - 150688904957231736995270509700047923324982247789190076396875/1550161694194104151574842635004253437952*t^3 + 11583440358846110334847444555125236612685284842502905396875/1550161694194104151574842635004253437952*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
Positive weights:   41 out of 41
Indefinite weights: 0 out of 41
Negative weights:   0 out of 41
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-5.727333477144802991 - 1.1380343850330343801e-942j)  +/-  (1e-245, 1e-245j)
| (5.727333477144802991 - 2.7308010254376905525e-955j)  +/-  (1.16e-245, 1.16e-245j)
| (-7.9832862171204967188 + 5.878275034022230872e-958j)  +/-  (3.77e-248, 3.77e-248j)
| (-6.7187436265958688625 + 1.6454206703809417004e-963j)  +/-  (1.96e-246, 1.96e-246j)
| (6.7187436265958688625 + 1.5631873470334881478e-978j)  +/-  (1.99e-246, 1.99e-246j)
| (7.2929117043139296862 + 5.1001145824587620456e-980j)  +/-  (4.32e-247, 4.32e-247j)
| (-5.27732018319278536 - 1.0323269011174199586e-976j)  +/-  (1.37e-245, 1.37e-245j)
| (-1.7320508075688772935 + 1.5136429325029135292e-993j)  +/-  (2.79e-248, 2.79e-248j)
| (-7.2929117043139296862 + 2.0784037089855064535e-991j)  +/-  (4.39e-247, 4.39e-247j)
| (5.27732018319278536 - 8.9984412864616370481e-990j)  +/-  (1.48e-245, 1.48e-245j)
| (1.7320508075688772935 - 1.9301605119378558166e-994j)  +/-  (2.59e-248, 2.59e-248j)
| (3.2560928287862987817 + 6.2772318380037037999e-992j)  +/-  (1.25e-246, 1.25e-246j)
| (7.9832862171204967188 + 9.1981403093739584876e-995j)  +/-  (3.81e-248, 3.81e-248j)
| (-4.8473539174557771608 - 3.4852449396059290221e-991j)  +/-  (1.34e-245, 1.34e-245j)
| (-6.2040926423565289022 - 2.0350178647334737894e-1000j)  +/-  (5.61e-246, 5.61e-246j)
| (2.8797230836984321947 - 1.6862693270666814999e-1003j)  +/-  (4.16e-247, 4.16e-247j)
| (4.8473539174557771608 + 2.0399238251293962586e-1001j)  +/-  (1.35e-245, 1.35e-245j)
| (4.4330036033628555891 + 6.01327707515976837e-1002j)  +/-  (1.07e-245, 1.07e-245j)
| (-1.0618191230944820454 + 1.1720042110126292662e-1008j)  +/-  (3.52e-251, 3.52e-251j)
| (2.5092509783965045198 + 3.1193053861980831656e-1005j)  +/-  (1.26e-247, 1.26e-247j)
| (4.0311370577414562601 + 3.5630558362113927614e-1004j)  +/-  (6.77e-246, 6.77e-246j)
| (1.7991150573675698482 + 6.0590356643873154149e-1007j)  +/-  (3.79e-248, 3.79e-248j)
| (-1.7991150573675698482 - 1.3385202900956211213e-1006j)  +/-  (3.9e-248, 3.9e-248j)
| (6.2040926423565289022 - 2.5376148768574862318e-1005j)  +/-  (5.66e-246, 5.66e-246j)
| (-1.4172699963314691162 + 3.8296056664187431472e-1009j)  +/-  (8.15e-250, 8.15e-250j)
| (-4.4330036033628555891 - 1.3078884524129965753e-1004j)  +/-  (1.15e-245, 1.15e-245j)
| (0.35330633665641422717 - 2.3673838277949832166e-1020j)  +/-  (1.02e-253, 1.02e-253j)
| (2.1442278604330504166 + 1.3142084397757529518e-1014j)  +/-  (4.71e-248, 4.71e-248j)
| (-3.6394295899854886995 - 8.8115850425101988302e-1013j)  +/-  (3.2e-246, 3.2e-246j)
| (-0.7071067811865475244 + 4.5672142327566146656e-1027j)  +/-  (2.06e-252, 2.06e-252j)
| (-2.5092509783965045198 - 3.3808164326642567956e-1021j)  +/-  (1.33e-247, 1.33e-247j)
| (3.4971545606912908149e-1048 - 1.4393127311210406989e-1048j)  +/-  (1.55e-1046, 1.55e-1046j)
| (0.7071067811865475244 + 1.3143396586376039185e-1032j)  +/-  (2.19e-252, 2.19e-252j)
| (-4.0311370577414562601 - 2.9057125247359356678e-1025j)  +/-  (6.91e-246, 6.91e-246j)
| (3.6394295899854886995 + 7.6914779419228998908e-1038j)  +/-  (3.17e-246, 3.17e-246j)
| (-0.35330633665641422717 + 2.7811066165661393762e-1045j)  +/-  (1.02e-253, 1.02e-253j)
| (-3.2560928287862987817 + 1.0592768336897740174e-1037j)  +/-  (1.38e-246, 1.38e-246j)
| (1.0618191230944820454 + 2.2281381484712966626e-1054j)  +/-  (3.56e-251, 3.56e-251j)
| (1.4172699963314691162 - 2.049959847175952376e-1053j)  +/-  (8.5e-250, 8.5e-250j)
