Starting with polynomial:
P : 2*t
Extension levels are: 1 6 50
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P2 : 2*t^7 - 21*t^5 + 105/2*t^3 - 105/4*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^57 - 9486404713707924363988176269132286335371473938329/6536537506862970963870041612472645306620540974*t^55 + 19164546566724001585274782691598315282298498199076535/39219225041177825783220249674835871839723245844*t^53 - 29193611267589114648740094774150568181880571547559779295/287607650301970722410281830948796393491303802856*t^51 + 8392485544137589723242753689303636583766799144716553352625/575215300603941444820563661897592786982607605712*t^49 - 38586693140491090221676977875332259421111340783207621031275/25009360895823541079154941821634468999243808944*t^47 + 6232289163141975104853664083976313680653778417881825688418775/50018721791647082158309883643268937998487617888*t^45 - 71606301945491080220021565020310287064749256622190228384318625/9094313053026742210601797026048897817906839616*t^43 + 3599656570306310632377806704825866198811903619507728718059758375/9094313053026742210601797026048897817906839616*t^41 - 1164615220822154136272980955265146437853463023273457814909947283125/72754504424213937684814376208391182543254716928*t^39 + 76350574765417696626481465593316954144812062190239006964438656243625/145509008848427875369628752416782365086509433856*t^37 - 4075795438051680668407164136075323112750092012976863036776450275208625/291018017696855750739257504833564730173018867712*t^35 + 177572033272013828746858248207215732055908875045185019593674784824251875/582036035393711501478515009667129460346037735424*t^33 - 1578924008774010257519292571038189597315651108178973480180544377385166875/291018017696855750739257504833564730173018867712*t^31 + 45774090060342018023626818345777751425327165639476274922287728414354934375/582036035393711501478515009667129460346037735424*t^29 - 1078067064943861775502857579497319724899484431503719090083224690073349301875/1164072070787423002957030019334258920692075470848*t^27 + 41042193613416579476634872922767410951468304119791546274719557848181014625625/4656288283149692011828120077337035682768301883392*t^25 - 1253831142573620794499997880842264349103064464633169632934147336259223339015625/18625153132598768047312480309348142731073207533568*t^23 + 15224374409652672275660689882277440055572248428813870234892569684654184013078125/37250306265197536094624960618696285462146415067136*t^21 - 145162176967367365062133128144079667183732984849799779612438010781117651206328125/74500612530395072189249921237392570924292830134272*t^19 + 1069897128374408161656526914555902583678039725188314016773491188760092606272796875/149001225060790144378499842474785141848585660268544*t^17 - 2986110380104523241970389556185864412846849952632336545894968388094105195570265625/149001225060790144378499842474785141848585660268544*t^15 + 12289220988841566935170670729354818350881215751686497352013437423810562783181328125/298002450121580288756999684949570283697171320537088*t^13 - 35959472704321700716862604579546944218336349629341403221880561259262241830873515625/596004900243160577513999369899140567394342641074176*t^11 + 8890091519570440470013334423795395721784966715729212467981251325429378022294140625/149001225060790144378499842474785141848585660268544*t^9 - 176580526496200316084417499422523508489665223819475281897557244700590807145551921875/4768039201945284620111994959193124539154741128593408*t^7 + 122463203540870776731868272354616512674335354101420905795428808846992256027234109375/9536078403890569240223989918386249078309482257186816*t^5 - 38583638692680639631987824976547091793239227202576336739486211715983009372662734375/19072156807781138480447979836772498156618964514373632*t^3 + 3451477926405291624802425198377682914298993076555670896287536604504143207440078125/38144313615562276960895959673544996313237929028747264*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: 0
