Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 30
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^35 - 68846340047732409363835016641/63227392892962910859160634*t^33 + 2367564651603713669857353746679/18064969397989403102617324*t^31 - 2333691488154707773585955043094185/252909571571851643436642536*t^29 + 30621734494585059989834459689485885/72259877591957612410469296*t^27 - 1937332891052733362494069706446855845/144519755183915224820938592*t^25 + 86926297719563174817810777355020553275/289039510367830449641877184*t^23 - 2806899376703369914691589984408081582075/578079020735660899283754368*t^21 + 65531580050397733340081217924981898976625/1156158041471321798567508736*t^19 - 1102432044747529245586899432849315422961375/2312316082942643597135017472*t^17 + 13218345042809828466067591589046118541359125/4624632165885287194270034944*t^15 - 110814785337642907245463434996697177417762125/9249264331770574388540069888*t^13 + 630725838101622388856010323993360236236786375/18498528663541148777080139776*t^11 - 2332962190056478136995217363274353516992914375/36997057327082297554160279552*t^9 + 5248097383577596322998342098484204439440325625/73994114654164595108320559104*t^7 - 6452457046425266291928538840323358106347715625/147988229308329190216641118208*t^5 + 3571266257783259757734601384452555209105169375/295976458616658380433282236416*t^3 - 283017090170541331628942043875739534919749375/295976458616658380433282236416*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:   35 out of 35
Indefinite weights: 0 out of 35
Negative weights:   0 out of 35
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-6.5768612536323514362 - 5.879941154265697309e-934j)  +/-  (4.78e-248, 4.78e-248j)
| (-2.4519776285278343649 - 1.7924380882681565312e-934j)  +/-  (1.55e-248, 1.55e-248j)
| (-4.9680519955752142466 - 2.4583070372280593205e-933j)  +/-  (5.79e-247, 5.79e-247j)
| (7.2853976927995190402 - 1.0663297415527928925e-934j)  +/-  (5.63e-249, 5.63e-249j)
| (5.4581240238034483397 + 2.1248117978987282708e-940j)  +/-  (3.83e-247, 3.83e-247j)
| (6.5768612536323514362 + 7.404103408843700792e-958j)  +/-  (5.18e-248, 5.18e-248j)
| (5.9870670273960682789 + 5.4930017426853038825e-971j)  +/-  (1.88e-247, 1.88e-247j)
| (4.9680519955752142466 - 1.4870266684649567385e-984j)  +/-  (5.8e-247, 5.8e-247j)
| (-5.9870670273960682789 - 3.687038419081773356e-995j)  +/-  (1.75e-247, 1.75e-247j)
| (2.8344807468650024196 - 4.5613193626599257413e-995j)  +/-  (4.85e-248, 4.85e-248j)
| (-7.2853976927995190402 - 5.0997996866398112415e-999j)  +/-  (6.35e-249, 6.35e-249j)
| (-5.4581240238034483397 - 4.2231461348742010197e-997j)  +/-  (4.1e-247, 4.1e-247j)
| (-2.8344807468650024196 + 8.7231792853713725106e-999j)  +/-  (5.03e-248, 5.03e-248j)
| (-2.0842762203546961211 + 4.588181338421937867e-1000j)  +/-  (3.86e-249, 3.86e-249j)
| (2.0842762203546961211 - 3.3658385561060611806e-1001j)  +/-  (3.83e-249, 3.83e-249j)
| (-4.5056524079423466028 - 4.815492202358613208e-997j)  +/-  (6.2e-247, 6.2e-247j)
| (1.7320508075688772935 + 1.9614955641064094692e-1001j)  +/-  (7.71e-250, 7.71e-250j)
| (2.4519776285278343649 + 4.7693771746599043822e-999j)  +/-  (1.44e-248, 1.44e-248j)
| (-1.3913079603831477717 - 3.5195458213118526623e-1006j)  +/-  (1.24e-250, 1.24e-250j)
| (4.5056524079423466028 - 1.3036091791059742058e-1001j)  +/-  (6.69e-247, 6.69e-247j)
| (-3.2305851811933308494 + 6.6887746334369131766e-1013j)  +/-  (1.46e-247, 1.46e-247j)
| (1.0522288907775354322 - 1.2932513604194160474e-1017j)  +/-  (1.37e-251, 1.37e-251j)
| (-3.6401698307760105844 + 2.5108319866271810205e-1012j)  +/-  (3.07e-247, 3.07e-247j)
| (-4.0643776950988779775 - 1.2790830097360986698e-1014j)  +/-  (4.84e-247, 4.84e-247j)
| (4.0643776950988779775 + 6.2481554626800724946e-1015j)  +/-  (5.43e-247, 5.43e-247j)
| (-4.0063211456752126545e-1037 + 4.0304572551847802256e-1037j)  +/-  (1.99e-1035, 1.99e-1035j)
