Starting with polynomial:
P : 2*t
Extension levels are: 1 2 68
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 68 Kronrod extension for:
P2 : 2*t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^71 - 682318202587104478637369101538978335987/281883215233401101190419706483682719*t^69 + 259685236589810023339269185894208000066269/187922143488934067460279804322455146*t^67 - 16923131749860167100598912556807256541028607/34167662452533466810959964422264572*t^65 + 1069077922133199071435341327815667510045117415/8541915613133366702739991105566143*t^63 - 405502280773255332088182854384820022527070421475/17083831226266733405479982211132286*t^61 + 119993931174191347596485022768076296267307984098555/34167662452533466810959964422264572*t^59 - 28429405677879375735470440633909547567266226683774155/68335324905066933621919928844529144*t^57 + 10984017605322382279863016810357642012616703128472002205/273341299620267734487679715378116576*t^55 - 1753075886953197450810099088284586800072539998669489233225/546682599240535468975359430756233152*t^53 + 233404106152086211546017895514130415659126044601243318541725/1093365198481070937950718861512466304*t^51 - 26106709339052528483842297658624734735638772606084959222721125/2186730396962141875901437723024932608*t^49 + 1232828285058821785385866259432015120610427021172446337836282125/2186730396962141875901437723024932608*t^47 - 98656035793607639903353860631717162811361005661778059794902052625/4373460793924283751802875446049865216*t^45 + 6703548675496484420935319563070612685925051604096851169405319050625/8746921587848567503605750892099730432*t^43 - 387128516156389001212035090684481805297412412031071680249502375670625/17493843175697135007211501784199460864*t^41 + 75994197419817376258171608452783109014938027086580148620664931621193125/139950745405577080057692014273595686912*t^39 - 3165684901731357669735066663329315230966748452513637451030868840374230625/279901490811154160115384028547191373824*t^37 + 111699923277583231979789580795195532981977274389963998744944857113678248125/559802981622308320230768057094382747648*t^35 - 3327913452037274050354321502794095233622104702208917369581042233917812003125/1119605963244616640461536114188765495296*t^33 + 20841847108414683149696323637790854030115742251821465958922470441114356315625/559802981622308320230768057094382747648*t^31 - 436645306024917203270484204336686475048638141100704568312079947349646968378125/1119605963244616640461536114188765495296*t^29 + 7599444681253853069993782928074983636761529442268051386304359453740694320253125/2239211926489233280923072228377530990592*t^27 - 108974797780430149888775418019735581962181489665396799205935301238265794874103125/4478423852978466561846144456755061981184*t^25 + 2549386537804004855778099370819040775822882272143659485739340965975263975869453125/17913695411913866247384577827020247924736*t^23 - 