Starting with polynomial:
P : 2*t
Extension levels are: 1 2 42
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P2 : 2*t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^45 - 762527411580585593007/800788896593667320*t^43 + 330621627713348403455121/1601577793187334640*t^41 - 8663631528680372585580561/320315558637466928*t^39 + 1535772869449538402062592667/640631117274933856*t^37 - 390704370723420465296997339291/2562524469099735424*t^35 + 36917652528360486778214899215909/5125048938199470848*t^33 - 330852861051256758479359872977199/1281262234549867712*t^31 + 18229453024076752829950312788309255/2562524469099735424*t^29 - 3108711955918656830557715636305084515/20500195752797883392*t^27 + 102773515632197187781378336592581435485/41000391505595766784*t^25 - 1314971476522493465593375286602560061275/41000391505595766784*t^23 + 25900578182441782978707719481374119881825/82000783011191533568*t^21 - 777877942203416774175780477037583950626375/328003132044766134272*t^19 + 8781680252601220464036986745916532717429625/656006264089532268544*t^17 - 18274177354789032174786779469600124085958375/328003132044766134272*t^15 + 6826317751510180805720393918312075278527375/41000391505595766784*t^13 - 3616185682017306092521939048990765354684416375/10496100225432516296704*t^11 + 9849018371448012774440664422186942602336295625/20992200450865032593408*t^9 - 8193392045325085515324066921275675746129670625/20992200450865032593408*t^7 + 7408941862531761611815879609450855109811466875/41984400901730065186816*t^5 - 5918878169021127078610941858630714939225504375/167937603606920260747264*t^3 + 652039258754883799125597180996577436696375625/335875207213840521494528*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:
| (6.3567000175395402988 - 2.151753283620546131e-897j)  +/-  (1.1e-244, 1.1e-244j)
| (7.3216709630548678933 + 5.5939662915193225195e-899j)  +/-  (1.6e-245, 1.6e-245j)
| (-6.8203877018484527808 + 3.660692955632961933e-896j)  +/-  (5.46e-245, 5.46e-245j)
| (6.8203877018484527808 - 9.2031320938675580661e-905j)  +/-  (5.27e-245, 5.27e-245j)
| (8.556223432219793567 + 2.255041517340683963e-908j)  +/-  (2.46e-247, 2.46e-247j)
| (-4.3357726344104760839 - 3.9881139674264782912e-904j)  +/-  (7.89e-245, 7.89e-245j)
| (-5.5028190219043495295 + 9.0422988071456519918e-913j)  +/-  (1.75e-244, 1.75e-244j)
| (-7.881750676746849348 + 4.6554299244311637976e-917j)  +/-  (3.11e-246, 3.11e-246j)
| (-7.3216709630548678933 - 4.7614527920732879491e-919j)  +/-  (1.79e-245, 1.79e-245j)
| (-3.9668981654738913964 - 5.9967650248193936993e-921j)  +/-  (3.82e-245, 3.82e-245j)
| (3.9668981654738913964 - 7.6454558928849648182e-925j)  +/-  (4.04e-245, 4.04e-245j)
| (7.881750676746849348 + 1.1728096080038751519e-926j)  +/-  (3.62e-246, 3.62e-246j)
| (4.7134934869085120232 + 5.9620716186756778688e-924j)  +/-  (1.33e-244, 1.33e-244j)
| (-2.9013858569909428867 - 1.414055854994138379e-927j)  +/-  (1.42e-246, 1.42e-246j)
| (-3.6055403893682161052 + 5.2165388652251064476e-926j)  +/-  (1.53e-245, 1.53e-245j)
| (1.550902522865103926 - 1.8209921279671106901e-934j)  +/-  (1.26e-249, 1.26e-249j)
| (3.6055403893682161052 + 1.1383617444633899665e-928j)  +/-  (1.63e-245, 1.63e-245j)
| (2.9013858569909428867 + 6.5672568625288147678e-932j)  +/-  (1.48e-246, 1.48e-246j)
