Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 12 20
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P3 : 4*t^17 - 3855458534/18122395*t^15 + 76689404679/18122395*t^13 - 1451963624397/36244790*t^11 + 2765036333631/14497916*t^9 - 12957851045997/28995832*t^7 + 27641768331177/57991664*t^5 - 23638263740091/115983328*t^3 + 3232373443299/115983328*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^37 - 275770854121382311206376023705664310036315616984765272017803000660420653253793520853735703223839942118090838/296246896185710938304554200393915299263986747233743795083330865212148833473368091501155397420631665875015*t^35 + 28401865784716907268077654505005876097810837471748400964181150772250851140807280076221697317810624865462795563/296246896185710938304554200393915299263986747233743795083330865212148833473368091501155397420631665875015*t^33 - 3429045819264892772698962900221791065307139422256570722901911899410360071343163074391597045572010496169312593329/592493792371421876609108400787830598527973494467487590166661730424297666946736183002310794841263331750030*t^31 + 54191795693746139715063552146702609120600365696976827935532647393032468854229089011799596564796372640135068605237/236997516948568750643643360315132239411189397786995036066664692169719066778694473200924317936505332700012*t^29 - 2964381279369501701809614173664502854362094572701530434214881236744562824941150458294545548979806479039860459956747/473995033897137501287286720630264478822378795573990072133329384339438133557388946401848635873010665400024*t^27 + 115813400216063060540306092187747016522028385895236684244477115973650558395235893704582765081533984435177483891468251/947990067794275002574573441260528957644757591147980144266658768678876267114777892803697271746021330800048*t^25 - 3287202806406687286268138519862366893951135669346210638778578946679197500624803911213277240215680990033086664771003769/1895980135588550005149146882521057915289515182295960288533317537357752534229555785607394543492042661600096*t^23 + 68306496467102120852281737301604522784094306835252244244320161215213867080985316241915022378589191543568194466569428567/3791960271177100010298293765042115830579030364591920577066635074715505068459111571214789086984085323200192*t^21 - 1039493849531555969960377470180425722399144022787714873318254047561873426704197696529357090918994447510354158188036475285/7583920542354200020596587530084231661158060729183841154133270149431010136918223142429578173968170646400384*t^19 + 11514023597923209516375958316968114306303072432688887822303613002551747106248655677113953252165599823398609778992272726445/15167841084708400041193175060168463322316121458367682308266540298862020273836446284859156347936341292800768*t^17 - 91638700727372879598684525814340388215359457769385669078923474187943867527577112601072928850984355228880973370320231719655/30335682169416800082386350120336926644632242916735364616533080597724040547672892569718312695872682585601536*t^15 + 513292406290775689709898294056809060361284241014944920166560319543435028218719892044852013150619956767040482138922313800855/60671364338833600164772700240673853289264485833470729233066161195448081095345785139436625391745365171203072*t^13 - 1961709479044381440148093600801797722990561355937816179577321889743194724618569617777320335732421664803744592311233461713065/121342728677667200329545400481347706578528971666941458466132322390896162190691570278873250783490730342406144*t^11 + 4889399494554241310261405047869067703214016505518883005993457070423397086230265565886769244982985401313532697692047075345225/242685457355334400659090800962695413157057943333882916932264644781792324381383140557746501566981460684812288*t^9 - 