Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 32
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^37 - 5838868489726800548162130892271/9511418586279068934499135305*t^35 + 27148807455524723480269219927847854/161694115966744171886485300185*t^33 - 1460415960564888543072060967999384984/53898038655581390628828433395*t^31 + 31050118696979860103472693184372718596/10779607731116278125765686679*t^29 - 2299366076322995373368198292959736712012/10779607731116278125765686679*t^27 + 40782467823535332947605619052715068548208/3593202577038759375255228893*t^25 - 1585681969307514856654967974634415883578360/3593202577038759375255228893*t^23 + 45388163228101436135565129900437300029254030/3593202577038759375255228893*t^21 - 956613511331894420037651441725786882613265650/3593202577038759375255228893*t^19 + 14753371466749477473003689986636966467991542300/3593202577038759375255228893*t^17 - 9669613379588888501214572967020010936426514200/211364857472868198544425229*t^15 + 76269020763925355107272892979912008918455552300/211364857472868198544425229*t^13 - 413188813377659229231575903549812248641064660900/211364857472868198544425229*t^11 + 1470773734613613343876209962705458126816873716000/211364857472868198544425229*t^9 - 3216877628323432252284145548219631413192575877000/211364857472868198544425229*t^7 + 3880855434973401355479390754977145967959486078125/211364857472868198544425229*t^5 - 2122969357311512709576123853728724890532848778875/211364857472868198544425229*t^3 + 333993069072844665051274551090522085064149644750/211364857472868198544425229*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:
| (4.4454280145314918473 - 4.8551654701453844094e-651j)  +/-  (3.67e-247, 3.67e-247j)
| (9.6630730858790715299 - 5.1217709278474305214e-666j)  +/-  (1.54e-247, 1.54e-247j)
| (-8.8385199260087264894 - 2.1540059760155633405e-678j)  +/-  (6.38e-247, 6.38e-247j)
| (7.4154423561626853831 - 1.2592714160652757462e-693j)  +/-  (2.44e-246, 2.44e-246j)
| (-10.654376739248960104 - 2.564688462463602328e-700j)  +/-  (1.75e-248, 1.75e-248j)
| (-9.6630730858790715299 - 1.4689101428050132396e-704j)  +/-  (1.67e-247, 1.67e-247j)
| (8.8385199260087264894 - 1.2650251217292586109e-714j)  +/-  (6.57e-247, 6.57e-247j)
| (10.654376739248960104 + 2.2977311426646773119e-729j)  +/-  (1.62e-248, 1.62e-248j)
| (-3.915651474362957147 - 1.3888809731468828232e-733j)  +/-  (1.37e-247, 1.37e-247j)
| (6.155454040948874354 - 5.4251376220962130334e-734j)  +/-  (2.44e-246, 2.44e-246j)
| (5.5648424558432987278 - 1.1692840643184507827e-747j)  +/-  (1.71e-246, 1.71e-246j)
| (6.7704474767116489336 - 6.5814253307252953573e-759j)  +/-  (2.69e-246, 2.69e-246j)
| (-4.4454280145314918473 - 3.7075809955889167418e-766j)  +/-  (4.11e-247, 4.11e-247j)
| (-1.492869041944917895 + 4.3506192140637896231e-777j)  +/-  (2.24e-251, 2.24e-251j)
| (-7.4154423561626853831 + 1.3027857740567796045e-776j)  +/-  (2.38e-246, 2.38e-246j)
| (4.9953036725263297395 - 4.942061040935396357e-782j)  +/-  (8.2e-247, 8.2e-247j)
| (2.921724496924793845 - 1.154485993916668237e-785j)  +/-  (9.24e-249, 9.24e-249j)
| (8.0995755103452120719 + 6.6885648158432063633e-783j)  +/-  (1.62e-246, 1.62e-246j)
| (-3.4077540822786294362 + 3.0431267847023532609e-785j)  +/-  (3.79e-248, 3.79e-248j)
| (-5.5648424558432987278 + 1.5580200853761383636e-782j)  +/-  (1.65e-246, 1.65e-246j)
| (2.4494897427831780982 - 4.0301462416744754227e-798j)  +/-  (1.62e-249, 1.62e-249j)
| (-6.155454040948874354 + 5.217183045289955391e-794j)  +/-  (2.44e-246, 2.44e-246j)
| (-8.0995755103452120719 + 3.281341937255268466e-804j)  +/-  (1.5e-246, 1.5e-246j)
| (-1.9761938065101770343 - 1.3863564236761594594e-813j)  +/-  (2.29e-250, 2.29e-250j)
| (-1 - 1.393922916353701944e-815j)  +/-  (1.78e-252, 1.78e-252j)
| (-6.7704474767116489336 + 7.1368552149859361169e-810j)  +/-  (2.79e-246, 2.79e-246j)
| (4.7199396321269534724e-840 + 8.3565639087970374057e-840j)  +/-  (3.55e-838, 3.55e-838j)
| (1.492869041944917895 - 4.3243498516219370871e-817j)  +/-  (2.12e-251, 2.12e-251j)
