Starting with polynomial:
P : 2*t
Extension levels are: 1 6 38
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 38 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^45 - 12050032700228448587776224934207827/13775531955568948500205568445646*t^43 + 52614686656685246950832319790047651117/303061703022516867004522505804212*t^41 - 100602978317247610255067719844713391852511/4848987248360269872072360092867392*t^39 + 16201438066088214512676370698573330775786251/9697974496720539744144720185734784*t^37 - 1864208036555688966057985938621082150305913623/19395948993441079488289440371469568*t^35 + 848148094822858393564514356567854787530492165/207443304742685342120742677769728*t^33 - 13619292266413616787086618871009403463265947325/103721652371342671060371338884864*t^31 + 668627934665672797011567255164666439258527077665/207443304742685342120742677769728*t^29 - 25250322598309037250702336464621065826452688883165/414886609485370684241485355539456*t^27 + 31945563889371882274195075186772732227964276295315/36077096476988755151433509177344*t^25 - 1429191840630651293309601276104625148677794156143125/144308385907955020605734036709376*t^23 + 24426112109167064204354977886344775271140754618143625/288616771815910041211468073418752*t^21 - 315758557605655763308824619322816128846691118052489125/577233543631820082422936146837504*t^19 + 3042933308325165608281195921670788174944957670733149125/1154467087263640164845872293675008*t^17 - 10715351200373550471378485263472461528328283830466453375/1154467087263640164845872293675008*t^15 + 53690507537399505333785818119428756094864811107995814375/2308934174527280329691744587350016*t^13 - 184517600443474308328424678891107178154394024669322173125/4617868349054560659383489174700032*t^11 + 413146006175578511908047973524178825087237555818173713125/9235736698109121318766978349400064*t^9 - 2234190975845848353343046241750660646038172949229833761875/73885893584872970550135826795200512*t^7 + 1613666619519183066043286176380616639795254761605815579375/147771787169745941100271653590401024*t^5 - 496981864782321270134895413711895298223090080722694246875/295543574339491882200543307180802048*t^3 + 38212832306298129804760493560748714492146332772084396875/591087148678983764401086614361604096*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
Positive weights:   45 out of 45
Indefinite weights: 0 out of 45
Negative weights:   0 out of 45
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (6.1256577986418893598 - 3.8618833597558266249e-864j)  +/-  (4.74e-245, 4.74e-245j)
| (-8.3422858379649871416 - 1.9157505333003288669e-879j)  +/-  (1.22e-247, 1.22e-247j)
| (-7.6627836309712674772 - 4.4381530954927852385e-878j)  +/-  (1.6e-246, 1.6e-246j)
| (6.5931035411654629904 - 1.3177417606237125793e-874j)  +/-  (2.43e-245, 2.43e-245j)
| (-7.0983716997121308063 + 2.2866153842736514201e-885j)  +/-  (8.66e-246, 8.66e-246j)
| (5.2647866137825735769 + 4.7274098897203034083e-886j)  +/-  (7.43e-245, 7.43e-245j)
| (-4.0888397945521289789 - 7.5648757623289574934e-896j)  +/-  (2.68e-245, 2.68e-245j)
| (2.9996317742003986026 - 4.9550055482966597044e-897j)  +/-  (1.61e-246, 1.61e-246j)
| (7.6627836309712674772 - 4.4153901204724265062e-897j)  +/-  (1.53e-246, 1.53e-246j)
| (5.685071292554447938 + 5.2107676093434965311e-902j)  +/-  (6.88e-245, 6.88e-245j)
| (7.0983716997121308063 + 1.036797559903445463e-916j)  +/-  (8.25e-246, 8.25e-246j)
| (4.0888397945521289789 + 1.7893261319019286235e-928j)  +/-  (2.79e-245, 2.79e-245j)