24028959686704230359088550506384283066223220302842277792262629938058096768449640625/35827390823827732494769155654040495849472*t^21 + 179777184549027139666060554992952824270575504709001982063732967426683447739657203125/71654781647655464989538311308080991698944*t^19 - 1048003963903704293042365536058514114680742944155811152408208696983480003341887828125/143309563295310929979076622616161983397888*t^17 + 2325160652802003418008748829297365593239994870613576063764358981595057462903013421875/143309563295310929979076622616161983397888*t^15 - 7622162975619866312277035946811230184027912829969625156083523048419816081291428359375/286619126590621859958153245232323966795776*t^13 + 17746666155466514026723744495894920855065195002824593383783630128491640609869818359375/573238253181243719916306490464647933591552*t^11 - 27811741018957279363999863037239850894876771471775770157943726393872476369709863359375/1146476506362487439832612980929295867183104*t^9 + 217237152955556046512376453203608096002708611446861484618054916586370313303630440859375/18343624101799799037321807694868733874929664*t^7 - 117198223380316004658298088500400248878243996139471569518392188126838034087191343671875/36687248203599598074643615389737467749859328*t^5 + 28280771221338496708447133010255315596321059757763212221343415045076057668256590234375/73374496407199196149287230779474935499718656*t^3 - 1893555149364347217457371831159728500253929669243317821514530273437289698914793359375/146748992814398392298574461558949870999437312*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   71 out of 71
Indefinite weights: 0 out of 71
Negative weights:   0 out of 71
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (7.5633423086933743889 - 1.3900885988533964036e-1831j)  +/-  (1.4e-493, 1.4e-493j)
| (11.058987437816725788 - 2.6604389349106870797e-1847j)  +/-  (8.12e-499, 8.12e-499j)
| (9.925180507298513288 - 8.4997908906964266948e-1844j)  +/-  (2.42e-496, 2.42e-496j)
| (8.6494403034305364826 - 1.0853283457590984159e-1842j)  +/-  (2.09e-494, 2.09e-494j)
| (7.9117087798009496256 - 2.0894138140209806392e-1854j)  +/-  (8.91e-494, 8.91e-494j)
| (-8.2728010560820775809 - 1.283105506683200305e-1862j)  +/-  (4.7e-494, 4.7e-494j)
| (9.045641439389421935 + 3.5164466964363454524e-1870j)  +/-  (6.26e-495, 6.26e-495j)
| (-3.3643852061072974926 - 1.6336529586833666265e-1883j)  +/-  (1.56e-497, 1.56e-497j)
| (6.2620782481697006987 + 9.2707217812391466061e-1890j)  +/-  (1.52e-493, 1.52e-493j)
| (10.438428889200761262 + 6.6253421091053538705e-1911j)  +/-  (2.23e-497, 2.23e-497j)
| (9.4674994234207911875 - 8.80894593943483955e-1909j)  +/-  (1.47e-495, 1.47e-495j)
| (6.8969643388649082301 + 3.2621039613255454429e-1921j)  +/-  (2.09e-493, 2.09e-493j)
| (-9.045641439389421935 - 1.7619061411504112126e-1938j)  +/-  (6.13e-495, 6.13e-495j)
| (-2.280486675569413074 - 5.9291741881048178497e-1949j)  +/-  (1.1e-500, 1.1e-500j)
