Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 32
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^37 - 11677736979453601096324261784542/9511418586279068934499135305*t^35 + 27148807455524723480269219927847854/161694115966744171886485300185*t^33 - 730207980282444271536030483999692492/53898038655581390628828433395*t^31 + 7762529674244965025868173296093179649/10779607731116278125765686679*t^29 - 574841519080748843342049573239934178003/21559215462232556251531373358*t^27 + 2548904238970958309225351190794691784263/3593202577038759375255228893*t^25 - 198210246163439357081870996829301985447295/14372810308155037501020915572*t^23 + 22694081614050718067782564950218650014627015/114982482465240300008167324576*t^21 - 478306755665947210018825720862893441306632825/229964964930480600016334649152*t^19 + 3688342866687369368250922496659241616997885575/229964964930480600016334649152*t^17 - 1208701672448611062651821620877501367053314275/13527350878263564706843214656*t^15 + 19067255190981338776818223244978002229613888075/54109403513054258827372858624*t^13 - 103297203344414807307893975887453062160266165225/108218807026108517654745717248*t^11 + 45961679206675416996131561334545566463027303625/27054701756527129413686429312*t^9 - 402109703540429031535518193527453926649071984625/216437614052217035309491434496*t^7 + 3880855434973401355479390754977145967959486078125/3463001824835472564951862951936*t^5 - 2122969357311512709576123853728724890532848778875/6926003649670945129903725903872*t^3 + 166996534536422332525637275545261042532074822375/6926003649670945129903725903872*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:
| (-6.832824506126309187 + 9.6903639610682188142e-942j)  +/-  (1.16e-247, 1.16e-247j)
| (-7.5337820416391561415 - 6.5745130645431216424e-943j)  +/-  (1.14e-248, 1.14e-248j)
| (4.7874293224501567585 + 3.3232677038363470381e-939j)  +/-  (1.87e-246, 1.87e-246j)
| (6.2497773753331927774 + 2.7389020749766462948e-946j)  +/-  (4.46e-247, 4.46e-247j)
| (-1.7320508075688772935 - 1.5054482903161394343e-950j)  +/-  (1.3e-249, 1.3e-249j)
| (6.832824506126309187 - 3.0897591667278222626e-951j)  +/-  (1.08e-247, 1.08e-247j)
| (7.5337820416391561415 + 7.2775191304974679431e-955j)  +/-  (1.15e-248, 1.15e-248j)
| (-5.7272647680975908671 - 6.9826484537874537983e-961j)  +/-  (1.24e-246, 1.24e-246j)
| (-4.3525632936370854429 - 1.2227632501667133457e-974j)  +/-  (1.61e-246, 1.61e-246j)
| (5.7272647680975908671 + 3.0251751334445269825e-977j)  +/-  (1.17e-246, 1.17e-246j)
| (-2.4096460201953588935 - 1.2302709945734597702e-980j)  +/-  (2.99e-248, 2.99e-248j)
| (1.0556178229827158961 + 1.0035368000575853509e-988j)  +/-  (1.62e-251, 1.62e-251j)
| (-6.2497773753331927774 + 1.8804008159740575289e-982j)  +/-  (4.71e-247, 4.71e-247j)
| (2.4096460201953588935 + 1.6085894155269360584e-985j)  +/-  (2.95e-248, 2.95e-248j)
| (-4.7874293224501567585 - 3.3032090402763888297e-988j)  +/-  (1.89e-246, 1.89e-246j)
| (1.3973800415222021888 - 4.5913342391711027622e-996j)  +/-  (1.54e-250, 1.54e-250j)
| (3.9349378367615971876 + 6.0128390265416760434e-998j)  +/-  (1.2e-246, 1.2e-246j)
| (-0.35446301921821254174 + 9.3935656796585809855e-1015j)  +/-  (8.54e-254, 8.54e-254j)
| (-5.2435095755405843874 + 8.9320815563501227591e-1006j)  +/-  (1.81e-246, 1.81e-246j)
| (-1.3973800415222021888 - 1.5779176874943790594e-1012j)  +/-  (1.69e-250, 1.69e-250j)
| (2.0659712045343758467 + 1.0204522474289799017e-1014j)  +/-  (7.76e-249, 7.76e-249j)
| (4.3525632936370854429 + 7.1545129188521841708e-1015j)  +/-  (1.77e-246, 1.77e-246j)
| (2.7687837102851497428 - 8.5619609602123459405e-1023j)  +/-  (8.86e-248, 8.86e-248j)
| (-3.5322131009294326936 - 1.9976781845548268109e-1024j)  +/-  (6.32e-247, 6.32e-247j)
| (-2.7687837102851497428 + 1.315588613842060227e-1037j)  +/-  (9.08e-248, 9.08e-248j)
| (5.2435095755405843874 + 4.1888701722394385396e-1044j)  +/-  (1.75e-246, 1.75e-246j)
| (0.35446301921821254174 + 8.2736262879525949533e-1055j)  +/-  (8.53e-254, 8.53e-254j)
| (-2.0659712045343758467 - 5.6457791841666186357e-1048j)  +/-  (7.22e-249, 7.22e-249j)