| (-1.3837651307473168472 + 4.9907527628318320395e-942j)  +/-  (7.3e-250, 7.3e-250j)
| (-4.4692396132714615431 + 1.7957630896933830065e-935j)  +/-  (5.26e-245, 5.26e-245j)
| (-6.1256577986418893598 - 3.2962681320746449583e-944j)  +/-  (4.75e-245, 4.75e-245j)
| (1.1046640428051525945 + 6.8286224682452790447e-957j)  +/-  (1.19e-250, 1.19e-250j)
| (0.81628788285896466304 - 6.5847346034798500321e-957j)  +/-  (1.06e-251, 1.06e-251j)
| (4.8605053674291990591 - 4.525222359635405801e-953j)  +/-  (6.82e-245, 6.82e-245j)
| (-0.23614908641254875601 + 9.4941323111286882553e-972j)  +/-  (3.77e-254, 3.77e-254j)
| (-4.8605053674291990591 - 1.0464020693185193622e-961j)  +/-  (7.22e-245, 7.22e-245j)
| (-6.5931035411654629904 + 4.6829770082709729056e-962j)  +/-  (2.49e-245, 2.49e-245j)
| (1.3837651307473168472 - 2.4615435238268717629e-969j)  +/-  (7.79e-250, 7.79e-250j)
| (-3.7177484559101721992 + 3.7227961636649823546e-963j)  +/-  (1.26e-245, 1.26e-245j)
| (-5.685071292554447938 - 8.7823733857675815064e-963j)  +/-  (6.97e-245, 6.97e-245j)
| (-5.2647866137825735769 - 1.1077478586510320866e-965j)  +/-  (8.67e-245, 8.67e-245j)
| (1.9848268679847799252 + 4.2980436147737351277e-967j)  +/-  (2.55e-248, 2.55e-248j)
| (2.6519613568352334924 - 4.1402160101211958254e-965j)  +/-  (4.68e-247, 4.68e-247j)
| (-1.673551628767471445 + 3.5026932479764371188e-972j)  +/-  (4.77e-249, 4.77e-249j)
| (-2.9996317742003986026 - 1.1315735524597555559e-968j)  +/-  (1.69e-246, 1.69e-246j)
| (-0.81628788285896466304 + 1.5281019682607605896e-975j)  +/-  (1.06e-251, 1.06e-251j)
| (-1.1046640428051525945 - 5.8824750619692931325e-974j)  +/-  (1.18e-250, 1.18e-250j)
| (3.7177484559101721992 - 5.1317011073426082651e-969j)  +/-  (1.32e-245, 1.32e-245j)
| (8.3422858379649871416 - 1.5137180071477340474e-980j)  +/-  (1.28e-247, 1.28e-247j)
| (-2.312795126156855154 + 2.2642298984015069742e-980j)  +/-  (1.14e-247, 1.14e-247j)
| (-3.2745522684188834342e-994 + 1.9825086376139413338e-994j)  +/-  (1.72e-992, 1.72e-992j)
| (-1.9848268679847799252 - 2.472603434617398221e-981j)  +/-  (2.28e-248, 2.28e-248j)
| (1.673551628767471445 + 2.2486066272377199561e-983j)  +/-  (4.61e-249, 4.61e-249j)
| (0.23614908641254875601 + 3.118796692055721077e-988j)  +/-  (3.77e-254, 3.77e-254j)
| (-2.6519613568352334924 - 7.6222972880640101423e-980j)  +/-  (4.78e-247, 4.78e-247j)
| (-3.3548844578691204228 - 7.3555616415533388058e-980j)  +/-  (5.17e-246, 5.17e-246j)
| (-0.51957132999702948893 - 7.6973438143910894573e-987j)  +/-  (7.85e-253, 7.85e-253j)
| (4.4692396132714615431 - 5.0664312823885918701e-979j)  +/-  (4.84e-245, 4.84e-245j)
| (2.312795126156855154 - 1.3492817455795347728e-990j)  +/-  (1.24e-247, 1.24e-247j)
| (0.51957132999702948893 - 3.9861597439778483365e-997j)  +/-  (7.22e-253, 7.22e-253j)
| (3.3548844578691204228 + 2.453172539117183395e-996j)  +/-  (4.79e-246, 4.79e-246j)
-------------------------------------------------
The weights are:
| (1.2908284169552422717e-17 + 3.3033923887302705335e-880j)  +/-  (2.4e-84, 1.4e-205j)
| (2.6387581082563099504e-31 + 1.9196820061553678425e-889j)  +/-  (1.38e-90, 8.04e-212j)
| (1.0800630268335076923e-26 - 5.2764223463609032482e-887j)  +/-  (4.27e-89, 2.49e-210j)
| (3.6132488240271286216e-20 + 4.5039711192340978317e-882j)  +/-  (7.16e-87, 4.18e-208j)
| (3.9158587152402001205e-23 + 4.1826066561657937896e-885j)  +/-  (3.45e-88, 2.02e-209j)
| (2.1293037018447237992e-13 + 1.1857656409105943265e-878j)  +/-  (1.47e-83, 8.57e-205j)