| (-9.4674994234207911875 + 3.4557522389984108404e-1943j)  +/-  (1.48e-495, 1.48e-495j)
| (6.5761173720691263024 - 1.5633802246802417271e-1941j)  +/-  (1.83e-493, 1.83e-493j)
| (1.4857404114615300372 - 5.3972429025337603508e-1964j)  +/-  (1.78e-503, 1.78e-503j)
| (3.9184705883544819656 - 5.9085065099530623284e-1956j)  +/-  (2.64e-496, 2.64e-496j)
| (-3.9184705883544819656 - 5.2592043831548227823e-1962j)  +/-  (2.58e-496, 2.58e-496j)
| (5.3532226488052705712 - 9.5299409302417316707e-1962j)  +/-  (3.57e-494, 3.57e-494j)
| (2.5487859666950801516 + 5.6300337270763121338e-1978j)  +/-  (7.77e-500, 7.77e-500j)
| (2.0138464430558607029 + 9.6198002866763978782e-1980j)  +/-  (1.32e-501, 1.32e-501j)
| (4.482744459306502353 + 7.1432715963847677658e-1973j)  +/-  (2.64e-495, 2.64e-495j)
| (-6.8969643388649082301 + 2.2193090964139026767e-1971j)  +/-  (1.9e-493, 1.9e-493j)
| (-3.0906162716985703143 + 1.1436580815356407372e-1982j)  +/-  (3.04e-498, 3.04e-498j)
| (3.0906162716985703143 - 1.9766974444387619972e-1983j)  +/-  (2.82e-498, 2.82e-498j)
| (1.7488857951255503792 + 8.0734763655458763938e-1988j)  +/-  (1.75e-502, 1.75e-502j)
| (-4.7693646605694914486 + 6.2721198326826271561e-1979j)  +/-  (7.17e-495, 7.17e-495j)
| (-10.438428889200761262 - 7.0598626947808759871e-1983j)  +/-  (2.23e-497, 2.23e-497j)
| (8.2728010560820775809 - 2.3847447374912543626e-1977j)  +/-  (4.85e-494, 4.85e-494j)
| (3.3643852061072974926 - 8.8867288435101668901e-1986j)  +/-  (1.4e-497, 1.4e-497j)
| (-7.2256233355106767537 - 1.2063709841669939927e-1979j)  +/-  (1.81e-493, 1.81e-493j)
| (0.96659719291702609606 + 2.0133238680165667188e-2004j)  +/-  (1.31e-505, 1.31e-505j)
| (-11.058987437816725788 + 2.6778928536993047958e-1997j)  +/-  (8.4e-499, 8.4e-499j)
| (-5.6512649043660282548 + 1.3637924389292386269e-1990j)  +/-  (6.28e-494, 6.28e-494j)
| (-1.7488857951255503792 - 2.110042223561430855e-2022j)  +/-  (1.59e-502, 1.59e-502j)
| (5.9540231085863150854 + 6.7257177739651390041e-2012j)  +/-  (1.07e-493, 1.07e-493j)
| (3.6402709591512928854 - 5.0196453706071827622e-2030j)  +/-  (6.51e-497, 6.51e-497j)
| (-7.5633423086933743889 + 1.3505712832394921346e-2027j)  +/-  (1.51e-493, 1.51e-493j)
| (-6.5761173720691263024 - 3.8041701315818416924e-2026j)  +/-  (1.87e-493, 1.87e-493j)
| (-9.925180507298513288 + 1.4259235026177475331e-2038j)  +/-  (2.56e-496, 2.56e-496j)
| (-2.5487859666950801516 - 1.4662734294597979553e-2045j)  +/-  (8.31e-500, 8.31e-500j)
| (5.6512649043660282548 + 1.4375185694393872382e-2037j)  +/-  (6.25e-494, 6.25e-494j)
| (-7.9117087798009496256 - 4.0471084263115213386e-2048j)  +/-  (8.62e-494, 8.62e-494j)
| (-4.482744459306502353 + 2.3864726116759062548e-2049j)  +/-  (2.66e-495, 2.66e-495j)
| (-5.9540231085863150854 + 3.9295675278789672126e-2047j)  +/-  (1.09e-493, 1.09e-493j)
| (-4.1992097365556198687 - 5.5475867745819029583e-2052j)  +/-  (8.82e-496, 8.82e-496j)
