Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 12 22
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P3 : t^17 - 1927729267/18122395*t^15 + 76689404679/18122395*t^13 - 1451963624397/18122395*t^11 + 2765036333631/3624479*t^9 - 12957851045997/3624479*t^7 + 27641768331177/3624479*t^5 - 23638263740091/3624479*t^3 + 6464746886598/3624479*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 9446485419007704990201383339770737887657613695569828628943626713697918668452148255942901170149409512117957766791011/17537363734931534868279543350836881065828954493064534279574685944947422579948997609283251648798498412113964834530*t^37 + 716189571033264207916953033495554014258877508698417988532182337511988549034279644752867528375163363304096658690743729117/5524269576503433483508056155513617535736120665315328298066026072658438112683934246924224269371526999815898922876950*t^35 - 102069951680948069387641078243783247625269032229105335768805016395232398419088028001583869799323614654058353009700527409549/5524269576503433483508056155513617535736120665315328298066026072658438112683934246924224269371526999815898922876950*t^33 + 458293070064181253477106519290746354151959123639048232162296226462664703014871003834866016725122528874152470640774604617167/263060456023973023024193150262553215987434317395968014193620289174211338699234964139248774731977476181709472517950*t^31 - 42364425436955529539791841106159925107641346063665858471150059149783879749602723674648244849924139757746355435580110389995777/368284638433562232233870410367574502382408044354355219871068404843895874178928949794948284624768466654393261525130*t^29 + 2022654368210633881353461615419858101195404454028430747984339203184393361795572855440849735826320749034229843113610730760922227/368284638433562232233870410367574502382408044354355219871068404843895874178928949794948284624768466654393261525130*t^27 - 23703263921963121418732886738720926622921887060030198921289661262782921023565295163452552875983104098338084039713450024527054717/122761546144520744077956803455858167460802681451451739957022801614631958059642983264982761541589488884797753841710*t^25 + 619253379244963340752654331664605077029977801040248396920306295005573445494865397191310544781258015667044136928509030135013474743/122761546144520744077956803455858167460802681451451739957022801614631958059642983264982761541589488884797753841710*t^23 - 12050771137352058692828834644475786740146946749766190640416589010756266560454059517188190404029099571537522376000060695362223940729/122761546144520744077956803455858167460802681451451739957022801614631958059642983264982761541589488884797753841710*t^21 + 4974186144288656902893591993104011495078597066932154429091143389835440910653104782647711248049146615675599255305852134777413530477/3507472746986306973655908670167376213165790898612906855914937188989484515989799521856650329759699682422792966906*t^19 - 52876068173775078447018871579012442282019135717664371025076859091027506179724416684249758414001336403157085795713843701627227752809/3507472746986306973655908670167376213165790898612906855914937188989484515989799521856650329759699682422792966906*t^17 + 31341028618165239236651408051507660608676091997619472847178116591352784732420086007990018934858055548157942208368121067549755799587/269805595922023613358146820782105862551214684508685142762687476076114193537676886296665409981515360186368689762*t^15 - 2225322207528554564829619605252917013000425489575988966709573344701242217777558831556338027593699833155681869999422043266423316905091/3507472746986306973655908670167376213165790898612906855914937188989484515989799521856650329759699682422792966906*t^13 + 641620292564118574957628943747404489707768405061583981697561167494338426355036369160482439123255871577406432046046786407154080909341/269805595922023613358146820782105862551214684508685142762687476076114193537676886296665409981515360186368689762*t^11 - 