Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 10 25
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 25 Kronrod extension for:
P2 : 16*t^14 - 3816/7*t^12 + 44964/7*t^10 - 225630/7*t^8 + 68715*t^6 - 108945/2*t^4 + 46845/4*t^2 - 2835/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^39 - 136109209028890579673992462132015181838459816/31953937920019321059559451508016970375107*t^37 + 4965051083577738069834042818977672073552056428/9850462065569865890540883547584178837439*t^35 - 782413006078681058071613995629375849307736101028010/22271894730253466778512937701087828351449579*t^33 + 2110996793586087228755617176622671948871383453163530/1310111454720792163441937511828695785379387*t^31 - 1146680146210652341214831601006425155595172422441265015/22271894730253466778512937701087828351449579*t^29 + 40315338811584764627713297741156332502029746468485805535/34062897822740596249490375307546090419864062*t^27 - 23089142487749139959525072362667784933688929107481944622585/1158138525973180272482672760456567074275378108*t^25 + 71901376142372336460294322436459855757672003041678006436375/289534631493295068120668190114141768568844527*t^23 - 379279335148713331861072334369751503383769313011028717010875/165448360853311467497524680065223867753625444*t^21 + 252142725096811659953748557704696554198736304095072379299875/16141303497884045609514602933192572463768336*t^19 - 5418875854159221527862735745886421809057245553119631933755125/69662467727710091577905128448515312738368608*t^17 + 4562931799259913851518401809722105606816290166114706252857875/16391168877108256841860030223180073585498496*t^15 - 22895348242002229883931092048209013967403669796960057836250625/32782337754216513683720060446360147170996992*t^13 + 5980141704531580164605660232774835121819077591706900476355625/5043436577571771335956932376363099564768768*t^11 - 13065454211761395134187273335053026692772390500977921621539375/10086873155143542671913864752726199129537536*t^9 + 34085073498241368907951010743537937692511276969577753356900625/40347492620574170687655459010904796518150144*t^7 - 23488796508238121512286769755164174390988520706906161175989375/80694985241148341375310918021809593036300288*t^5 + 6699307328947459913648224063952737677502852871353954934990625/161389970482296682750621836043619186072600576*t^3 - 372829467881574034182337011699076919358056582095430286496875/322779940964593365501243672087238372145201152*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:
| (3.0185080459514659421 + 2.374127256336070826e-864j)  +/-  (1.03e-245, 1.03e-245j)
| (4.3559625069287016722 - 2.0267502896810591362e-876j)  +/-  (1.45e-246, 1.45e-246j)
| (7.1541811715255699808 - 1.4750876589244795355e-882j)  +/-  (7.53e-249, 7.53e-249j)
| (5.847745416250336068 - 4.9640314218347985757e-881j)  +/-  (2.52e-247, 2.52e-247j)
| (-4.8216840140562965618 + 3.7979207825484465534e-881j)  +/-  (1.01e-246, 1.01e-246j)
| (6.4413498868620107609 + 2.0590383006490240805e-883j)  +/-  (6.92e-248, 6.92e-248j)
| (-6.4413498868620107609 - 1.8477684639719713016e-882j)  +/-  (6.06e-248, 6.06e-248j)
| (-5.847745416250336068 + 4.8102884798875004142e-882j)  +/-  (2.57e-247, 2.57e-247j)