| (7.2256233355106767537 + 3.8277688428605340127e-2050j)  +/-  (1.76e-493, 1.76e-493j)
| (-2.0138464430558607029 - 1.2682507215620525999e-2067j)  +/-  (1.31e-501, 1.31e-501j)
| (-1.4857404114615300372 + 8.5665803120591389234e-2070j)  +/-  (1.8e-503, 1.8e-503j)
| (-8.6494403034305364826 + 3.0996371847244033713e-2061j)  +/-  (2.01e-494, 2.01e-494j)
| (-3.6402709591512928854 + 2.3473825387763049016e-2062j)  +/-  (6.72e-497, 6.72e-497j)
| (2.280486675569413074 + 6.2686598702217819167e-2066j)  +/-  (1.07e-500, 1.07e-500j)
| (5.0593991636278341087 + 3.9688937010367290212e-2059j)  +/-  (1.69e-494, 1.69e-494j)
| (1.2247448713915890491 - 1.444331954255460605e-2076j)  +/-  (1.75e-504, 1.75e-504j)
| (-5.0593991636278341087 + 5.7268305610840164558e-2065j)  +/-  (1.71e-494, 1.71e-494j)
| (-0.22803341902061273703 + 5.2369242601688968946e-2082j)  +/-  (4.57e-509, 4.57e-509j)
| (-5.3532226488052705712 + 9.1516143928937281599e-2068j)  +/-  (3.6e-494, 3.6e-494j)
| (1.9850415099572145413e-2113 - 1.794959398582140442e-2113j)  +/-  (1.9e-2111, 1.9e-2111j)
| (0.46542623400005983528 - 6.0421118482876224532e-2082j)  +/-  (8.95e-508, 8.95e-508j)
| (4.7693646605694914486 - 3.797620844894877609e-2068j)  +/-  (6.98e-495, 6.98e-495j)
| (-1.2247448713915890491 + 7.3626465701108769582e-2083j)  +/-  (1.66e-504, 1.66e-504j)
| (-0.96659719291702609606 - 4.3410132601276734464e-2084j)  +/-  (1.41e-505, 1.41e-505j)
| (4.1992097365556198687 - 1.1707524187120773979e-2076j)  +/-  (8.61e-496, 8.61e-496j)
| (0.71266837866095782522 - 6.0566639813301818674e-2089j)  +/-  (1.1e-506, 1.1e-506j)
| (-6.2620782481697006987 - 1.2245525150970223915e-2085j)  +/-  (1.49e-493, 1.49e-493j)
| (-2.8187956837172955194 + 1.6097831998228713869e-2091j)  +/-  (5.28e-499, 5.28e-499j)
| (-0.71266837866095782522 + 5.522239895208707743e-2099j)  +/-  (1.03e-506, 1.03e-506j)
| (-0.46542623400005983528 - 6.0329418115859886307e-2100j)  +/-  (8.26e-508, 8.26e-508j)
| (2.8187956837172955194 - 4.7688723570302408734e-2094j)  +/-  (5.31e-499, 5.31e-499j)
| (0.22803341902061273703 + 1.2895691174321528724e-2104j)  +/-  (4.57e-509, 4.57e-509j)
-------------------------------------------------
The weights are:
| (2.7729943194273629903e-26 + 2.9661613016991092245e-1856j)  +/-  (2.68e-167, 1.25e-411j)
| (3.1074412487326806142e-54 - 7.9939478253848315579e-1872j)  +/-  (2.84e-179, 1.33e-423j)
| (4.4814507820604122252e-44 - 1.5827117283599342893e-1866j)  +/-  (4.91e-176, 2.29e-420j)
| (7.027304973657126042e-34 + 4.9433434520576274475e-1861j)  +/-  (2.5e-172, 1.17e-416j)
| (1.3065111923524306545e-28 + 7.2622814394092251224e-1858j)  +/-  (5.9e-170, 2.75e-414j)
| (3.9342541734910161518e-31 + 8.3856383651151445187e-1861j)  +/-  (3.86e-177, 1.81e-421j)
| (6.7033288151120476034e-37 - 1.0698523006208015154e-1862j)  +/-  (7.5e-174, 3.51e-418j)