1575341027013524018474615444417935917603574887484449028128334788789758696791911802258646118126569503063819161573917130053063860013865/269805595922023613358146820782105862551214684508685142762687476076114193537676886296665409981515360186368689762*t^9 + 2370128724183197868950946193391029507994418628104396964442806842080032815662037996359102831920338541580185931347626606972009661252905/269805595922023613358146820782105862551214684508685142762687476076114193537676886296665409981515360186368689762*t^7 - 997416677519421226948340704502245499290635330613112505123703876746579523141316036159426801457232278281118674012132792287390409304585/134902797961011806679073410391052931275607342254342571381343738038057096768838443148332704990757680093184344881*t^5 + 418699332260420309178423059954575942711810881989827656752994499264572131078024533634475762503394237398944202018031024528692397051210/134902797961011806679073410391052931275607342254342571381343738038057096768838443148332704990757680093184344881*t^3 - 67712880735389784606275306732028861258917363540907738423257620737733143889896949830658124229013269664667418364035002745517093781580/134902797961011806679073410391052931275607342254342571381343738038057096768838443148332704990757680093184344881*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:
| (2.7115912369476517044 + 1.0738594921879408833e-915j)  +/-  (3.18e-248, 3.18e-248j)
| (-8.9637006736921204565 + 1.0463946487670336175e-922j)  +/-  (1.82e-247, 1.82e-247j)
| (9.9581351520204520109 - 7.0980981743652414236e-931j)  +/-  (1.67e-248, 1.67e-248j)
| (8.1562468806046928381 + 5.7043758113453284569e-957j)  +/-  (8.08e-247, 8.08e-247j)
| (6.3696949628033208131 + 4.1217425022465095331e-971j)  +/-  (4.93e-246, 4.93e-246j)
| (7.4773796165925521817 - 1.9327506245703263626e-985j)  +/-  (2.43e-246, 2.43e-246j)
| (-4.6399522220814205716 + 7.1182517175086915456e-995j)  +/-  (1.82e-246, 1.82e-246j)
| (-3.8203749878684176307 - 9.0628799671857649818e-997j)  +/-  (4.97e-247, 4.97e-247j)
| (-6.3696949628033208131 + 3.824248943353994217e-995j)  +/-  (4.9e-246, 4.9e-246j)
| (8.9637006736921204565 + 5.09742930825121463e-995j)  +/-  (1.74e-247, 1.74e-247j)
| (-9.9581351520204520109 + 5.4514741978044111183e-1001j)  +/-  (1.78e-248, 1.78e-248j)
| (2.2505372135205841436 + 1.1365536845681411672e-999j)  +/-  (6.58e-249, 6.58e-249j)
| (3.3008613454059083377 - 1.3488321816496024501e-996j)  +/-  (9.52e-248, 9.52e-248j)
| (-8.1562468806046928381 + 1.2277303535277079447e-1001j)  +/-  (7.71e-247, 7.71e-247j)
| (-3.3008613454059083377 + 2.8291777892329260542e-1002j)  +/-  (9.62e-248, 9.62e-248j)
| (4.2051618777898870634 + 3.7291778205134164743e-999j)  +/-  (1.22e-246, 1.22e-246j)
| (-6.9128405848372067263 + 1.0413512534753205293e-1006j)  +/-  (4.27e-246, 4.27e-246j)
| (-5.1972139741334507794 - 3.8982900356741180275e-1006j)  +/-  (2.5e-246, 2.5e-246j)
| (-0.71204982265423767718 + 4.9822479866018507902e-1013j)  +/-  (3.43e-251, 3.43e-251j)
| (4.6399522220814205716 + 1.0699631404017912627e-1006j)  +/-  (1.86e-246, 1.86e-246j)
| (-7.4773796165925521817 + 6.7317075179117787306e-1015j)  +/-  (2.51e-246, 2.51e-246j)
| (1 + 7.2097964486599965615e-1020j)  +/-  (1.1e-251, 1.1e-251j)
| (-2.7115912369476517044 - 1.0732051840044344616e-1016j)  +/-  (3.57e-248, 3.57e-248j)
| (-5.7872227242082666353 + 1.7902788138664534457e-1015j)  +/-  (3.94e-246, 3.94e-246j)
| (6.9128405848372067263 - 4.16195724636567487e-1013j)  +/-  (4.25e-246, 4.25e-246j)
| (5.7872227242082666353 - 1.7015896922341805129e-1022j)  +/-  (3.85e-246, 3.85e-246j)
| (-2.4494897427831780982 + 1.7929590859056171483e-1035j)  +/-  (2.28e-248, 2.28e-248j)
| (1.638713499982732431 + 1.7087409917578325828e-1036j)  +/-  (1.12e-250, 1.12e-250j)
| (-1.638713499982732431 - 2.377505547816406482e-1038j)  +/-  (9.83e-251, 9.83e-251j)
| (-0.72406087233068678388 + 5.6350132388022771023e-1038j)  +/-  (3.48e-251, 3.48e-251j)
| (-2.2505372135205841436 + 4.1687183920009558179e-1036j)  +/-  (7.2e-249, 7.2e-249j)
| (0.71204982265423767718 + 2.1308196709962598351e-1037j)  +/-  (3.1e-251, 3.1e-251j)
| (0.72406087233068678388 - 3.3594072003373982391e-1037j)  +/-  (3.22e-251, 3.22e-251j)