| (-3.9349378367615971876 + 2.7680573229577521547e-1050j)  +/-  (1.15e-246, 1.15e-246j)
| (-0.7071067811865475244 + 1.3110705230341406082e-1056j)  +/-  (1.32e-252, 1.32e-252j)
| (3.5322131009294326936 + 1.081828962153617935e-1052j)  +/-  (5.82e-247, 5.82e-247j)
| (3.1433922943518680143 + 3.0097328772433066308e-1062j)  +/-  (2.92e-247, 2.92e-247j)
| (0.7071067811865475244 + 1.1518102774079388894e-1067j)  +/-  (1.39e-252, 1.39e-252j)
| (-8.077664083378933654e-1068 - 6.3210446745653233441e-1069j)  +/-  (3e-1066, 3e-1066j)
| (-1.0556178229827158961 + 4.8604948742557269839e-1065j)  +/-  (1.42e-251, 1.42e-251j)
| (-3.1433922943518680143 + 6.7216510295715758001e-1070j)  +/-  (2.58e-247, 2.58e-247j)
| (1.7320508075688772935 + 8.6134893499576931927e-1072j)  +/-  (1.27e-249, 1.27e-249j)
-------------------------------------------------
The weights are:
| (1.8714618177393840979e-21 - 3.0490600016437715529e-956j)  +/-  (1.85e-95, 2.47e-219j)
| (1.0211839891846899099e-25 + 1.7312825061412837776e-958j)  +/-  (5.27e-97, 7.05e-221j)
| (2.790200176736680466e-11 - 4.8630322684076339515e-949j)  +/-  (1.13e-91, 1.51e-215j)
| (3.3613909465124077028e-18 - 1.2396775334333287604e-953j)  +/-  (6.02e-96, 8.05e-220j)
| (0.0093423484227622431033 - 1.5434883841420101999e-945j)  +/-  (5e-79, 6.69e-203j)
| (1.8714618177393840979e-21 + 1.7322326371650466512e-955j)  +/-  (1.35e-97, 1.81e-221j)
| (1.0211839891846899099e-25 - 7.7672030853784912736e-958j)  +/-  (1.77e-99, 2.36e-223j)
| (1.6050115675267297265e-15 - 4.5377993846367872084e-953j)  +/-  (1.31e-96, 1.75e-220j)
| (1.4221331899019205489e-09 + 8.9319272330346728763e-950j)  +/-  (7.86e-94, 1.05e-217j)
| (1.6050115675267297265e-15 + 5.0768033586009744716e-952j)  +/-  (1.39e-96, 1.86e-220j)
| (0.00059586016705136135625 - 2.5933525938233276958e-946j)  +/-  (1.84e-87, 2.46e-211j)
| (0.063968051722463913103 - 6.5627909122582349338e-945j)  +/-  (1.25e-79, 1.67e-203j)
| (3.3613909465124077028e-18 + 1.6424791627473737651e-954j)  +/-  (5.99e-98, 8.01e-222j)
| (0.00059586016705136135625 - 7.8495623298576687728e-946j)  +/-  (1.86e-89, 2.49e-213j)
| (2.790200176736680466e-11 - 9.6842991099623787867e-951j)  +/-  (2.76e-95, 3.69e-219j)
| (0.027045564094342098019 + 5.0150104916790621153e-945j)  +/-  (9.71e-85, 1.3e-208j)
| (4.3611649899373873963e-08 - 6.6379784271601630919e-948j)  +/-  (1.12e-94, 1.51e-218j)
| (0.17608433392127374896 - 7.0027663014601731143e-945j)  +/-  (5.23e-84, 7e-208j)
| (3.030595676363577619e-13 + 7.9033852936798979067e-952j)  +/-  (2.19e-96, 2.94e-220j)
| (0.027045564094342098019 + 2.7488537176130580033e-945j)  +/-  (7.23e-87, 9.68e-211j)
| (0.0026647555958902509104 + 1.78420898430876272e-945j)  +/-  (3.84e-89, 5.14e-213j)
| (1.4221331899019205489e-09 + 1.8773084779099768768e-948j)  +/-  (1.51e-95, 2.02e-219j)
| (9.7015503334893907127e-05 + 2.86880093547437918e-946j)  +/-  (5.26e-92, 7.04e-216j)
| (8.5176574767581823901e-07 + 3.8292430621280433452e-948j)  +/-  (8.29e-95, 1.11e-218j)
| (9.7015503334893907127e-05 + 7.664012753633314535e-947j)  +/-  (3.56e-93, 4.76e-217j)
| (3.030595676363577619e-13 - 1.7382555658636898697e-950j)  +/-  (2.94e-98, 3.94e-222j)
| (0.17608433392127374896 - 8.122658163854745003e-945j)  +/-  (1.69e-89, 2.26e-213j)
| (0.0026647555958902509104 + 7.0850204686918340739e-946j)  +/-  (7.78e-92, 1.04e-215j)
| (4.3611649899373873963e-08 - 6.4877100603042529292e-949j)  +/-  (1.49e-95, 1.99e-219j)
| (0.12011784230832902211 + 5.6870583512755073409e-945j)  +/-  (8.53e-91, 1.14e-214j)
| (8.5176574767581823901e-07 + 2.5380439291887181283e-947j)  +/-  (1.8e-95, 2.41e-219j)
| (1.101835331986230321e-05 - 9.040786513485658027e-947j)  +/-  (8.45e-95, 1.13e-218j)
| (0.12011784230832902211 + 7.658155961283260738e-945j)  +/-  (6.66e-92, 8.95e-216j)
| (0.20014462616699034285 + 7.881403213914547597e-945j)  +/-  (8.63e-92, 1.17e-215j)
| (0.063968051722463913103 - 4.1914945761529074299e-945j)  +/-  (8.45e-93, 1.14e-216j)
| (1.101835331986230321e-05 - 1.8741292845859615295e-947j)  +/-  (1.43e-95, 1.96e-219j)
| (0.0093423484227622431033 - 3.2934514324284263408e-945j)  +/-  (1.3e-93, 1.56e-217j)