| (1.8819991944892585673e-06 + 6.4684254356812647472e-1848j)  +/-  (1.19e-152, 5.55e-397j)
| (1.6361254254211259833e-18 + 2.7451332539363399167e-1853j)  +/-  (2.67e-166, 1.25e-410j)
| (1.4893031296353834532e-48 + 7.1276512427184444266e-1869j)  +/-  (4.1e-179, 1.91e-423j)
| (2.9181909282432165187e-40 + 1.6604967619528370597e-1864j)  +/-  (1.54e-175, 7.18e-420j)
| (4.0193866457940867375e-22 + 7.6333430020103955327e-1855j)  +/-  (1.04e-168, 4.85e-413j)
| (6.7033288151120476034e-37 + 9.5480925217139989633e-1864j)  +/-  (1.82e-183, 8.5e-428j)
| (0.00083194306321715147291 + 2.1959079541472110551e-1846j)  +/-  (1.8e-148, 8.41e-393j)
| (2.9181909282432165187e-40 - 1.8565416630536880947e-1865j)  +/-  (5.96e-185, 2.78e-429j)
| (2.9626548490967589364e-20 - 4.6380940253219899971e-1854j)  +/-  (9.07e-169, 4.24e-413j)
| (0.016266764088012793848 - 2.3334426460080141447e-1845j)  +/-  (2.19e-139, 1.02e-383j)
| (3.383457805855403177e-08 + 2.2397911237396377722e-1848j)  +/-  (6.9e-161, 3.22e-405j)
| (3.383457805855403177e-08 + 7.110158822117449727e-1849j)  +/-  (4.03e-164, 1.88e-408j)
| (5.9831758909703450711e-14 - 3.6107661029969282883e-1851j)  +/-  (8.98e-167, 4.19e-411j)
| (0.00022913629909474075222 - 2.0346729616669475049e-1846j)  +/-  (4.21e-153, 1.97e-397j)
| (0.0025982681046509296954 - 7.738716404396072648e-1846j)  +/-  (1.8e-148, 8.42e-393j)
| (3.0141370573010082925e-10 + 2.191093542465156757e-1849j)  +/-  (8.76e-164, 4.09e-408j)
| (4.0193866457940867375e-22 + 3.5176927686681760875e-1856j)  +/-  (3.36e-180, 1.57e-424j)
| (1.0936514891889982915e-05 - 1.7371070686665484829e-1847j)  +/-  (1.05e-160, 4.89e-405j)
| (1.0936514891889982915e-05 - 4.1377599714813419231e-1847j)  +/-  (4.04e-158, 1.89e-402j)
| (0.0069958535403269614107 + 1.380932694848055824e-1845j)  +/-  (6.99e-148, 3.26e-392j)
| (2.149790900853768803e-11 - 1.3749620359979214653e-1850j)  +/-  (1.11e-171, 5.2e-416j)
| (1.4893031296353834532e-48 - 1.1383665647785737806e-1869j)  +/-  (6.57e-192, 3.07e-436j)
| (3.9342541734910161518e-31 - 1.8717955320715484368e-1859j)  +/-  (8.73e-177, 4.08e-421j)
| (1.8819991944892585673e-06 + 1.6833987317326177579e-1847j)  +/-  (1.04e-160, 4.88e-405j)
| (3.976100482353193346e-24 - 3.266206758249570234e-1857j)  +/-  (7.93e-182, 3.7e-426j)
| (0.056817662174198717186 - 5.745554342810130152e-1845j)  +/-  (2.43e-150, 1.14e-394j)
| (3.1074412487326806142e-54 + 1.5005643847279384092e-1872j)  +/-  (2.36e-194, 1.1e-438j)
| (2.2857170893383133693e-15 + 1.1186516202781035517e-1852j)  +/-  (1.35e-177, 6.29e-422j)
| (0.0069958535403269614107 + 8.6223973605900151687e-1846j)  +/-  (5.06e-157, 2.36e-401j)
| (6.9222176002411168584e-17 - 1.5179003740189500492e-1852j)  +/-  (9.12e-173, 4.26e-417j)
| (2.7468295387226137177e-07 - 6.3731911997553563416e-1848j)  +/-  (1.1e-164, 5.15e-409j)
| (2.7729943194273629903e-26 + 2.5482833057090178818e-1858j)  +/-  (2.29e-183, 1.07e-427j)