| (0.7071067811865475244 + 2.1867935546446564918e-1034j)  +/-  (1.25e-252, 1.25e-252j)
| (3.2305851811933308494 + 4.9624001913450103153e-1032j)  +/-  (1.34e-247, 1.34e-247j)
| (-1.7320508075688772935 + 7.6895744321757143678e-1047j)  +/-  (8.33e-250, 8.33e-250j)
| (-0.7071067811865475244 - 5.6182353092812945141e-1049j)  +/-  (1.17e-252, 1.17e-252j)
| (-1.0522288907775354322 - 4.7154855548807597877e-1049j)  +/-  (1.29e-251, 1.29e-251j)
| (1.3913079603831477717 + 5.1839300855214993842e-1048j)  +/-  (1.27e-250, 1.27e-250j)
| (3.6401698307760105844 - 3.5019953635627595215e-1061j)  +/-  (3.31e-247, 3.31e-247j)
| (0.35534741239234300702 - 3.0749283629296759716e-1071j)  +/-  (7.67e-254, 7.67e-254j)
| (-0.35534741239234300702 + 3.4086673011725339007e-1071j)  +/-  (7.67e-254, 7.67e-254j)
-------------------------------------------------
The weights are:
| (5.8571986938541090325e-20 - 3.2220117358360005663e-947j)  +/-  (6.38e-94, 6.98e-217j)
| (0.00051856693927624149234 - 2.9907547194806731354e-937j)  +/-  (4.71e-80, 5.15e-203j)
| (5.1160711474220354169e-12 + 7.9850697271382940997e-943j)  +/-  (6.69e-90, 7.31e-213j)
| (4.0943339194035396742e-24 - 9.1670168811531056028e-950j)  +/-  (5e-97, 5.47e-220j)
| (3.2989088102284431287e-14 + 1.8299336966880625197e-944j)  +/-  (2.16e-93, 2.36e-216j)
| (5.8571986938541090325e-20 + 1.4570709602281919775e-947j)  +/-  (5.21e-96, 5.7e-219j)
| (8.468812642060597331e-17 - 7.1856244698788226966e-946j)  +/-  (8.47e-95, 9.26e-218j)
| (5.1160711474220354169e-12 - 2.9499614129787892541e-943j)  +/-  (4.29e-93, 4.7e-216j)
| (8.468812642060597331e-17 + 1.7419675580831782481e-945j)  +/-  (4.39e-97, 4.8e-220j)
| (7.1221419880776765029e-05 + 4.9307643885630034356e-939j)  +/-  (2.48e-89, 2.71e-212j)
| (4.0943339194035396742e-24 + 1.8604744491114226797e-949j)  +/-  (1.73e-100, 1.89e-223j)
| (3.2989088102284431287e-14 - 4.9638362258230660807e-944j)  +/-  (4.11e-96, 4.5e-219j)
| (7.1221419880776765029e-05 - 6.7810972306559936674e-938j)  +/-  (1.32e-90, 1.45e-213j)
| (0.0026356464268870000834 + 7.5566689572781341653e-937j)  +/-  (5e-88, 5.47e-211j)
| (0.0026356464268870000834 + 6.143528585621706542e-938j)  +/-  (1.61e-89, 1.76e-212j)
| (3.8817465481049163237e-10 - 1.1028654367311058332e-941j)  +/-  (3.34e-95, 3.65e-218j)
| (0.0096966512359379528397 - 1.6248580048637290461e-937j)  +/-  (1.56e-88, 1.71e-211j)
| (0.00051856693927624149234 - 1.9026354926194108715e-938j)  +/-  (5.73e-91, 6.27e-214j)
| (0.027528816650870248404 + 1.2502670966196424959e-936j)  +/-  (5.05e-88, 5.52e-211j)
| (3.8817465481049163237e-10 + 3.3550963005758777401e-942j)  +/-  (1.07e-96, 1.17e-219j)
| (6.6661758184120604075e-06 + 7.7909639649648896865e-939j)  +/-  (1.97e-93, 2.16e-216j)
| (0.063664638886837947481 - 6.0015142811888252496e-937j)  +/-  (5.6e-89, 6.13e-212j)
| (4.1340988476815772714e-07 - 9.8994495752898917436e-940j)  +/-  (9.06e-95, 9.91e-218j)
| (1.6328411610914271166e-08 + 1.1465449928188907343e-940j)  +/-  (1.22e-95, 1.33e-218j)
| (1.6328411610914271166e-08 - 2.8784457954670128802e-941j)  +/-  (8.15e-98, 8.92e-221j)
| (0.20081917819586679111 + 1.4067525671212608276e-936j)  +/-  (4.74e-92, 5.17e-215j)
| (0.11936106097674822736 + 8.8781825842069946045e-937j)  +/-  (3.47e-92, 3.79e-215j)
| (6.6661758184120604075e-06 - 1.0745423712255080588e-939j)  +/-  (1.61e-96, 1.76e-219j)
| (0.0096966512359379528397 - 9.4214278682032793289e-937j)  +/-  (1.23e-93, 1.34e-216j)
| (0.11936106097674822736 + 1.6060323368120495198e-936j)  +/-  (3.62e-93, 3.94e-216j)
| (0.063664638886837947481 - 1.5005107258974124748e-936j)  +/-  (3.34e-93, 3.65e-216j)
| (0.027528816650870248404 + 3.4566042501032933904e-937j)  +/-  (4.38e-94, 4.82e-217j)
| (4.1340988476815772714e-07 + 1.9487024111345365339e-940j)  +/-  (1.65e-97, 1.8e-220j)
| (0.1761067120581896191 - 1.1688973082109518129e-936j)  +/-  (9.79e-94, 1.09e-216j)
| (0.1761067120581896191 - 1.5644627977800466542e-936j)  +/-  (7.14e-94, 7.31e-217j)