  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
Positive weights:   57 out of 57
Indefinite weights: 0 out of 57
Negative weights:   0 out of 57
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-9.5954745989076564932 - 2.2385464677522992134e-912j)  +/-  (8.16e-246, 8.16e-246j)
| (7.0648445568510835145 - 7.8306203052463866925e-908j)  +/-  (3.05e-242, 3.05e-242j)
| (-8.4075047161710409174 + 5.8635970441205128569e-909j)  +/-  (1.04e-243, 1.04e-243j)
| (2.3846239261132012662 + 2.8047752519736238638e-916j)  +/-  (1.13e-245, 1.13e-245j)
| (7.926584165542998308 - 1.5182931831273516846e-912j)  +/-  (5.13e-243, 5.13e-243j)
| (-8.945852012280202311 - 1.1710744696666389952e-914j)  +/-  (1.53e-244, 1.53e-244j)
| (9.5954745989076564932 - 1.0161881706396715149e-915j)  +/-  (8.36e-246, 8.36e-246j)
| (5.916212373039825966 + 1.1283211783411429922e-911j)  +/-  (7.5e-242, 7.5e-242j)
| (8.945852012280202311 + 5.1649874392851009946e-916j)  +/-  (1.55e-244, 1.55e-244j)
| (8.4075047161710409174 - 9.5182211467644730256e-915j)  +/-  (1.08e-243, 1.08e-243j)
| (3.8820546701630152773 + 7.4422447643537109686e-914j)  +/-  (3.42e-243, 3.42e-243j)
| (5.5579527444337975851 + 2.6751408423142661116e-912j)  +/-  (6.23e-242, 6.23e-242j)
| (-7.0648445568510835145 - 2.4470180567446370242e-917j)  +/-  (3.11e-242, 3.11e-242j)
| (-1.9455381356125743266 + 8.2679449880027417753e-941j)  +/-  (6.16e-247, 6.16e-247j)
| (-6.6671227495498542846 + 4.9453619020438405868e-935j)  +/-  (5e-242, 5e-242j)
| (6.2852200732331744937 + 2.629110208192323558e-944j)  +/-  (6.86e-242, 6.86e-242j)
| (7.4825539087220421063 + 4.9420502515897969393e-948j)  +/-  (1.33e-242, 1.33e-242j)
| (4.2048057121854126285 - 8.7875776130294225512e-952j)  +/-  (8.76e-243, 8.76e-243j)
| (-1.3878995193696646365 - 7.2548797658376588987e-959j)  +/-  (4.41e-249, 4.41e-249j)
| (2.6519613568352334924 + 3.3866031219370842244e-954j)  +/-  (3.47e-245, 3.47e-245j)
| (4.8675287444305077982 + 2.1705409176998531984e-950j)  +/-  (3.4e-242, 3.4e-242j)
| (2.1718491667094401131 - 1.118978923160409188e-960j)  +/-  (3.74e-246, 3.74e-246j)
| (1.9455381356125743266 + 1.16077359998985935e-960j)  +/-  (6.02e-247, 6.02e-247j)
| (-5.2088124559500218551 - 3.797756052957787741e-954j)  +/-  (4.75e-242, 4.75e-242j)
| (-5.5579527444337975851 + 1.5150259285667562864e-972j)  +/-  (6.45e-242, 6.45e-242j)
| (-4.8675287444305077982 + 3.2171275219776963951e-985j)  +/-  (3.22e-242, 3.22e-242j)
| (-2.6519613568352334924 - 6.1725248275540710891e-1002j)  +/-  (3.43e-245, 3.43e-245j)
| (-6.2852200732331744937 - 1.594484514027105422e-997j)  +/-  (6.63e-242, 6.63e-242j)
| (-4.2048057121854126285 + 1.3890954327742944861e-1005j)  +/-  (9.15e-243, 9.15e-243j)
| (-2.3846239261132012662 + 5.1917243394433717713e-1011j)  +/-  (1.08e-245, 1.08e-245j)
| (-7.4825539087220421063 - 5.4640224194823339386e-1007j)  +/-  (1.3e-242, 1.3e-242j)
| (3.2524615818597856806 - 1.698077325938262019e-1013j)  +/-  (4.03e-244, 4.03e-244j)
| (1.3878995193696646365 + 2.2176808872089778777e-1018j)  +/-  (4.63e-249, 4.63e-249j)
| (-7.926584165542998308 + 1.7194446250581041269e-1011j)  +/-  (4.93e-243, 4.93e-243j)
