Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 30
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^35 - 68846340047732409363835016641/126454785785925821718321268*t^33 + 2367564651603713669857353746679/18064969397989403102617324*t^31 - 2333691488154707773585955043094185/126454785785925821718321268*t^29 + 30621734494585059989834459689485885/18064969397989403102617324*t^27 - 1937332891052733362494069706446855845/18064969397989403102617324*t^25 + 86926297719563174817810777355020553275/18064969397989403102617324*t^23 - 2806899376703369914691589984408081582075/18064969397989403102617324*t^21 + 65531580050397733340081217924981898976625/18064969397989403102617324*t^19 - 1102432044747529245586899432849315422961375/18064969397989403102617324*t^17 + 13218345042809828466067591589046118541359125/18064969397989403102617324*t^15 - 110814785337642907245463434996697177417762125/18064969397989403102617324*t^13 + 630725838101622388856010323993360236236786375/18064969397989403102617324*t^11 - 2332962190056478136995217363274353516992914375/18064969397989403102617324*t^9 + 5248097383577596322998342098484204439440325625/18064969397989403102617324*t^7 - 6452457046425266291928538840323358106347715625/18064969397989403102617324*t^5 + 3571266257783259757734601384452555209105169375/18064969397989403102617324*t^3 - 283017090170541331628942043875739534919749375/9032484698994701551308662*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:
| (4.568737377645151167 + 3.3695399976703061771e-582j)  +/-  (1.71e-247, 1.71e-247j)
| (-9.3010863827329875334 + 1.3785447055066565202e-590j)  +/-  (6.55e-248, 6.55e-248j)
| (9.3010863827329875334 + 1.458818035284870207e-588j)  +/-  (6.9e-248, 6.9e-248j)
| (-7.7189530195772465134 - 1.8976273859480493239e-596j)  +/-  (5.22e-247, 5.22e-247j)
| (10.303108224438735381 - 3.3028797292926397123e-595j)  +/-  (8.71e-249, 8.71e-249j)
| (2.947611698557344843 + 8.740955200897857922e-602j)  +/-  (5.73e-249, 5.73e-249j)
| (1.9676065870114964064 + 1.5665420827748803865e-611j)  +/-  (1.75e-250, 1.75e-250j)
| (6.3719547426510596848 - 5.8839198335861890597e-628j)  +/-  (9.15e-247, 9.15e-247j)
| (-8.4669913889802903703 - 5.7567827242711566603e-644j)  +/-  (2.4e-247, 2.4e-247j)
| (1.4880763680583887226 - 1.1143252044533793479e-644j)  +/-  (1.79e-251, 1.79e-251j)
| (1 + 9.0820880011280073936e-649j)  +/-  (1.63e-252, 1.63e-252j)
| (-1.4880763680583887226 - 2.002273490517789731e-648j)  +/-  (2.01e-251, 2.01e-251j)
| (7.7189530195772465134 + 4.8083653803447204581e-653j)  +/-  (5.53e-247, 5.53e-247j)
| (-2.947611698557344843 - 2.0810316102671762588e-664j)  +/-  (4.88e-249, 4.88e-249j)
| (-5.1479775440248084934 + 1.9133071173722524272e-668j)  +/-  (3.83e-247, 3.83e-247j)
| (0.50253712995943670566 + 2.1810830495754168818e-677j)  +/-  (9.6e-254, 9.6e-254j)
| (8.4669913889802903703 - 7.3562943129754657326e-678j)  +/-  (2.38e-247, 2.38e-247j)
| (-10.303108224438735381 - 4.1055878491579798222e-688j)  +/-  (8.02e-249, 8.02e-249j)
| (-3.4676200168994821663 - 2.2840290806526360991e-685j)  +/-  (1.99e-248, 1.99e-248j)
| (-6.3719547426510596848 - 9.1932065142354207343e-687j)  +/-  (9.21e-247, 9.21e-247j)
| (2.4494897427831780982 + 5.2037869618744053363e-702j)  +/-  (1.05e-249, 1.05e-249j)
| (-2.4494897427831780982 + 1.4645306083582439618e-729j)  +/-  (9.73e-250, 9.73e-250j)
| (5.7478980590155333612 + 6.3451851435647083679e-755j)  +/-  (7.19e-247, 7.19e-247j)
| (5.1479775440248084934 + 1.722925153784910068e-792j)  +/-  (3.82e-247, 3.82e-247j)
| (7.0258865107171875803 + 1.7062007720140482567e-813j)  +/-  (7.88e-247, 7.88e-247j)
| (-7.0258865107171875803 - 2.3047743696941190799e-818j)  +/-  (8.02e-247, 8.02e-247j)
| (3.4676200168994821663 + 2.777028481268785957e-818j)  +/-  (2.03e-248, 2.03e-248j)