| (2.9626548490967589364e-20 - 3.2383430368527904392e-1855j)  +/-  (5.77e-181, 2.7e-425j)
| (4.4814507820604122252e-44 + 2.1374641281896315088e-1867j)  +/-  (2.2e-191, 1.03e-435j)
| (0.00022913629909474075222 - 1.0089846495175614246e-1846j)  +/-  (5.19e-167, 2.43e-411j)
| (2.2857170893383133693e-15 + 7.7311419175668799007e-1852j)  +/-  (7.32e-175, 3.42e-419j)
| (1.3065111923524306545e-28 - 1.6348478223235279676e-1859j)  +/-  (1.01e-184, 4.7e-429j)
| (3.0141370573010082925e-10 + 5.6033782461658026823e-1850j)  +/-  (6.47e-176, 3.02e-420j)
| (6.9222176002411168584e-17 - 1.8071466889810408859e-1853j)  +/-  (1.77e-180, 8.25e-425j)
| (3.4973829922790500784e-09 - 2.0846770232069698601e-1849j)  +/-  (3.68e-175, 1.72e-419j)
| (3.976100482353193346e-24 - 1.4302962927844996615e-1855j)  +/-  (6.8e-182, 3.18e-426j)
| (0.0025982681046509296954 - 4.4841942458002925856e-1846j)  +/-  (2.12e-168, 9.89e-413j)
| (0.016266764088012793848 - 1.5672014380941844684e-1845j)  +/-  (8.91e-167, 4.16e-411j)
| (7.027304973657126042e-34 - 3.3115570220264890146e-1862j)  +/-  (2.62e-188, 1.23e-432j)
| (2.7468295387226137177e-07 - 2.2316446670533724663e-1848j)  +/-  (5.7e-174, 2.67e-418j)
| (0.00083194306321715147291 + 4.0917533748740809712e-1846j)  +/-  (4.62e-171, 2.16e-415j)
| (1.2581761082202506733e-12 + 1.5454583304060711454e-1850j)  +/-  (1.66e-178, 7.78e-423j)
| (0.032696895546569166727 + 3.7485550892083554698e-1845j)  +/-  (2.98e-169, 1.39e-413j)
| (1.2581761082202506733e-12 + 3.0656888607678226907e-1851j)  +/-  (7e-179, 3.27e-423j)
| (0.12421750407426661789 + 1.3695805451395486992e-1844j)  +/-  (3.72e-170, 1.74e-414j)
| (5.9831758909703450711e-14 - 6.1782874763914564661e-1852j)  +/-  (9e-180, 4.21e-424j)
| (0.12745532529391227277 - 1.5544638719147319815e-1844j)  +/-  (2.87e-170, 1.34e-414j)
| (0.11029960032431284359 - 1.1606188403064294486e-1844j)  +/-  (1.37e-170, 6.4e-415j)
| (2.149790900853768803e-11 - 6.0691265355003187287e-1850j)  +/-  (1.03e-178, 4.8e-423j)
| (0.032696895546569166727 + 2.7037262142648576015e-1845j)  +/-  (2.42e-172, 1.13e-416j)
| (0.056817662174198717186 - 4.4434028566327642902e-1845j)  +/-  (2.19e-172, 1.02e-416j)
| (3.4973829922790500784e-09 - 7.2889880101914850769e-1849j)  +/-  (1.14e-177, 5.32e-422j)
| (0.085251442565289790961 + 8.4057862975119433017e-1845j)  +/-  (4.66e-172, 2.16e-416j)
| (1.6361254254211259833e-18 + 2.5837501506762610954e-1854j)  +/-  (8.77e-183, 4.08e-427j)
| (5.4136719870868537218e-05 + 4.3358550668803723329e-1847j)  +/-  (2.77e-175, 1.29e-419j)
| (0.085251442565289790961 + 6.9580989229241313382e-1845j)  +/-  (1.6e-173, 7.44e-418j)
| (0.11029960032431284359 - 1.0260571193947136857e-1844j)  +/-  (2.26e-173, 1.03e-417j)
| (5.4136719870868537218e-05 + 9.4878286963134196541e-1847j)  +/-  (2.18e-176, 1.17e-420j)
| (0.12421750407426661789 + 1.4547330967306565594e-1844j)  +/-  (1.61e-173, 6.63e-418j)