| (5.1972139741334507794 + 1.5708173236221301298e-1035j)  +/-  (2.62e-246, 2.62e-246j)
| (-1 + 5.5988178467867908205e-1040j)  +/-  (1.14e-251, 1.14e-251j)
| (3.8203749878684176307 - 1.3993230088537615981e-1039j)  +/-  (4.61e-247, 4.61e-247j)
| (-4.2051618777898870634 + 7.4397052672908817824e-1043j)  +/-  (1.26e-246, 1.26e-246j)
| (2.4494897427831780982 - 2.0798913321538010542e-1047j)  +/-  (2.28e-248, 2.28e-248j)
| (-2.679478270441271914e-1174 + 7.1533895886185067021e-1175j)  +/-  (1.08e-1172, 1.08e-1172j)
-------------------------------------------------
The weights are:
| (0.0069156227803054795491 - 4.6268995753685721803e-917j)  +/-  (5.25e-68, 1.74e-191j)
| (1.2548833882934289688e-18 + 2.2444316889198125316e-930j)  +/-  (3.37e-88, 1.12e-211j)
| (1.3468927925387245884e-22 + 1.22649115147959085e-932j)  +/-  (5.87e-90, 1.95e-213j)
| (1.0601207828194007383e-15 + 4.1730375943274325616e-928j)  +/-  (7.11e-87, 2.36e-210j)
| (3.48800361535481721e-10 - 3.719700578275905972e-924j)  +/-  (8.69e-84, 2.89e-207j)
| (1.7752483213953228418e-13 - 1.7943338057225869089e-926j)  +/-  (9.48e-86, 3.15e-209j)
| (4.3648400922346068931e-06 - 1.8174341822561644635e-921j)  +/-  (7.1e-82, 2.36e-205j)
| (0.00012462905199118764375 - 3.3704074401209045508e-920j)  +/-  (2.65e-79, 8.82e-203j)
| (3.48800361535481721e-10 + 1.4983616026864879317e-924j)  +/-  (6.43e-87, 2.14e-210j)
| (1.2548833882934289688e-18 - 4.1912886199353957459e-930j)  +/-  (2.5e-90, 8.31e-214j)
| (1.3468927925387245884e-22 - 7.0150070469032166128e-933j)  +/-  (3.83e-94, 1.27e-217j)
| (0.023989297835878199795 - 4.8365796794679624644e-917j)  +/-  (1.96e-74, 6.51e-198j)
| (0.00095518010384075112607 - 1.2593190766267370479e-918j)  +/-  (6.09e-79, 2.02e-202j)
| (1.0601207828194007383e-15 - 2.0906414362227949222e-928j)  +/-  (4.65e-91, 1.55e-214j)
| (0.00095518010384075112607 + 1.2342369086610420661e-919j)  +/-  (7.37e-81, 2.45e-204j)
| (2.043823131801607724e-05 - 5.0505506425696116067e-920j)  +/-  (2.29e-83, 7.61e-207j)
| (8.9148195620470675292e-12 - 1.4149446550715763705e-925j)  +/-  (4.35e-89, 1.45e-212j)
| (3.1643223682361584832e-07 + 1.6565701514144896181e-922j)  +/-  (3.23e-86, 1.07e-209j)
| (4.0698290921664087352 - 8.4187426209092566892e-916j)  +/-  (2.06e-79, 6.86e-203j)
| (4.3648400922346068931e-06 + 6.9286541667565379173e-921j)  +/-  (4.29e-86, 1.43e-209j)
| (1.7752483213953228418e-13 + 8.3928154508869365884e-927j)  +/-  (1.77e-90, 5.9e-214j)
| (0.22764633771099316534 - 6.627715553246172755e-917j)  +/-  (9.31e-81, 3.09e-204j)
| (0.0069156227803054795491 - 1.3693817611341261966e-918j)  +/-  (1.16e-82, 3.87e-206j)
| (1.2619079666739739585e-08 - 1.5311124320295325646e-923j)  +/-  (1.66e-87, 5.53e-211j)
| (8.9148195620470675292e-12 + 3.2414258798606731438e-925j)  +/-  (3.07e-91, 1.02e-214j)
| (1.2619079666739739585e-08 + 4.2308838907205833893e-923j)  +/-  (1.05e-89, 3.5e-213j)
| (-0.0070354374072136680108 + 4.4943735200631905306e-918j)  +/-  (1.97e-83, 6.54e-207j)
| (0.061245055686508316109 + 1.5429988880847012237e-917j)  +/-  (6.02e-83, 2e-206j)
| (0.061245055686508316109 + 3.8053636590982559375e-918j)  +/-  (4.51e-83, 1.5e-206j)
| (-4.0025767573886204464 + 8.6207717329820578189e-916j)  +/-  (2.75e-80, 9.14e-204j)
| (0.023989297835878199795 - 4.4938871355530530557e-918j)  +/-  (1.83e-83, 6.07e-207j)
| (4.0698290921664087352 - 1.4414681637049507762e-915j)  +/-  (4.52e-82, 1.5e-205j)
| (-4.0025767573886204464 + 1.490189690445478959e-915j)  +/-  (4.61e-82, 1.53e-205j)
| (3.1643223682361584832e-07 - 5.2709087545249706568e-922j)  +/-  (2.75e-91, 9.13e-215j)
| (0.22764633771099316534 - 3.0563548456008303175e-917j)  +/-  (1.15e-84, 3.82e-208j)
| (0.00012462905199118764375 + 1.9855438487718325275e-919j)  +/-  (3.71e-89, 1.23e-212j)
| (2.043823131801607724e-05 + 1.0905917899274806314e-920j)  +/-  (1.85e-89, 6.14e-213j)
| (-0.0070354374072136680108 + 8.8499402737318211608e-917j)  +/-  (4.53e-87, 1.51e-210j)
| (0.23776369395857554261 + 1.7191068616394971744e-917j)  +/-  (4.01e-86, 1.26e-209j)