| (-5.7478980590155333612 + 1.8476021998714168565e-823j)  +/-  (6.5e-247, 6.5e-247j)
| (6.4329827635687913181e-833 - 1.350951633413915232e-832j)  +/-  (5.24e-831, 5.24e-831j)
| (-4.0085611145019061375 - 2.8762076157145787723e-824j)  +/-  (6e-248, 6e-248j)
| (-1.9676065870114964064 + 7.3511800748553943817e-827j)  +/-  (1.61e-250, 1.61e-250j)
| (-4.568737377645151167 + 1.0361131289838234357e-823j)  +/-  (1.7e-247, 1.7e-247j)
| (4.0085611145019061375 + 4.563027745085583688e-823j)  +/-  (6.15e-248, 6.15e-248j)
| (-1 - 6.2055092313375109514e-837j)  +/-  (1.7e-252, 1.7e-252j)
| (-0.50253712995943670566 - 2.0105317318976133641e-838j)  +/-  (1.17e-253, 1.17e-253j)
-------------------------------------------------
The weights are:
| (6.6661758184120604075e-06 - 6.146103960734666132e-587j)  +/-  (3.83e-87, 1.08e-209j)
| (5.8571986938541090325e-20 + 3.4873801320965514948e-596j)  +/-  (3.59e-98, 1.01e-220j)
| (5.8571986938541090325e-20 - 1.0221001825059490293e-595j)  +/-  (4e-98, 1.13e-220j)
| (3.2989088102284431287e-14 + 4.3317474329610138042e-593j)  +/-  (4.3e-96, 1.22e-218j)
| (4.0943339194035396742e-24 + 5.7228236996213953707e-598j)  +/-  (8.88e-100, 2.51e-222j)
| (0.0026356464268870000834 + 6.325613660599824791e-586j)  +/-  (6.5e-84, 1.84e-206j)
| (0.027528816650870248404 + 1.8797120207785312221e-585j)  +/-  (1.97e-79, 5.56e-202j)
| (3.8817465481049163237e-10 - 4.7609623583325497121e-590j)  +/-  (9.99e-94, 2.82e-216j)
| (8.468812642060597331e-17 - 1.7104460578724610246e-594j)  +/-  (2.57e-98, 7.25e-221j)
| (0.063664638886837947481 - 2.5128320946328552056e-585j)  +/-  (2.17e-78, 6.14e-201j)
| (0.11936106097674822736 + 2.8932838407361670209e-585j)  +/-  (2.03e-78, 5.73e-201j)
| (0.063664638886837947481 - 1.2780950814386083904e-585j)  +/-  (1.75e-79, 4.94e-202j)
| (3.2989088102284431287e-14 - 1.6896358022832765012e-592j)  +/-  (1.93e-96, 5.46e-219j)
| (0.0026356464268870000834 + 1.3643079422233711391e-586j)  +/-  (9.67e-88, 2.73e-210j)
| (4.1340988476815772714e-07 + 4.4940677258700160701e-589j)  +/-  (6.29e-94, 1.78e-216j)
| (0.1761067120581896191 - 2.9714868328875129637e-585j)  +/-  (3.68e-80, 1.04e-202j)
| (8.468812642060597331e-17 + 5.7197172928075084988e-594j)  +/-  (6.18e-98, 1.75e-220j)
| (4.0943339194035396742e-24 - 2.2066389244841225182e-598j)  +/-  (3.1e-102, 8.77e-225j)
| (0.00051856693927624149234 - 4.271720477144712367e-587j)  +/-  (1.27e-90, 3.59e-213j)
| (3.8817465481049163237e-10 + 7.8468984450778654029e-591j)  +/-  (2.47e-96, 6.97e-219j)
| (0.0096966512359379528397 - 1.1805361231929120658e-585j)  +/-  (1.57e-87, 4.45e-210j)
| (0.0096966512359379528397 - 3.5647868671324614653e-586j)  +/-  (1.47e-88, 4.14e-211j)
| (1.6328411610914271166e-08 + 5.8505771343263159918e-589j)  +/-  (4.08e-95, 1.15e-217j)
| (4.1340988476815772714e-07 - 7.5387684531430043007e-588j)  +/-  (2.28e-94, 6.44e-217j)
| (5.1160711474220354169e-12 + 3.2759413966891486224e-591j)  +/-  (4.39e-97, 1.24e-219j)
| (5.1160711474220354169e-12 - 6.9424214535724763278e-592j)  +/-  (7.48e-99, 2.11e-221j)
| (0.00051856693927624149234 - 3.1176579053012867054e-586j)  +/-  (2.92e-93, 8.25e-216j)
| (1.6328411610914271166e-08 - 6.6870352863355645364e-590j)  +/-  (2.39e-97, 6.74e-220j)
| (0.20081917819586679111 + 2.7804558980038181382e-585j)  +/-  (2.37e-91, 6.69e-214j)
| (7.1221419880776765029e-05 + 1.1180134344937099204e-587j)  +/-  (1.18e-95, 3.34e-218j)
| (0.027528816650870248404 + 7.4802930219231420527e-586j)  +/-  (1.66e-93, 4.7e-216j)
| (6.6661758184120604075e-06 - 2.4582225016419053164e-588j)  +/-  (2.16e-96, 6.11e-219j)
| (7.1221419880776765029e-05 + 1.7118781313716175348e-586j)  +/-  (1.29e-95, 3.68e-218j)
| (0.11936106097674822736 + 1.8541671991969510065e-585j)  +/-  (8.95e-94, 2.54e-216j)
| (0.1761067120581896191 - 2.382568815346808001e-585j)  +/-  (1.58e-93, 4.39e-216j)