| (-2.4494897427831780982 - 1.9726838336822039465e-815j)  +/-  (1.91e-249, 1.91e-249j)
| (-4.9953036725263297395 + 4.8523802068818029247e-812j)  +/-  (8.33e-247, 8.33e-247j)
| (0.50128640913811121138 + 2.7882809740737049436e-818j)  +/-  (1.14e-253, 1.14e-253j)
| (1 + 4.6919184324366654737e-818j)  +/-  (1.88e-252, 1.88e-252j)
| (1.9761938065101770343 - 7.3386570222832194441e-816j)  +/-  (2.16e-250, 2.16e-250j)
| (3.4077540822786294362 + 2.2379700796373418849e-813j)  +/-  (3.65e-248, 3.65e-248j)
| (-0.50128640913811121138 + 8.5064824706393489643e-820j)  +/-  (1.14e-253, 1.14e-253j)
| (-2.921724496924793845 - 3.0579115199960166459e-816j)  +/-  (8.81e-249, 8.81e-249j)
| (3.915651474362957147 - 4.2572734287732572694e-819j)  +/-  (1.28e-247, 1.28e-247j)
-------------------------------------------------
The weights are:
| (1.101835331986230321e-05 + 1.4547196460143577626e-655j)  +/-  (8.95e-79, 9.05e-203j)
| (1.8714618177393840979e-21 - 2.4440598177865714679e-665j)  +/-  (4.12e-91, 4.16e-215j)
| (3.3613909465124077028e-18 - 4.9117384789401352326e-664j)  +/-  (1.4e-90, 1.41e-214j)
| (3.030595676363577619e-13 + 9.6072539503639799774e-661j)  +/-  (1.19e-87, 1.2e-211j)
| (1.0211839891846899099e-25 - 5.0845504407645404708e-668j)  +/-  (6.41e-94, 6.48e-218j)
| (1.8714618177393840979e-21 + 9.0386899158137165821e-666j)  +/-  (3.65e-92, 3.69e-216j)
| (3.3613909465124077028e-18 + 1.4852245199178794981e-663j)  +/-  (6.13e-91, 6.19e-215j)
| (1.0211839891846899099e-25 + 1.236533305721356228e-667j)  +/-  (3.17e-94, 3.21e-218j)
| (9.7015503334893907127e-05 - 2.4928782329415728818e-656j)  +/-  (2.02e-83, 2.05e-207j)
| (1.4221331899019205489e-09 + 1.7182696684725461691e-658j)  +/-  (3.99e-87, 4.04e-211j)
| (4.3611649899373873963e-08 - 1.8194406864137931395e-657j)  +/-  (2.35e-86, 2.38e-210j)
| (2.790200176736680466e-11 - 1.4354134660794288497e-659j)  +/-  (3.06e-88, 3.09e-212j)
| (1.101835331986230321e-05 + 6.0169603918437543843e-657j)  +/-  (2.13e-87, 2.15e-211j)
| (0.063968051722463913103 + 1.4843942728865068839e-654j)  +/-  (6.14e-77, 6.2e-201j)
| (3.030595676363577619e-13 - 2.4056988336011953176e-661j)  +/-  (1.93e-93, 1.96e-217j)
| (8.5176574767581823901e-07 + 2.0852402743797819653e-656j)  +/-  (2.5e-86, 2.53e-210j)
| (0.0026647555958902509104 - 1.1469641119135293931e-654j)  +/-  (8.52e-84, 8.62e-208j)
| (1.6050115675267297265e-15 - 4.6995795800466459386e-662j)  +/-  (2.97e-91, 3e-215j)
| (0.00059586016705136135625 + 8.5541127357790572674e-656j)  +/-  (1.9e-86, 1.92e-210j)
| (4.3611649899373873963e-08 + 2.0346185305476676912e-658j)  +/-  (1.8e-91, 1.82e-215j)
| (0.0093423484227622431033 + 1.814563206393874186e-654j)  +/-  (6.51e-85, 6.58e-209j)
| (1.4221331899019205489e-09 - 2.7717371423565719814e-659j)  +/-  (9.66e-93, 9.77e-217j)
| (1.6050115675267297265e-15 + 1.3689081011217593257e-662j)  +/-  (5.63e-96, 5.7e-220j)
| (0.027045564094342098019 - 9.5287526649564159429e-655j)  +/-  (8.51e-87, 8.61e-211j)
| (0.12011784230832902211 - 2.0653307051377154899e-654j)  +/-  (2.1e-85, 2.13e-209j)
| (2.790200176736680466e-11 + 2.9755717665694623007e-660j)  +/-  (5.62e-94, 5.68e-218j)
| (0.20014462616699034285 - 3.0548877626438924529e-654j)  +/-  (3.79e-86, 3.83e-210j)
| (0.063968051722463913103 + 2.9854692905965049164e-654j)  +/-  (1.3e-87, 1.32e-211j)
| (0.0093423484227622431033 + 5.2527909362017041966e-655j)  +/-  (1.34e-88, 1.36e-212j)
| (8.5176574767581823901e-07 - 1.2145487298657259272e-657j)  +/-  (1.46e-91, 1.48e-215j)
| (0.17608433392127374896 + 3.2858143997782706557e-654j)  +/-  (1.31e-86, 1.33e-210j)
| (0.12011784230832902211 - 3.2642126416790937724e-654j)  +/-  (4.27e-87, 4.31e-211j)
| (0.027045564094342098019 - 2.4780981019061304501e-654j)  +/-  (5.72e-89, 5.77e-213j)
| (0.00059586016705136135625 + 6.4738067424387910819e-655j)  +/-  (2.95e-91, 2.98e-215j)
| (0.17608433392127374896 + 2.6198636452015550517e-654j)  +/-  (3.3e-89, 3.75e-213j)
| (0.0026647555958902509104 - 2.3721963800445711241e-655j)  +/-  (9.52e-91, 1.08e-214j)
| (9.7015503334893907127e-05 - 3.9343291900257632099e-655j)  +/-  (7.11e-92, 7.11e-216j)