| (-2.3166778458612639611 - 1.1841537707401953861e-882j)  +/-  (6.81e-248, 6.81e-248j)
| (4.8216840140562965618 - 1.2787401734412221718e-879j)  +/-  (1.09e-246, 1.09e-246j)
| (-1.9724705929583410451 + 3.9034386605448033187e-884j)  +/-  (1.25e-248, 1.25e-248j)
| (-1.3323433031643804902 + 1.1330764147526000604e-886j)  +/-  (3.85e-250, 3.85e-250j)
| (-5.3152093761393522469 + 7.5168490880900731581e-883j)  +/-  (5.83e-247, 5.83e-247j)
| (-7.1541811715255699808 - 3.2882025248958446812e-885j)  +/-  (6.99e-249, 6.99e-249j)
| (-2.6906791930059200974 - 4.5431352867741902407e-882j)  +/-  (4.52e-247, 4.52e-247j)
| (2.3166778458612639611 + 2.2212606450032748722e-881j)  +/-  (6.22e-248, 6.22e-248j)
| (1.9724705929583410451 - 8.1368293208125151364e-884j)  +/-  (1.18e-248, 1.18e-248j)
| (5.3152093761393522469 + 3.2695248971366626068e-883j)  +/-  (6.01e-247, 6.01e-247j)
| (-1.6506801238857845559 + 1.8915609270435083406e-890j)  +/-  (2.24e-249, 2.24e-249j)
| (3.911506869286660161 - 5.2528803185369962724e-886j)  +/-  (1.5e-246, 1.5e-246j)
| (0.80702741666489763021 + 7.2713112127733764535e-901j)  +/-  (1.11e-251, 1.11e-251j)
| (-1.0363502036603261655 - 4.0744070090389479439e-904j)  +/-  (6.62e-251, 6.62e-251j)
| (3.4839550558153729453 + 2.1228561531875666341e-902j)  +/-  (1.47e-246, 1.47e-246j)
| (-4.3559625069287016722 + 5.5938758202019000322e-913j)  +/-  (1.5e-246, 1.5e-246j)
| (-3.0486879132310133212 + 4.0613970016441800771e-911j)  +/-  (1.08e-245, 1.08e-245j)
| (-3.4839550558153729453 + 1.1006192855584205622e-917j)  +/-  (1.44e-246, 1.44e-246j)
| (1.6506801238857845559 - 4.0366400094412276028e-918j)  +/-  (2.34e-249, 2.34e-249j)
| (1.0363502036603261655 - 4.0778216943061667521e-926j)  +/-  (6.84e-251, 6.84e-251j)
| (-3.911506869286660161 - 2.4745394494679309721e-927j)  +/-  (1.39e-246, 1.39e-246j)
| (-0.52464762327529031788 + 1.8468825314216075145e-933j)  +/-  (7.39e-253, 7.39e-253j)
| (0.18980675578014987883 - 9.0069634790575433309e-933j)  +/-  (3.06e-254, 3.06e-254j)
| (3.0486879132310133212 - 1.8279382567570976852e-950j)  +/-  (1.02e-245, 1.02e-245j)
| (1.3323433031643804902 - 7.0724954361781632245e-972j)  +/-  (3.64e-250, 3.64e-250j)
| (-0.18980675578014987883 + 1.5579747141905230564e-975j)  +/-  (3.45e-254, 3.45e-254j)
| (-3.0185080459514659421 + 7.189595743086741263e-971j)  +/-  (1.03e-245, 1.03e-245j)
| (-0.80702741666489763021 + 4.3406844669735190107e-984j)  +/-  (1.06e-251, 1.06e-251j)
| (3.0815415459130847764e-984 + 2.3664128135026572619e-983j)  +/-  (9.31e-982, 9.31e-982j)
| (0.52464762327529031788 - 5.909570033292316439e-983j)  +/-  (7.04e-253, 7.04e-253j)
| (2.6906791930059200974 - 1.0428605160752979304e-994j)  +/-  (4.59e-247, 4.59e-247j)
-------------------------------------------------
The weights are:
| (-2.5855086571300987087e-05 - 1.6446299502112542241e-867j)  +/-  (2e-80, 6.07e-202j)
| (1.4731079143028757384e-09 - 7.8498139766406397962e-874j)  +/-  (1.12e-86, 3.41e-208j)
| (2.7389136088818206683e-23 + 6.1305013592038845271e-883j)  +/-  (1.65e-95, 5.02e-217j)
| (4.4338524657948327458e-16 + 1.709302914375953208e-878j)  +/-  (2.98e-92, 9.06e-214j)