| (-1.673551628767471445 - 6.5422757890855480279e-1017j)  +/-  (5.51e-248, 5.51e-248j)
| (-3.5645655611190689876 - 4.4411463959290846207e-1012j)  +/-  (1.24e-243, 1.24e-243j)
| (-0.81628788285896466304 - 4.2265907236323546175e-1022j)  +/-  (2.26e-251, 2.26e-251j)
| (-0.26575404743026636735 - 1.2426999346164612342e-1023j)  +/-  (1.06e-253, 1.06e-253j)
| (6.6671227495498542846 - 2.5702229524709191117e-1013j)  +/-  (4.84e-242, 4.84e-242j)
| (-1.100710049485282483 - 2.5333823247219126127e-1020j)  +/-  (3.23e-250, 3.23e-250j)
| (3.5645655611190689876 - 5.7438133277896526191e-1014j)  +/-  (1.27e-243, 1.27e-243j)
| (4.5331139309631950774 - 2.2466213244373084798e-1012j)  +/-  (1.78e-242, 1.78e-242j)
| (2.9468404083299233356 - 1.488444776528465125e-1015j)  +/-  (1.21e-244, 1.21e-244j)
| (0.53738384846928779558 - 1.3129223217804640478e-1023j)  +/-  (1.7e-252, 1.7e-252j)
| (1.100710049485282483 - 6.7396269878727171998e-1021j)  +/-  (3.29e-250, 3.29e-250j)
| (-3.8820546701630152773 + 4.60262531313459327e-1013j)  +/-  (3.56e-243, 3.56e-243j)
| (-5.916212373039825966 - 3.1714693181409694004e-1017j)  +/-  (7.33e-242, 7.33e-242j)
| (-4.5331139309631950774 + 1.0100857985364600715e-1024j)  +/-  (1.74e-242, 1.74e-242j)
| (0.81628788285896466304 + 5.4150849985515497034e-1037j)  +/-  (2.13e-251, 2.13e-251j)
| (-2.9468404083299233356 - 2.0456368778370237515e-1030j)  +/-  (1.21e-244, 1.21e-244j)
| (-0.53738384846928779558 + 6.9409504510581664925e-1038j)  +/-  (1.4e-252, 1.4e-252j)
| (-3.2524615818597856806 - 8.8445661745436459062e-1030j)  +/-  (4.05e-244, 4.05e-244j)
| (5.2088124559500218551 + 8.5433548993568866867e-1036j)  +/-  (5.13e-242, 5.13e-242j)
| (1.673551628767471445 - 2.963301269528363806e-1042j)  +/-  (5.37e-248, 5.37e-248j)
| (0.26575404743026636735 - 7.5508392487032925299e-1048j)  +/-  (1.06e-253, 1.06e-253j)
| (-2.1718491667094401131 + 7.8234821681863831789e-1043j)  +/-  (3.77e-246, 3.77e-246j)
| (-9.6865448429655287951e-1184 - 4.561274408710180324e-1185j)  +/-  (5.53e-1182, 5.53e-1182j)
-------------------------------------------------
The weights are:
| (4.3622962228443769364e-41 - 4.657156440758950749e-940j)  +/-  (1.36e-66, 5.26e-188j)
| (4.8347670785095203873e-23 + 2.39099242890794343e-929j)  +/-  (7.26e-60, 2.8e-181j)
| (5.7011683379299562726e-32 - 2.778307111972092124e-935j)  +/-  (9.02e-64, 3.48e-185j)
| (0.00046131823206685715281 + 2.4910154153336218487e-918j)  +/-  (2.32e-35, 8.93e-157j)
| (1.3406446787906799345e-28 - 9.1851314155881840609e-933j)  +/-  (6.61e-63, 2.55e-184j)
| (5.7353453792023495549e-36 + 2.202524507979685064e-937j)  +/-  (1.63e-65, 6.3e-187j)
| (4.3622962228443769364e-41 + 1.4528903003476837202e-939j)  +/-  (2.42e-68, 9.33e-190j)
| (1.2904246636700197453e-16 - 4.0167424082397501784e-927j)  +/-  (8.41e-58, 3.24e-179j)
| (5.7353453792023495549e-36 - 7.9264594158173602256e-937j)  +/-  (1.17e-66, 4.51e-188j)
| (5.7011683379299562726e-32 + 1.1866388718366712942e-934j)  +/-  (4.95e-65, 1.91e-186j)
| (5.1491722329091991829e-08 - 1.902246422361122548e-920j)  +/-  (1.17e-51, 4.5e-173j)
| (7.6568129359767082034e-15 - 2.6060214800771749466e-925j)  +/-  (1.61e-57, 6.2e-179j)
| (4.8347670785095203873e-23 + 1.568400803535417253e-930j)  +/-  (1.68e-66, 6.48e-188j)
| (0.0032737332899493496369 + 2.5242950821049828002e-918j)  +/-  (3.96e-43, 1.53e-164j)
| (1.0889963382729770044e-20 - 2.9377612217950071814e-929j)  +/-  (1.5e-65, 5.79e-187j)
| (1.47618725626685955e-18 - 4.0646317415372727577e-928j)  +/-  (9.28e-61, 3.58e-182j)
| (1.1719379982589031984e-25 + 5.3574597839149852849e-931j)  +/-  (6.21e-64, 2.4e-185j)