7447055826185708139971679984325950995709190795250496319355685363719159173238792939229441119467985844518011222418309742039075/485370914710668801318181601925390826314115886667765833864529289563584648762766281115493003133962921369624576*t^7 + 3170700591423806624411609215186459350086448052306705693902148802688446331495402334142209940365807284121874672246654702933025/485370914710668801318181601925390826314115886667765833864529289563584648762766281115493003133962921369624576*t^5 - 337101196512942568187414759798559915335990263525098771070385072482317690522500952292046849821082139187342197777671382414225/242685457355334400659090800962695413157057943333882916932264644781792324381383140557746501566981460684812288*t^3 + 1728831376655429028767577783003269839498677363940547128483187839547869954649866480195142345281119085400882067830936771775/15167841084708400041193175060168463322316121458367682308266540298862020273836446284859156347936341292800768*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:
| (-6.8027838831131794444 - 5.4608315994723014465e-918j)  +/-  (3.75e-249, 3.75e-249j)
| (-3.3056124979668202458 + 3.5285830399406581881e-915j)  +/-  (6.54e-247, 6.54e-247j)
| (6.088641750590594434 - 2.6458657458441190957e-921j)  +/-  (3.4e-248, 3.4e-248j)
| (5.4987716897604477292 + 2.4589345019929010444e-920j)  +/-  (1.35e-247, 1.35e-247j)
| (-4.9768465623237249085 + 1.0420617172360379433e-918j)  +/-  (3.37e-247, 3.37e-247j)
| (-5.4987716897604477292 - 2.4319585036205673605e-922j)  +/-  (1.4e-247, 1.4e-247j)
| (6.8027838831131794444 - 2.2971616239564349812e-925j)  +/-  (3.81e-249, 3.81e-249j)
| (-1.5573796299154648856 - 1.7136325239767448001e-923j)  +/-  (2.04e-249, 2.04e-249j)
| (4.0724162926035838799 - 4.508038267712706117e-924j)  +/-  (6.81e-247, 6.81e-247j)
| (-6.088641750590594434 + 1.2091689524072930405e-930j)  +/-  (3.67e-248, 3.67e-248j)
| (-1.7320508075688772935 - 8.4435874865607307483e-934j)  +/-  (8.83e-249, 8.83e-249j)
| (2.3340614410930684954 - 1.1242071881388039721e-946j)  +/-  (5.42e-248, 5.42e-248j)
| (-2.3340614410930684954 + 1.686041760415211748e-955j)  +/-  (5.56e-248, 5.56e-248j)
| (-4.5040545022880217428 - 1.8539495924075149317e-960j)  +/-  (5.83e-247, 5.83e-247j)
| (-9.6828158058487139215e-973 + 6.2067783811447762052e-973j)  +/-  (4.26e-971, 4.26e-971j)
| (3.6749852443872490457 - 6.3270444173506427424e-966j)  +/-  (7.92e-247, 7.92e-247j)
| (4.5040545022880217428 + 2.4497062388049448826e-967j)  +/-  (6.19e-247, 6.19e-247j)
| (2.67070745936200384 + 1.9082830762260333881e-966j)  +/-  (1.66e-247, 1.66e-247j)
| (2.9734984797723849738 + 8.3732103876397974966e-968j)  +/-  (4.26e-247, 4.26e-247j)
| (4.9768465623237249085 + 2.8476607775857006507e-972j)  +/-  (3.34e-247, 3.34e-247j)
| (-4.0724162926035838799 + 1.7086772645095924316e-970j)  +/-  (6.94e-247, 6.94e-247j)
| (1.1587454282597314315 - 1.3836128481883505139e-980j)  +/-  (6.74e-251, 6.74e-251j)
| (1.5573796299154648856 - 1.7872115954380479393e-979j)  +/-  (2.22e-249, 2.22e-249j)
| (-1.9609600121800473653 - 3.5032210694448568893e-979j)  +/-  (1.73e-248, 1.73e-248j)
| (-2.67070745936200384 - 3.356079508694629194e-992j)  +/-  (1.71e-247, 1.71e-247j)
| (1.7320508075688772935 + 2.5818391250465027901e-1004j)  +/-  (8.41e-249, 8.41e-249j)
| (0.51384337431417705408 + 3.3290608828727294847e-1005j)  +/-  (1.13e-250, 1.13e-250j)
| (0.51198835281687566252 - 3.9940483823495647986e-1007j)  +/-  (9.78e-251, 9.78e-251j)
| (-0.7071067811865475244 + 2.025673041603548663e-1005j)  +/-  (6.36e-252, 6.36e-252j)
| (-2.9734984797723849738 - 3.5612206423974077911e-1007j)  +/-  (3.95e-247, 3.95e-247j)
| (-0.51384337431417705408 - 9.9238778390961115185e-1018j)  +/-  (1.13e-250, 1.13e-250j)
| (1.9609600121800473653 - 6.744298143359584513e-1021j)  +/-  (1.63e-248, 1.63e-248j)