| (1.1621621440811011102e-08 - 5.1368161341384017279e-877j)  +/-  (1.58e-80, 9.26e-202j)
| (2.4529111888444241283e-05 + 2.0794331686843198013e-874j)  +/-  (1.24e-75, 7.23e-197j)
| (1.0800630268335076923e-26 + 4.733095947673349409e-886j)  +/-  (6.44e-91, 3.76e-212j)
| (2.2286941233070799428e-15 - 1.87016225233577567e-879j)  +/-  (5.31e-85, 3.1e-206j)
| (3.9158587152402001205e-23 - 5.6862468748695543441e-884j)  +/-  (4.33e-89, 2.53e-210j)
| (1.1621621440811011102e-08 - 2.5760767988842643032e-876j)  +/-  (1.03e-81, 6.03e-203j)
| (0.023340379363890948352 - 2.8617053195119467968e-872j)  +/-  (2.56e-69, 1.5e-190j)
| (4.6008716716073751848e-10 + 7.4531890797721581145e-878j)  +/-  (1.85e-85, 1.08e-206j)
| (1.2908284169552422717e-17 + 4.068974261697878478e-882j)  +/-  (1.41e-90, 8.22e-212j)
| (0.046900016461179660195 + 8.0817712431705881316e-872j)  +/-  (1.75e-69, 1.02e-190j)
| (0.085386582028030155124 - 1.2429854874901481383e-871j)  +/-  (1.81e-69, 1.06e-190j)
| (1.2319974767068336586e-11 - 7.8624070170113016557e-878j)  +/-  (1.98e-85, 1.15e-206j)
| (0.1408200371075250033 - 2.6766479593693410363e-871j)  +/-  (6.32e-71, 3.69e-192j)
| (1.2319974767068336586e-11 - 9.054246876171007022e-879j)  +/-  (1.95e-87, 1.14e-208j)
| (3.6132488240271286216e-20 - 1.6553200959321592624e-883j)  +/-  (7.52e-92, 4.39e-213j)
| (0.023340379363890948352 - 4.5318941293205536235e-872j)  +/-  (2.09e-75, 1.22e-196j)
| (2.0569689012531468075e-07 + 3.0305683707886231518e-876j)  +/-  (1.56e-85, 9.1e-207j)
| (2.2286941233070799428e-15 - 6.9764385095119417885e-881j)  +/-  (3.57e-90, 2.09e-211j)
| (2.1293037018447237992e-13 + 8.9618230447794427995e-880j)  +/-  (3.63e-89, 2.12e-210j)
| (0.0035213529032379859983 - 7.4092448409634844661e-873j)  +/-  (8.8e-82, 5.14e-203j)
| (0.00017109327545178923313 - 7.4084333307769369215e-874j)  +/-  (2.2e-84, 1.28e-205j)
| (0.010306662866693177038 + 1.1513738500144643785e-872j)  +/-  (2.52e-81, 1.47e-202j)
| (2.4529111888444241283e-05 + 7.1234585483604857013e-875j)  +/-  (4.37e-86, 2.55e-207j)
| (0.085386582028030155124 - 9.5066571474640073244e-872j)  +/-  (5.49e-79, 3.21e-200j)
| (0.046900016461179660195 + 5.6122706344060875506e-872j)  +/-  (3.35e-79, 1.96e-200j)
| (2.0569689012531468075e-07 + 1.2388803484616902688e-875j)  +/-  (2.98e-88, 1.74e-209j)
| (2.6387581082563099504e-31 - 1.2529775213764307789e-888j)  +/-  (1.53e-100, 8.94e-222j)
| (0.00089621792235750495541 + 1.1012482533575926411e-873j)  +/-  (3.66e-85, 2.14e-206j)
| (0.12285802279960634144 + 3.4366439758226587036e-871j)  +/-  (2.38e-81, 1.39e-202j)
| (0.0035213529032379859983 - 3.7828109504373956848e-873j)  +/-  (2.79e-84, 1.63e-205j)
| (0.010306662866693177038 + 2.0169792549577719843e-872j)  +/-  (2.38e-84, 1.39e-205j)
| (0.1408200371075250033 - 2.8912967530592711056e-871j)  +/-  (6.08e-83, 3.55e-204j)
| (0.00017109327545178923313 - 2.9318483799128632549e-874j)  +/-  (3.24e-86, 1.89e-207j)
| (2.6207393098748566905e-06 - 1.5597792599753682554e-875j)  +/-  (9.96e-88, 5.82e-209j)
| (0.12720127902949840592 + 1.5845072234665389804e-871j)  +/-  (6.63e-83, 3.87e-204j)
| (4.6008716716073751848e-10 + 4.7672607309700228893e-877j)  +/-  (7.27e-92, 4.25e-213j)
| (0.00089621792235750495541 + 2.4372321645718945309e-873j)  +/-  (7.18e-88, 4.23e-209j)
| (0.12720127902949840592 + 1.87821105058055382e-871j)  +/-  (1.82e-85, 1.18e-206j)
| (2.6207393098748566905e-06 - 5.3369768531499429165e-875j)  +/-  (7.78e-90, 4.52e-211j)
