Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 12 22
-------------------------------------------------
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 22 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^39 - 9446485419007704990201383339770737887657613695569828628943626713697918668452148255942901170149409512117957766791011/8768681867465767434139771675418440532914477246532267139787342972473711289974498804641625824399249206056982417265*t^37 + 716189571033264207916953033495554014258877508698417988532182337511988549034279644752867528375163363304096658690743729117/5524269576503433483508056155513617535736120665315328298066026072658438112683934246924224269371526999815898922876950*t^35 - 102069951680948069387641078243783247625269032229105335768805016395232398419088028001583869799323614654058353009700527409549/11048539153006866967016112311027235071472241330630656596132052145316876225367868493848448538743053999631797845753900*t^33 + 458293070064181253477106519290746354151959123639048232162296226462664703014871003834866016725122528874152470640774604617167/1052241824095892092096772601050212863949737269583872056774481156696845354796939856556995098927909904726837890071800*t^31 - 42364425436955529539791841106159925107641346063665858471150059149783879749602723674648244849924139757746355435580110389995777/2946277107468497857870963282940596019059264354834841758968547238751166993431431598359586276998147733235146092201040*t^29 + 2022654368210633881353461615419858101195404454028430747984339203184393361795572855440849735826320749034229843113610730760922227/5892554214936995715741926565881192038118528709669683517937094477502333986862863196719172553996295466470292184402080*t^27 - 23703263921963121418732886738720926622921887060030198921289661262782921023565295163452552875983104098338084039713450024527054717/3928369476624663810494617710587461358745685806446455678624729651668222657908575464479448369330863644313528122934720*t^25 + 619253379244963340752654331664605077029977801040248396920306295005573445494865397191310544781258015667044136928509030135013474743/7856738953249327620989235421174922717491371612892911357249459303336445315817150928958896738661727288627056245869440*t^23 - 12050771137352058692828834644475786740146946749766190640416589010756266560454059517188190404029099571537522376000060695362223940729/15713477906498655241978470842349845434982743225785822714498918606672890631634301857917793477323454577254112491738880*t^21 + 4974186144288656902893591993104011495078597066932154429091143389835440910653104782647711248049146615675599255305852134777413530477/897913023228494585255912619562848310570442470044904155114223920381308036093388677595302484418483118700234999527936*t^19 - 52876068173775078447018871579012442282019135717664371025076859091027506179724416684249758414001336403157085795713843701627227752809/1795826046456989170511825239125696621140884940089808310228447840762616072186777355190604968836966237400469999055872*t^17 + 31341028618165239236651408051507660608676091997619472847178116591352784732420086007990018934858055548157942208368121067549755799587/276280930224152180078742344480876403252443836936893586188991975501940934182581131567785379821071728830841538316288*t^15 - 2225322207528554564829619605252917013000425489575988966709573344701242217777558831556338027593699833155681869999422043266423316905091/7183304185827956682047300956502786484563539760359233240913791363050464288747109420762419875347864949601879996223488*t^13 + 641620292564118574957628943747404489707768405061583981697561167494338426355036369160482439123255871577406432046046786407154080909341/1105123720896608720314969377923505613009775347747574344755967902007763736730324526271141519284286915323366153265152*t^11 - 1575341027013524018474615444417935917603574887484449028128334788789758696791911802258646118126569503063819161573917130053063860013865/2210247441793217440629938755847011226019550695495148689511935804015527473460649052542283038568573830646732306530304*t^9 + 2370128724183197868950946193391029507994418628104396964442806842080032815662037996359102831920338541580185931347626606972009661252905/4420494883586434881259877511694022452039101390990297379023871608031054946921298105084566077137147661293464613060608*t^7 - 997416677519421226948340704502245499290635330613112505123703876746579523141316036159426801457232278281118674012132792287390409304585/4420494883586434881259877511694022452039101390990297379023871608031054946921298105084566077137147661293464613060608*t^5 + 209349666130210154589211529977287971355905440994913828376497249632286065539012266817237881251697118699472101009015512264346198525605/4420494883586434881259877511694022452039101390990297379023871608031054946921298105084566077137147661293464613060608*t^3 - 16928220183847446151568826683007215314729340885226934605814405184433285972474237457664531057253317416166854591008750686379273445395/4420494883586434881259877511694022452039101390990297379023871608031054946921298105084566077137147661293464613060608*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (4.0921844325245502664 + 2.4342441513379527609e-467j)  +/-  (1.19e-118, 1.19e-118j)
| (4.888116454799967955 + 1.2646192402231964133e-480j)  +/-  (1.44e-118, 1.44e-118j)
| (-7.0414648939657929279 - 1.6140465214868504015e-493j)  +/-  (5.39e-121, 5.39e-121j)
| (7.0414648939657929279 - 1.9465449198161795374e-491j)  +/-  (4.89e-121, 4.89e-121j)
| (-5.7673374783072033502 + 7.0419242490838487235e-493j)  +/-  (2.86e-119, 2.86e-119j)
| (-6.3382935308941228512 - 3.0393241470734993924e-494j)  +/-  (5.99e-120, 5.99e-120j)
| (-5.2873058323986604183 - 5.4944282241732350527e-493j)  +/-  (7.82e-119, 7.82e-119j)
| (-4.888116454799967955 - 1.4116718277856659115e-492j)  +/-  (1.43e-118, 1.43e-118j)
| (5.7673374783072033502 + 1.0338047158911248279e-494j)  +/-  (2.88e-119, 2.88e-119j)
| (5.2873058323986604183 + 4.7527026500162994672e-510j)  +/-  (8.11e-119, 8.11e-119j)
| (1.7320508075688772935 - 4.3558954114969651708e-522j)  +/-  (6.56e-121, 6.56e-121j)
| (-3.6749852443872490457 - 2.9492095051206707359e-519j)  +/-  (8.59e-119, 8.59e-119j)
| (6.3382935308941228512 - 9.3738216785671561917e-521j)  +/-  (6.05e-120, 6.05e-120j)
| (-1.7320508075688772935 + 1.6547403066480900346e-522j)  +/-  (7.02e-121, 7.02e-121j)
| (4.5040545022880217428 + 7.7901465271116864126e-519j)  +/-  (1.65e-118, 1.65e-118j)
| (2.9734984797723849738 - 5.1583166384631461361e-526j)  +/-  (3.78e-119, 3.78e-119j)
| (1.9173845514517028947 - 2.2381801904445156999e-526j)  +/-  (9.92e-121, 9.92e-121j)
| (-2.7014130605972323387 - 6.8633329108413085812e-525j)  +/-  (1.39e-119, 1.39e-119j)
| (-1.1587454282597314315 - 1.5031817205003773234e-529j)  +/-  (3.07e-123, 3.07e-123j)
| (-2.3340614410930684954 + 2.5677789476249689148e-526j)  +/-  (2.89e-120, 2.89e-120j)
| (3.6749852443872490457 - 2.5424139496025903511e-524j)  +/-  (7.79e-119, 7.79e-119j)
| (3.2809416806153620206 - 2.4037729277924379512e-526j)  +/-  (5.89e-119, 5.89e-119j)
| (-4.0921844325245502664 - 3.2201772573944803228e-525j)  +/-  (1.19e-118, 1.19e-118j)
| (0.7071067811865475244 + 1.2828567218956241715e-532j)  +/-  (2.97e-124, 2.97e-124j)
| (-1.9173845514517028947 + 5.9487780296124412491e-528j)  +/-  (1.06e-120, 1.06e-120j)
| (-2.9734984797723849738 - 1.2234842767652511453e-526j)  +/-  (3.73e-119, 3.73e-119j)
| (2.7014130605972323387 - 3.3021396514206362168e-528j)  +/-  (1.46e-119, 1.46e-119j)
| (0.51198835281687566252 + 4.3016472162394868064e-532j)  +/-  (1.04e-123, 1.04e-123j)
| (-1.0005614933123768798e-547 + 1.1442387550432722511e-547j)  +/-  (5.93e-546, 5.93e-546j)
| (-0.7071067811865475244 - 3.0201517865491757887e-533j)  +/-  (3.33e-124, 3.33e-124j)
| (-0.50349525814149001159 + 7.6788389001153902281e-532j)  +/-  (9.7e-124, 9.7e-124j)
| (1.1587454282597314315 + 2.8815214831578683194e-532j)  +/-  (3.5e-123, 3.5e-123j)
| (1.5913701249930820768 + 1.359140371135560623e-530j)  +/-  (2.03e-121, 2.03e-121j)
