Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 14 31
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P2 : 4*t^16 - 935281/4314*t^14 + 38001691/8628*t^12 - 245286041/5752*t^10 + 2383796415/11504*t^8 - 11245499265/23008*t^6 + 22854346515/46016*t^4 - 15081381315/92032*t^2 + 1321665345/184064
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^47 - 1732125991151833729636853908176152627054278575186609793780268990181976454747178650212465373000768373163/1073680216591424305473978241064322678500045691591461397310006456321533714374686191619620217432165722*t^45 + 13981127972967022109745464846606073441213823118237353482756684884332319269570437866494648752830883273993151/47241929530022669440855042606830197854002010430024301481640284078147483432486192431263289567015291768*t^43 - 2065389527889724425033412350927540655964996273183407523691369691126129759380477764513543623822412293510478457/62989239373363559254473390142440263805336013906699068642187045437529977909981589908351052756020389024*t^41 + 309563480198497495670036301900653258605493021127910292130039635850844425937041031808836967299470755303897101195/125978478746727118508946780284880527610672027813398137284374090875059955819963179816702105512040778048*t^39 - 632855880918823320916021307863158433972723086287285243765251263330622106517784406459934804887283044440987732577025/4787182192375630503339977650825460049205537056909129216806215453252278321158600833034680009457549565824*t^37 + 78258166055709033366837692757520155643255032439341198710841672098056159198280110527558055522705526838249363751433115/14796744958251948828505385466187785606635296357719126670128302310052496629035675302107192756505153203456*t^35 - 2379924573500361689875291515828268328421102521877587261406467590429560080725024996647009816581074206657136803643784595/14796744958251948828505385466187785606635296357719126670128302310052496629035675302107192756505153203456*t^33 + 111537356546861793676692305170899470578138847903836339801671985067991397811316205131136131677560365762478624699016939835/29593489916503897657010770932375571213270592715438253340256604620104993258071350604214385513010306406912*t^31 - 4059136033556172424365999895226519884339485753632223610592364202469296347708985486281668648201659739490757807698135100575/59186979833007795314021541864751142426541185430876506680513209240209986516142701208428771026020612813824*t^29 + 3110358782714704171129427596981887147800252885149470172870462502902409750119077682465374346263162609939107089892371652175/3199296207189610557514677938635196887921145158425757117865578877849188460332037903158311947352465557504*t^27 - 1270241635076104772320121356824965251551305289934462078623924544537539040224924777962541833234093509082054520766564164948375/118373959666015590628043083729502284853082370861753013361026418480419973032285402416857542052041225627648*t^25 + 21744838766906101287160553662834009038783519950863989246108157818106636955310900929068411523839338517314627082998320529390375/236747919332031181256086167459004569706164741723506026722052836960839946064570804833715084104082451255296*t^23 - 12456117266728613466786008306496118136390208626138053399971052170993282310064940300170597740224645250633514640983867898521625/20586775594089667935311840648609093017927368845522263193221985822681734440397461289888268182963691413504*t^21 + 62440578638815486160810954369181222767308026391311496394252307408342855362126522381228109439616324322237481898828045337024375/20586775594089667935311840648609093017927368845522263193221985822681734440397461289888268182963691413504*t^19 - 98723289823771858925219327042456464612605020716347718037473205181376826183360754757264299067013876104371018412755703339801875/8668116039616702288552353957309091797022050040219900291882941399023888185430510016795060287563659542528*t^17 + 31986749098583582937513896323822477477511444146707005046294608540100006361331117930806544094537565760528771449504570015700625/1019778357601964975123806347918716682002594122378811799045051929296928021815354119622948269125136416768*t^15 - 125618380358749398311133798480569597885981731667585242312295080247019615446902556814763445356058031070342828352359949751894375/2039556715203929950247612695837433364005188244757623598090103858593856043630708239245896538250272833536*t^13 + 5289813726115922816113988788617725232866161123545875741059975790532684350032645433003070083446126049071967147535506259654375/63736147350122810945237896744919792625162132648675737440315745581058001363459632476434266820321026048*t^11 - 1187360231992559729377559653342786101109280446030105280154449132884703766869209560971844013150083534775006871628525897720384375/16316453721631439601980901566699466912041505958060988784720830868750848349045665913967172306002182668288*t^9 + 1253331878592363327058401995792140857623932843882077829393440665185005797372719269503470039791673433937630400764481276585528125/32632907443262879203961803133398933824083011916121977569441661737501696698091331827934344612004365336576*t^7 - 704466284715521764115660713634314446981219727024655387590185056679462707361507885103437102164119507545717907475908258301578125/65265814886525758407923606266797867648166023832243955138883323475003393396182663655868689224008730673152*t^5 + 170162263710157537339166355161491188915640234291350639283447249397195981995596705844562445364810537797659323134085761390515625/130531629773051516815847212533595735296332047664487910277766646950006786792365327311737378448017461346304*t^3 - 76279256453084276840471975895347039104748116150525158051544198923118499467928905948703945410074344146192737981695260921875/1763940942879074551565502872075618044545027671141728517267116850675767389086017936645099708756992720896*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:
| (8.0213936657874249958 - 1.4527221070098403423e-583j)  +/-  (1.14e-247, 1.14e-247j)
| (5.342714742037232715 + 9.3610604404515871101e-593j)  +/-  (1.16e-244, 1.16e-244j)
| (6.7655653800817560714 + 4.1870758009928729538e-615j)  +/-  (7.98e-246, 7.98e-246j)
| (-5.342714742037232715 - 3.2869999349802490862e-634j)  +/-  (1.11e-244, 1.11e-244j)
| (3.7042296813249592447 + 1.1071544504065080042e-652j)  +/-  (9.71e-245, 9.71e-245j)
| (-8.0213936657874249958 - 1.1180422269637522275e-667j)  +/-  (1.11e-247, 1.11e-247j)
| (-4.1938041935633698607 + 8.457048967526839405e-663j)  +/-  (3.39e-244, 3.39e-244j)
| (-4.0042305672529875788 - 9.1062476630349648559e-669j)  +/-  (2.9e-244, 2.9e-244j)
| (-3.7042296813249592447 - 5.6798548959694395499e-686j)  +/-  (9.28e-245, 9.28e-245j)
| (4.1938041935633698607 + 4.8056701278852430924e-708j)  +/-  (3.35e-244, 3.35e-244j)
| (0.97759216693259945335 - 2.6955982397600809646e-732j)  +/-  (1e-250, 1e-250j)
| (4.5281459663671905541 + 1.2748235247063937048e-722j)  +/-  (2.34e-244, 2.34e-244j)
| (-7.3352820290566010602 + 2.3608249179780030009e-733j)  +/-  (1.5e-246, 1.5e-246j)
| (-1.2306846131070304577 - 1.0020633350118471317e-736j)  +/-  (7.16e-250, 7.16e-250j)
| (-1.7883518963075274379 - 2.4159523915906665647e-735j)  +/-  (2.63e-248, 2.63e-248j)