| (2.1593756445207352674e-11 - 6.614116074406912511e-876j)  +/-  (3.64e-92, 1.1e-213j)
| (3.4399628981357199914e-19 - 1.849703846831855322e-880j)  +/-  (6.06e-94, 1.84e-215j)
| (3.4399628981357199914e-19 + 6.6927471481936960894e-881j)  +/-  (3.82e-97, 1.16e-218j)
| (4.4338524657948327458e-16 - 5.4544162346765740942e-879j)  +/-  (1.27e-95, 3.86e-217j)
| (0.00094610834465046493107 + 1.5071079208157387719e-869j)  +/-  (4.24e-84, 1.29e-205j)
| (2.1593756445207352674e-11 + 2.8758114154261754948e-875j)  +/-  (4.39e-92, 1.33e-213j)
| (0.0038042664485364612323 - 5.3366137803475402557e-869j)  +/-  (2.71e-82, 8.24e-204j)
| (0.030261499946285487052 - 5.4314614752023956353e-868j)  +/-  (2.16e-78, 6.57e-200j)
| (1.5489649528702826154e-13 + 2.3359486811837502085e-877j)  +/-  (1.35e-94, 4.1e-216j)
| (2.7389136088818206683e-23 - 2.4923350330956307847e-883j)  +/-  (7.38e-100, 2.24e-221j)
| (0.00015779837105192167709 - 5.1586592540581630643e-870j)  +/-  (5.63e-87, 1.71e-208j)
| (0.00094610834465046493107 + 1.145676107344983068e-868j)  +/-  (8.5e-87, 2.58e-208j)
| (0.0038042664485364612323 - 2.5462688076403746204e-868j)  +/-  (1.54e-85, 4.68e-207j)
| (1.5489649528702826154e-13 - 8.476128770293062777e-877j)  +/-  (2.68e-95, 8.14e-217j)
| (0.01175828837929458259 + 1.7268666183752362285e-868j)  +/-  (1.84e-84, 5.57e-206j)
| (5.5668236669358118159e-08 + 2.0419315484945265272e-872j)  +/-  (2.96e-92, 8.98e-214j)
| (0.068633260631689634103 - 5.0848035901729127204e-867j)  +/-  (3.07e-84, 9.32e-206j)
| (0.050076328016055492339 + 1.6498141398378806069e-867j)  +/-  (1.72e-84, 5.21e-206j)
| (1.2701991700596579725e-06 - 7.0614745458559859297e-871j)  +/-  (2.51e-91, 7.63e-213j)
| (1.4731079143028757384e-09 + 1.4236640645452386095e-874j)  +/-  (2.62e-95, 7.96e-217j)
| (4.1549403570042083144e-05 - 8.4370755281165278197e-870j)  +/-  (5.74e-92, 1.74e-213j)
| (1.2701991700596579725e-06 + 5.0546110930155512323e-872j)  +/-  (6.65e-94, 2.01e-215j)
| (0.01175828837929458259 + 5.8947949923565762951e-868j)  +/-  (5.27e-90, 1.59e-211j)
| (0.050076328016055492339 + 3.3749897876509639909e-867j)  +/-  (1.56e-88, 4.7e-210j)
| (5.5668236669358118159e-08 - 2.6312244525504456781e-873j)  +/-  (3.14e-95, 9.5e-217j)
| (0.13836014239146626467 + 4.0771407628603816245e-867j)  +/-  (1.45e-88, 4.41e-210j)
| (0.18007262532971739669 - 1.0880995448474840388e-866j)  +/-  (8.93e-89, 2.71e-210j)
| (4.1549403570042083144e-05 + 1.6961436601834885633e-867j)  +/-  (1.16e-92, 3.46e-214j)
| (0.030261499946285487052 - 1.4014930384548519516e-867j)  +/-  (5.76e-90, 1.77e-211j)
| (0.18007262532971739669 - 9.5935367211593529853e-867j)  +/-  (2.4e-89, 7.43e-211j)
| (-2.5855086571300987087e-05 + 1.0167815491882940479e-869j)  +/-  (3.71e-92, 1.14e-213j)
| (0.068633260631689634103 - 2.9394433153959863748e-867j)  +/-  (7.59e-90, 2.35e-211j)
| (0.031825320923979627256 + 1.5007449766653955865e-866j)  +/-  (1.94e-89, 6e-211j)
| (0.13836014239146626467 + 5.792603417900652138e-867j)  +/-  (2.72e-90, 8.34e-212j)
| (0.00015779837105192167709 - 8.9838802529803659938e-869j)  +/-  (2.65e-93, 7.47e-215j)