| (-3.2809416806153620206 - 1.624227512946670342e-526j)  +/-  (5.64e-119, 5.64e-119j)
| (-0.51198835281687566252 + 1.178286778589288316e-532j)  +/-  (1.08e-123, 1.08e-123j)
| (-1.5913701249930820768 + 1.8486647521364551678e-529j)  +/-  (2.05e-121, 2.05e-121j)
| (2.3340614410930684954 - 2.130259631321565601e-530j)  +/-  (3.01e-120, 3.01e-120j)
| (0.50349525814149001159 - 3.3903739642051474333e-533j)  +/-  (8.71e-124, 8.71e-124j)
| (-4.5040545022880217428 - 3.6153100070968961566e-533j)  +/-  (1.41e-118, 1.41e-118j)
-------------------------------------------------
The weights are:
| (1.2619079666739739585e-08 - 1.6682921189678536712e-474j)  +/-  (2.91e-24, 3.38e-82j)
| (8.9148195620470675292e-12 + 4.0389175484786801123e-477j)  +/-  (2.93e-27, 3.4e-85j)
| (1.3468927925387245884e-22 - 1.8844482753340508184e-485j)  +/-  (1.23e-34, 1.43e-92j)
| (1.3468927925387245884e-22 + 7.1138660923505621812e-485j)  +/-  (2.16e-34, 2.5e-92j)
| (1.0601207828194007383e-15 - 5.4399294819655072492e-481j)  +/-  (7.77e-32, 9.02e-90j)
| (1.2548833882934289688e-18 + 5.9305687049663040939e-483j)  +/-  (2.72e-33, 3.15e-91j)
| (1.7752483213953228418e-13 + 2.1522125938254885903e-479j)  +/-  (4.15e-31, 4.82e-89j)
| (8.9148195620470675292e-12 - 3.5797283994146065557e-478j)  +/-  (1.78e-30, 2.06e-88j)
| (1.0601207828194007383e-15 + 3.2018032057339407105e-480j)  +/-  (1.65e-34, 1.91e-92j)
| (1.7752483213953228418e-13 - 1.6890884117678622388e-478j)  +/-  (3.84e-33, 4.46e-91j)
| (-0.0070354374072136680108 + 2.3200623481843181577e-470j)  +/-  (9.04e-22, 1.05e-79j)
| (3.1643223682361584832e-07 + 3.9818448171339107353e-475j)  +/-  (1.3e-30, 1.5e-88j)
| (1.2548833882934289688e-18 - 2.7540365796387252545e-482j)  +/-  (1.93e-36, 2.24e-94j)
| (-0.0070354374072136680108 + 9.4015041189435062897e-471j)  +/-  (1.24e-23, 1.44e-81j)
| (3.48800361535481721e-10 - 7.7988429831380360861e-476j)  +/-  (1.47e-31, 1.71e-89j)
| (2.043823131801607724e-05 + 1.591778833732628451e-472j)  +/-  (5.77e-29, 6.69e-87j)
| (0.0069156227803054795491 - 8.0609433284975817912e-471j)  +/-  (8.19e-25, 9.5e-83j)
| (0.00012462905199118764375 - 7.6498502721932846904e-473j)  +/-  (1.52e-29, 1.76e-87j)
| (0.061245055686508316109 + 7.4422806137462656046e-471j)  +/-  (7.75e-23, 8.99e-81j)
| (0.00095518010384075112607 + 2.7259586744130055608e-472j)  +/-  (2.44e-28, 2.83e-86j)
| (3.1643223682361584832e-07 + 7.413165030328988296e-474j)  +/-  (3.27e-31, 3.8e-89j)
| (4.3648400922346068931e-06 - 3.8878795643971494459e-473j)  +/-  (2.01e-30, 2.34e-88j)
| (1.2619079666739739585e-08 - 3.753242477279853773e-476j)  +/-  (1.89e-34, 2.19e-92j)
| (0.22764633771099316534 - 7.9108234431853055538e-470j)  +/-  (5.43e-25, 6.28e-83j)
| (0.0069156227803054795491 - 2.9171707054025866871e-471j)  +/-  (3.42e-28, 3.97e-86j)
| (2.043823131801607724e-05 + 2.5202102093851844875e-473j)  +/-  (1.99e-31, 2.31e-89j)
| (0.00012462905199118764375 - 3.7367754816458217843e-472j)  +/-  (2.89e-30, 3.34e-88j)
| (-4.0025767573886204464 + 1.9528771597728745603e-468j)  +/-  (2.79e-25, 3.22e-83j)
| (0.23776369395857554261 + 2.6890464767418108509e-470j)  +/-  (1.22e-25, 1.41e-83j)
| (0.22764633771099316534 - 5.5797305161860359426e-470j)  +/-  (1.28e-26, 1.49e-84j)
| (4.0698290921664087352 - 1.4805126376866087553e-468j)  +/-  (1.42e-26, 1.65e-84j)
| (0.061245055686508316109 + 1.3321870149759672201e-470j)  +/-  (2.12e-28, 2.48e-86j)
| (0.023989297835878199795 - 2.1049177469072726314e-470j)  +/-  (9.36e-29, 1.1e-86j)
| (4.3648400922346068931e-06 - 4.2777162203860346043e-474j)  +/-  (1.93e-33, 2.27e-91j)
| (-4.0025767573886204464 + 1.518553598559405688e-468j)  +/-  (8.5e-27, 9.77e-85j)
| (0.023989297835878199795 - 9.2618243818560910258e-471j)  +/-  (9.47e-30, 1.1e-87j)
| (0.00095518010384075112607 + 9.9638539331287871137e-472j)  +/-  (1.98e-31, 2.23e-89j)
| (4.0698290921664087352 - 1.8959462717916887554e-468j)  +/-  (1.66e-27, 1.82e-85j)
| (3.48800361535481721e-10 + 3.7366457911392158359e-477j)  +/-  (9.17e-37, 1.09e-94j)