| (5.785152443691402798 + 1.0238206858437772878e-730j)  +/-  (5.89e-245, 5.89e-245j)
| (3.0091043993715327196 + 1.0111807505841685932e-736j)  +/-  (7.69e-246, 7.69e-246j)
| (-6.2559350619597458374 + 7.3839920029298920828e-739j)  +/-  (2.61e-245, 2.61e-245j)
| (-0.97759216693259945335 + 9.5993537864370543315e-745j)  +/-  (9.43e-251, 9.43e-251j)
| (6.2559350619597458374 - 2.9200927873264051027e-738j)  +/-  (2.61e-245, 2.61e-245j)
| (2.6829629428200923782 - 1.360927049287776872e-744j)  +/-  (2.41e-246, 2.41e-246j)
| (2.3782295662273317563 + 1.529865369909405048e-746j)  +/-  (6.28e-247, 6.28e-247j)
| (1.7883518963075274379 + 4.1595921312411355017e-748j)  +/-  (2.57e-248, 2.57e-248j)
| (7.3352820290566010602 - 3.2715173783411833515e-745j)  +/-  (1.58e-246, 1.58e-246j)
| (-2.3782295662273317563 - 5.298769478843075504e-755j)  +/-  (6.57e-247, 6.57e-247j)
| (-6.7655653800817560714 + 7.2201222703792018149e-753j)  +/-  (7.98e-246, 7.98e-246j)
| (2.0844047524688900149 + 3.4805270622537274665e-754j)  +/-  (1.38e-247, 1.38e-247j)
| (0.22680478892243133872 - 1.0814373976478892065e-761j)  +/-  (5.97e-254, 5.97e-254j)
| (-4.5281459663671905541 + 1.1315604390227911582e-751j)  +/-  (2.45e-244, 2.45e-244j)
| (-1.4972501979074933164 + 5.4326123871687700618e-758j)  +/-  (3.82e-249, 3.82e-249j)
| (1.4972501979074933164 - 6.4557328037951935731e-758j)  +/-  (3.84e-249, 3.84e-249j)
| (-5.785152443691402798 - 1.8844920877112284338e-754j)  +/-  (6.28e-245, 6.28e-245j)
| (4.0042305672529875788 - 5.5181666452594051052e-753j)  +/-  (2.77e-244, 2.77e-244j)
| (1.2306846131070304577 - 1.8585781714461368233e-765j)  +/-  (7.23e-250, 7.23e-250j)
| (-4.923407347306486103 - 9.3317712498557205525e-761j)  +/-  (1.53e-244, 1.53e-244j)
| (-3.0091043993715327196 - 1.3686043439114280964e-763j)  +/-  (8.12e-246, 8.12e-246j)
| (3.3531863631306657378 - 6.4096715952152657206e-763j)  +/-  (2.57e-245, 2.57e-245j)
| (0.4442685851365052661 + 3.4068443497933360481e-779j)  +/-  (6.91e-253, 6.91e-253j)
| (-2.6829629428200923782 + 2.3315401260400754859e-770j)  +/-  (2.29e-246, 2.29e-246j)
| (-3.3531863631306657378 - 1.3095805703073858787e-770j)  +/-  (2.53e-245, 2.53e-245j)
| (-0.7071067811865475244 - 1.1104381280028206668e-776j)  +/-  (7.71e-252, 7.71e-252j)
| (-0.22680478892243133872 - 1.0579190410622101274e-778j)  +/-  (5.97e-254, 5.97e-254j)
| (9.0070122152827159015e-788 + 4.8955477773579137268e-787j)  +/-  (2.34e-785, 2.34e-785j)
| (0.7071067811865475244 + 5.2561706365352308572e-778j)  +/-  (7.87e-252, 7.87e-252j)
| (-2.0844047524688900149 + 1.1899642494599643342e-777j)  +/-  (1.61e-247, 1.61e-247j)
| (-0.4442685851365052661 + 9.6229983583303873327e-784j)  +/-  (6.87e-253, 6.87e-253j)
| (4.923407347306486103 + 2.4141440289614940415e-781j)  +/-  (1.62e-244, 1.62e-244j)
-------------------------------------------------
The weights are:
| (5.082713221149957591e-29 + 6.7410236954115624775e-611j)  +/-  (2.14e-89, 4.91e-211j)
| (9.7387506393500140466e-14 - 6.3089562762477562251e-603j)  +/-  (8.35e-82, 1.91e-203j)
| (3.9865563529578817766e-21 + 2.4616802388525610701e-607j)  +/-  (3.73e-86, 8.54e-208j)
| (9.7387506393500140466e-14 - 1.2518151154432999863e-603j)  +/-  (6.72e-84, 1.54e-205j)
| (2.1455908165639936094e-07 + 2.555235956003544798e-598j)  +/-  (4.31e-76, 9.89e-198j)
| (5.082713221149957591e-29 + 4.6055608744965559325e-613j)  +/-  (4.54e-92, 1.04e-213j)
| (3.2882452731046489394e-09 + 9.997642830388635297e-600j)  +/-  (7.33e-80, 1.68e-201j)