| (3.8496557513102393181e-09 - 2.3335050991098198133e-921j)  +/-  (1.71e-55, 6.59e-177j)
| (0.023625017752111842632 + 4.5873271600696131454e-918j)  +/-  (3.41e-41, 1.31e-162j)
| (0.00014234796152392442166 - 1.1826002742394866134e-918j)  +/-  (2.57e-49, 9.92e-171j)
| (9.7789884665329470253e-12 - 2.1473403762258430436e-923j)  +/-  (8.45e-58, 3.26e-179j)
| (0.0010121498170993995733 - 4.6702859049336841316e-918j)  +/-  (7.08e-47, 2.73e-168j)
| (0.0032737332899493496369 + 6.5400763974004918967e-918j)  +/-  (5.44e-46, 2.1e-167j)
| (3.2071434899922759974e-13 - 4.1548484311113329471e-925j)  +/-  (3.1e-66, 1.2e-187j)
| (7.6568129359767082034e-15 + 4.9761744862163386405e-926j)  +/-  (2.29e-67, 8.81e-189j)
| (9.7789884665329470253e-12 + 3.0035152923782819481e-924j)  +/-  (1.05e-65, 4.05e-187j)
| (0.00014234796152392442166 - 2.079155811500184085e-919j)  +/-  (4.92e-58, 1.9e-179j)
| (1.47618725626685955e-18 + 4.2899924443506778534e-928j)  +/-  (1.1e-69, 4.25e-191j)
| (3.8496557513102393181e-09 + 1.0839624301365588907e-922j)  +/-  (8.36e-65, 3.22e-186j)
| (0.00046131823206685715281 + 7.8449243938325979608e-919j)  +/-  (1.93e-57, 7.43e-179j)
| (1.1719379982589031984e-25 - 6.203265080804007994e-932j)  +/-  (1.38e-73, 5.31e-195j)
| (4.4407315351346448893e-06 - 1.2444912102952837011e-919j)  +/-  (3.17e-61, 1.22e-182j)
| (0.023625017752111842632 + 9.0183033909593862236e-918j)  +/-  (1.28e-53, 4.95e-175j)
| (1.3406446787906799345e-28 + 1.685030331296268411e-933j)  +/-  (4.73e-75, 1.82e-196j)
| (0.0096748149739090408548 - 3.281983670897726442e-918j)  +/-  (2.25e-56, 8.69e-178j)
| (5.3870695763144512896e-07 + 2.6335356134848482661e-921j)  +/-  (1.82e-64, 7.01e-186j)
| (0.081734330661398683675 + 9.5633257682009664509e-918j)  +/-  (2.11e-54, 8.12e-176j)
| (0.14091710716831026051 + 1.6946267025982461057e-917j)  +/-  (1.25e-54, 4.8e-176j)
| (1.0889963382729770044e-20 - 7.6846135858689350103e-929j)  +/-  (6.85e-71, 2.64e-192j)
| (0.048095224141129063854 - 6.6426203824703735175e-918j)  +/-  (4.51e-55, 1.74e-176j)
| (5.3870695763144512896e-07 + 5.6352736042512251319e-920j)  +/-  (5.2e-63, 2e-184j)
| (2.2244018473065671533e-10 + 2.0515177075531529484e-922j)  +/-  (8.37e-66, 3.23e-187j)
| (2.8794555913610749434e-05 + 3.5558504133561271525e-919j)  +/-  (1.93e-61, 7.46e-183j)
| (0.11640568125978333565 - 1.7082256390152188316e-917j)  +/-  (7.07e-58, 2.72e-179j)
| (0.048095224141129063854 - 1.1290861336332547571e-917j)  +/-  (3.72e-58, 1.43e-179j)
| (5.1491722329091991829e-08 - 5.5708967374183044174e-922j)  +/-  (4.8e-67, 1.85e-188j)
| (1.2904246636700197453e-16 - 5.0666604882131144463e-927j)  +/-  (9.27e-72, 3.57e-193j)
| (2.2244018473065671533e-10 - 1.9098756724660065256e-923j)  +/-  (1.35e-68, 5.19e-190j)
| (0.081734330661398683675 + 1.4124032328822791464e-917j)  +/-  (6.2e-62, 2.39e-183j)
| (2.8794555913610749434e-05 + 4.9663705602687070511e-920j)  +/-  (4.27e-66, 1.64e-187j)
| (0.11640568125978333565 - 1.3236233583449552361e-917j)  +/-  (9.07e-63, 3.53e-184j)
| (4.4407315351346448893e-06 - 1.166932590306069555e-920j)  +/-  (1.02e-66, 3.93e-188j)
| (3.2071434899922759974e-13 + 2.3309335601173753214e-924j)  +/-  (3.76e-71, 1.48e-192j)
| (0.0096748149739090408548 - 7.4703937794335962168e-918j)  +/-  (1.88e-64, 7.32e-186j)
| (0.14091710716831026051 + 1.921564992580630784e-917j)  +/-  (1.03e-63, 4.09e-185j)
| (0.0010121498170993995733 - 1.7424487569257643472e-918j)  +/-  (5.93e-65, 2.16e-186j)
| (0.14924889034877221981 - 1.9293666461579931887e-917j)  +/-  (6.03e-64, 2.5e-185j)