| (-2.8797230836984321947 + 3.8810465360492451023e-1053j)  +/-  (4.58e-247, 4.58e-247j)
| (-2.1442278604330504166 - 4.2854732257029593558e-1074j)  +/-  (4.67e-248, 4.67e-248j)
-------------------------------------------------
The weights are:
| (1.4797633399774673061e-15 - 1.0293623572378608854e-956j)  +/-  (1.38e-87, 3.75e-209j)
| (1.4797633399774673061e-15 - 1.4701619604459569309e-958j)  +/-  (1.56e-88, 4.23e-210j)
| (9.4051827539035886834e-29 + 9.224648179350386926e-965j)  +/-  (7.77e-94, 2.11e-215j)
| (7.5609921482026178512e-21 + 2.7136313585948522962e-960j)  +/-  (1.02e-90, 2.76e-212j)
| (7.5609921482026178512e-21 - 2.1615820377483419687e-961j)  +/-  (3.59e-92, 9.77e-214j)
| (2.7733986397374461971e-24 + 3.3221341242980590602e-963j)  +/-  (9.38e-94, 2.55e-215j)
| (1.9899708086432890804e-13 + 5.2066703726989244839e-956j)  +/-  (3.27e-88, 8.89e-210j)
| (0.0031469524477469398666 + 1.4096807880664973784e-949j)  +/-  (5.84e-74, 1.59e-195j)
| (2.7733986397374461971e-24 - 2.7628770043755593597e-962j)  +/-  (6.93e-93, 1.88e-214j)
| (1.9899708086432890804e-13 + 2.1291636767921855739e-957j)  +/-  (1.23e-89, 3.35e-211j)
| (0.0031469524477469398666 + 7.5503191781338712991e-950j)  +/-  (3.23e-76, 8.77e-198j)
| (5.325417581633320121e-06 - 4.436538444907323355e-953j)  +/-  (2.01e-84, 5.47e-206j)
| (9.4051827539035886834e-29 - 1.517828573733331624e-965j)  +/-  (1.45e-96, 3.94e-218j)
| (1.4849978978786392596e-11 - 2.7901932515942037207e-955j)  +/-  (5.38e-89, 1.46e-210j)
| (5.3481089447008417754e-18 - 1.7825269661153748673e-958j)  +/-  (2.18e-91, 5.92e-213j)
| (5.2714743223789138855e-05 + 2.1001993419013547725e-952j)  +/-  (4.36e-84, 1.18e-205j)
| (1.4849978978786392596e-11 - 2.3218776474014795555e-956j)  +/-  (7.31e-90, 1.99e-211j)
| (6.7170989641437272741e-10 + 2.0020564953205143529e-955j)  +/-  (2.65e-89, 7.2e-211j)
| (0.064907677061683366805 + 3.6625958448245237157e-950j)  +/-  (2.54e-78, 6.91e-200j)
| (0.00038241927235135300689 - 9.5599529035337969799e-952j)  +/-  (9.54e-85, 2.6e-206j)
| (1.9602004213180781964e-08 - 1.416545098653257029e-954j)  +/-  (1.01e-88, 2.73e-210j)
| (0.005704974419221083748 - 6.3725577679406001885e-950j)  +/-  (1.39e-82, 3.78e-204j)
| (0.005704974419221083748 - 1.2209791551343509388e-949j)  +/-  (2.86e-84, 7.78e-206j)
| (5.3481089447008417754e-18 + 7.1226696609941405429e-960j)  +/-  (6.38e-94, 1.74e-215j)
| (0.026869556229618940853 - 4.6600954719562138237e-950j)  +/-  (2.98e-83, 8.1e-205j)
| (6.7170989641437272741e-10 + 1.5715907713137445909e-954j)  +/-  (3.58e-93, 9.74e-215j)
| (0.17602355055598552405 + 3.0526511766246317883e-950j)  +/-  (1.61e-83, 4.37e-205j)
| (0.0020571335407555590894 + 4.8814931899142335677e-951j)  +/-  (1.68e-85, 4.56e-207j)
| (3.8636914469841875677e-07 + 3.8067912759599701668e-953j)  +/-  (1.57e-92, 4.26e-214j)
| (0.12120705627942982897 - 3.5161299009710053578e-950j)  +/-  (4.78e-85, 1.3e-206j)
| (0.00038241927235135300689 - 2.4468409219347727791e-951j)  +/-  (2.46e-90, 6.68e-212j)
| (0.19928446674898542392 - 3.3082180803327906357e-950j)  +/-  (1.38e-85, 3.75e-207j)
| (0.12120705627942982897 - 2.7433263013754710158e-950j)  +/-  (3.53e-86, 9.6e-208j)
| (1.9602004213180781964e-08 - 8.1495948514184148013e-954j)  +/-  (2.76e-93, 7.52e-215j)
| (3.8636914469841875677e-07 + 8.4855507134205349866e-954j)  +/-  (1.76e-91, 4.78e-213j)
| (0.17602355055598552405 + 3.4540339668893186066e-950j)  +/-  (4.29e-87, 1.17e-208j)
| (5.325417581633320121e-06 - 1.6127654827853662433e-952j)  +/-  (2.17e-92, 5.9e-214j)
| (0.064907677061683366805 + 2.5169405510944712147e-950j)  +/-  (1.54e-88, 4.17e-210j)
| (0.026869556229618940853 - 2.8112557100393261252e-950j)  +/-  (1.04e-88, 2.82e-210j)
| (5.2714743223789138855e-05 + 6.3479661987484638617e-952j)  +/-  (3.71e-92, 1.02e-213j)
| (0.0020571335407555590894 + 1.0723929789894795237e-950j)  +/-  (9.34e-91, 2.49e-212j)