| (1.3112249925287926693e-08 - 3.22793380252242357e-599j)  +/-  (3.06e-79, 7.02e-201j)
| (2.1455908165639936094e-07 + 9.4010616701671015256e-599j)  +/-  (2.04e-78, 4.67e-200j)
| (3.2882452731046489394e-09 + 3.194168323226677614e-599j)  +/-  (1.68e-81, 3.85e-203j)
| (0.056551900928008830745 - 5.8212746519593823481e-594j)  +/-  (1.11e-65, 2.55e-187j)
| (2.6614411506659930801e-10 - 2.1940884866337536355e-600j)  +/-  (7.46e-83, 1.71e-204j)
| (1.4818790179708539068e-24 - 1.8374717334010167211e-610j)  +/-  (4.96e-93, 1.14e-214j)
| (0.031392368271138387686 + 2.3020656155397827849e-594j)  +/-  (1.11e-65, 2.54e-187j)
| (0.0068334127763717993444 + 3.1082111502430825845e-595j)  +/-  (3.27e-71, 7.5e-193j)
| (7.4960116990045926579e-16 + 2.7835900521299531937e-604j)  +/-  (1.13e-87, 2.58e-209j)
| (2.2173248199897728623e-05 + 3.9747141311688146342e-597j)  +/-  (3.3e-79, 7.57e-201j)
| (2.7724520575276205887e-18 - 1.211901310050523037e-606j)  +/-  (5.26e-91, 1.21e-212j)
| (0.056551900928008830745 - 4.5560314184436328637e-594j)  +/-  (9.62e-69, 2.21e-190j)
| (2.7724520575276205887e-18 - 9.7837911882080280961e-606j)  +/-  (2.28e-89, 5.24e-211j)
| (0.00013295384920783184835 - 1.6381296457014867246e-596j)  +/-  (1.74e-78, 3.98e-200j)
| (0.0005844996165535390526 + 5.8273794680091738841e-596j)  +/-  (1.11e-77, 2.55e-199j)
| (0.0068334127763717993444 + 4.8928022425106363553e-595j)  +/-  (1.4e-75, 3.2e-197j)
| (1.4818790179708539068e-24 - 4.1091762635227195248e-609j)  +/-  (1.17e-93, 2.69e-215j)
| (0.0005844996165535390526 + 3.1611613283755930053e-596j)  +/-  (9.93e-81, 2.28e-202j)
| (3.9865563529578817766e-21 + 2.0930578279776302416e-608j)  +/-  (2.59e-94, 5.93e-216j)
| (0.0021530438883757313916 - 1.7544017517060732492e-595j)  +/-  (3.34e-78, 7.65e-200j)
| (0.11228221402213119011 + 2.6505206306105309835e-593j)  +/-  (2.18e-75, 5e-197j)
| (2.6614411506659930801e-10 - 6.0973662586625343156e-601j)  +/-  (5.8e-88, 1.33e-209j)
| (0.016882103979961639809 - 9.1452709119109578813e-595j)  +/-  (4.4e-78, 1.01e-199j)
| (0.016882103979961639809 - 1.3345053280941700852e-594j)  +/-  (4.34e-78, 9.94e-200j)
| (7.4960116990045926579e-16 + 4.5240903169666618818e-605j)  +/-  (4.94e-92, 1.13e-213j)
| (1.3112249925287926693e-08 - 9.6720468978838770442e-599j)  +/-  (6.78e-86, 1.55e-207j)
| (0.031392368271138387686 + 3.1368921827779838123e-594j)  +/-  (2.64e-78, 6.05e-200j)
| (6.8410701081600976238e-12 + 2.8652068780548343337e-602j)  +/-  (1.53e-89, 3.52e-211j)
| (2.2173248199897728623e-05 + 1.8053075578866224055e-597j)  +/-  (3.97e-86, 9.1e-208j)
| (2.5859773856641228265e-06 - 9.3671781527644462892e-598j)  +/-  (1e-85, 2.3e-207j)
| (0.11145824216848332302 - 1.8653028287359553371e-593j)  +/-  (1.38e-81, 3.16e-203j)
| (0.00013295384920783184835 - 8.1666132751801337004e-597j)  +/-  (1.52e-85, 3.48e-207j)
| (2.5859773856641228265e-06 - 3.8421815319181226745e-598j)  +/-  (8.75e-87, 2e-208j)
| (0.094164345497957052851 + 8.5024334393107418046e-594j)  +/-  (1.38e-82, 3.16e-204j)
| (0.11228221402213119011 + 2.5046970810292293398e-593j)  +/-  (9.2e-83, 2.13e-204j)
| (0.13507984908712986487 - 2.8258514196486389434e-593j)  +/-  (1.14e-82, 2.69e-204j)
| (0.094164345497957052851 + 1.0147121312148121992e-593j)  +/-  (1.63e-83, 3.95e-205j)
| (0.0021530438883757313916 - 1.0304228291568834238e-595j)  +/-  (8.67e-86, 2.14e-207j)
| (0.11145824216848332302 - 1.6694483969212916967e-593j)  +/-  (3.08e-83, 6.62e-205j)
| (6.8410701081600976238e-12 + 1.2012117855804758762e-601j)  +/-  (6.5e-93, 1.88e-214j)