| (0.7071067811865475244 - 6.3123580871051235411e-1025j)  +/-  (6.17e-252, 6.17e-252j)
| (-3.6749852443872490457 + 2.9281405003041818943e-1028j)  +/-  (7.05e-247, 7.05e-247j)
| (-0.51198835281687566252 - 2.4704564034442228209e-1037j)  +/-  (1.06e-250, 1.06e-250j)
| (-1.1587454282597314315 - 8.9380310369397118941e-1039j)  +/-  (6.53e-251, 6.53e-251j)
| (3.3056124979668202458 + 7.8403189901633242394e-1046j)  +/-  (6.15e-247, 6.15e-247j)
-------------------------------------------------
The weights are:
| (3.7112612025153023163e-21 + 1.1373171512998867779e-931j)  +/-  (1.72e-96, 2.59e-220j)
| (3.587507358127395944e-06 + 7.573895524957396194e-920j)  +/-  (1.86e-85, 2.79e-209j)
| (2.8521422904039545853e-17 + 1.0349276905382446278e-929j)  +/-  (1.24e-95, 1.87e-219j)
| (2.2969780265081665293e-14 - 8.2852014799663172966e-928j)  +/-  (4.03e-94, 6.06e-218j)
| (4.891688558466824596e-12 - 1.6979172589317453404e-925j)  +/-  (9.41e-93, 1.41e-216j)
| (2.2969780265081665293e-14 + 3.3262578059737248772e-927j)  +/-  (2.76e-94, 4.15e-218j)
| (3.7112612025153023163e-21 - 3.9346706172308156651e-932j)  +/-  (1.2e-98, 1.81e-222j)
| (0.019172352762454920146 + 1.5846455524982905721e-917j)  +/-  (9.58e-80, 1.44e-203j)
| (1.4620105501409031624e-08 + 1.5683433749875881685e-923j)  +/-  (2.55e-92, 3.83e-216j)
| (2.8521422904039545853e-17 - 3.493557169187082859e-929j)  +/-  (3.46e-96, 5.2e-220j)
| (0.00073473839254811076669 - 1.5258178599153331132e-917j)  +/-  (7.93e-82, 1.19e-205j)
| (0.00087466127946270921673 - 2.1380922491417026677e-919j)  +/-  (5.56e-87, 8.36e-211j)
| (0.00087466127946270921673 - 1.2411138006868002841e-918j)  +/-  (7.24e-86, 1.09e-209j)
| (3.9400032069822203011e-10 + 5.7918363180162574381e-924j)  +/-  (1.8e-92, 2.71e-216j)
| (0.23973784145239524466 - 2.3294617440834500933e-917j)  +/-  (4.89e-82, 7.36e-206j)
| (2.9468941100980440268e-07 - 1.9882011220061488742e-922j)  +/-  (5.62e-92, 8.44e-216j)
| (3.9400032069822203011e-10 - 8.888475322844050655e-925j)  +/-  (3.04e-94, 4.57e-218j)
| (0.00014036397789546449403 + 5.3720083701571334739e-920j)  +/-  (9.2e-90, 1.38e-213j)
| (2.5219392745758652604e-05 - 1.2732753451474495957e-920j)  +/-  (9.08e-91, 1.37e-214j)
| (4.891688558466824596e-12 + 3.4268299211936593523e-926j)  +/-  (6.36e-96, 9.56e-220j)
| (1.4620105501409031624e-08 - 1.508982027524990055e-922j)  +/-  (7.56e-95, 1.14e-218j)
| (0.060177808135462837501 - 6.3643026913729857204e-918j)  +/-  (3.27e-86, 4.91e-210j)
| (0.019172352762454920146 + 5.6967829496940783314e-918j)  +/-  (5.28e-88, 7.94e-212j)
| (0.0045746627746214707619 + 5.6035510432275629855e-918j)  +/-  (1.49e-89, 2.24e-213j)
| (0.00014036397789546449403 + 5.0565898547413040316e-919j)  +/-  (3.59e-92, 5.4e-216j)
| (0.00073473839254811076669 - 4.7660587860244472341e-918j)  +/-  (1.04e-88, 1.56e-212j)
| (-19.31011757351190177 - 6.0503299293125088881e-915j)  +/-  (2.38e-86, 3.58e-210j)
| (19.367280302627233046 + 6.0152427809219803337e-915j)  +/-  (2.38e-86, 3.58e-210j)
| (0.23726464622749018391 + 7.7664147726631752841e-917j)  +/-  (8.55e-90, 1.29e-213j)
| (2.5219392745758652604e-05 - 2.4072895236596023841e-919j)  +/-  (9.53e-95, 1.44e-218j)
| (-19.31011757351190177 - 8.277524821458540896e-915j)  +/-  (8.09e-90, 1.22e-213j)
| (0.0045746627746214707619 + 1.4306974204397959306e-918j)  +/-  (4.1e-93, 6.44e-217j)
| (0.23726464622749018391 + 5.0292851722129168966e-917j)  +/-  (6.51e-91, 9.89e-215j)
| (2.9468941100980440268e-07 + 3.7573307350703034318e-921j)  +/-  (1.95e-97, 2.95e-221j)
| (19.367280302627233046 + 8.220062936964770194e-915j)  +/-  (7.67e-90, 1.15e-213j)
| (0.060177808135462837501 - 1.3234372118315682644e-917j)  +/-  (6.53e-93, 9.39e-217j)
| (3.587507358127395944e-06 + 1.9147740956170215607e-921j)  +/-  (7.39e-97, 1.37e-220j)