| (-1.2247448713915890491 + 1.5689320528539474225e-935j)  +/-  (1.36e-250, 1.36e-250j)
| (-8.556223432219793567 - 4.1173680944693705337e-929j)  +/-  (2.41e-247, 2.41e-247j)
| (5.9196926158205636575 + 4.0636026286264735485e-935j)  +/-  (1.56e-244, 1.56e-244j)
| (0.90474145945777276151 + 2.4331668557384341056e-948j)  +/-  (1.22e-251, 1.22e-251j)
| (-4.7134934869085120232 - 4.1629225840786901203e-950j)  +/-  (1.32e-244, 1.32e-244j)
| (2.557115748374794161 + 1.3537592940641050695e-969j)  +/-  (3.11e-247, 3.11e-247j)
| (-0.59309345231253182974 + 6.8460695086176623923e-973j)  +/-  (1.15e-252, 1.15e-252j)
| (-5.1017640005200679021 + 8.0470154242381257435e-968j)  +/-  (1.88e-244, 1.88e-244j)
| (1.2247448713915890491 + 9.0734491449710141437e-981j)  +/-  (1.43e-250, 1.43e-250j)
| (-2.2173842748007174651 - 1.571660824985222807e-978j)  +/-  (6.04e-248, 6.04e-248j)
| (1.1844309050060060817e-990 + 6.0297245240296929246e-991j)  +/-  (5.98e-989, 5.98e-989j)
| (1.8819579510567160979 - 4.2069950778120582199e-978j)  +/-  (9.43e-249, 9.43e-249j)
| (-0.29207016845871853896 - 2.6517856355770093145e-983j)  +/-  (8.01e-254, 8.01e-254j)
| (0.29207016845871853896 + 2.807400745976447637e-984j)  +/-  (8.01e-254, 8.01e-254j)
| (5.1017640005200679021 + 8.3630405363160688439e-973j)  +/-  (1.84e-244, 1.84e-244j)
| (3.2506470317953445149 + 8.9348189677090618054e-982j)  +/-  (5.14e-246, 5.14e-246j)
| (-1.8819579510567160979 - 5.1733170756995795408e-985j)  +/-  (9.2e-249, 9.2e-249j)
| (-0.90474145945777276151 + 2.3084720579780622955e-988j)  +/-  (1.13e-251, 1.13e-251j)
| (5.5028190219043495295 + 2.7033685765223666613e-980j)  +/-  (1.79e-244, 1.79e-244j)
| (-2.557115748374794161 + 6.8529111062563478011e-986j)  +/-  (3.18e-247, 3.18e-247j)
| (0.59309345231253182974 - 1.0013937255961660944e-992j)  +/-  (1.14e-252, 1.14e-252j)
| (-3.2506470317953445149 + 1.3407261161836438003e-983j)  +/-  (5.44e-246, 5.44e-246j)
| (-1.550902522865103926 + 3.328755081326432912e-994j)  +/-  (1.28e-249, 1.28e-249j)
| (-5.9196926158205636575 - 7.2508377459730771661e-993j)  +/-  (1.53e-244, 1.53e-244j)
| (2.2173842748007174651 - 1.0273864938915950742e-1015j)  +/-  (5.94e-248, 5.94e-248j)
| (-6.3567000175395402988 + 1.1486299668497650326e-1017j)  +/-  (1.11e-244, 1.11e-244j)
| (4.3357726344104760839 - 2.2205223395123340596e-1025j)  +/-  (8.52e-245, 8.52e-245j)
-------------------------------------------------
The weights are:
| (7.1590329599101369508e-19 + 9.9278560052946549856e-915j)  +/-  (5.08e-87, 3.15e-208j)
| (1.5524151650503832455e-24 - 2.168244209708366358e-918j)  +/-  (4.31e-90, 2.67e-211j)
| (1.69980244122030279e-21 + 4.2825101933704054454e-916j)  +/-  (4.04e-91, 2.5e-212j)
| (1.69980244122030279e-21 + 1.5555029273952564087e-916j)  +/-  (1.15e-88, 7.13e-210j)
| (7.0496588321346598955e-33 - 5.833093794323937475e-923j)  +/-  (7.36e-94, 4.56e-215j)
| (1.4418555397992200922e-09 + 2.3927975557836154862e-911j)  +/-  (4.45e-84, 2.76e-205j)
| (1.6278091606361898758e-14 - 1.5927259781272803925e-913j)  +/-  (3.42e-88, 2.12e-209j)
| (3.5639359957775766053e-28 - 2.5173815966527095202e-920j)  +/-  (3.8e-95, 2.35e-216j)
| (1.5524151650503832455e-24 + 3.6378499748992400896e-918j)  +/-  (2.08e-93, 1.29e-214j)
| (3.0160795556688670445e-08 - 9.97193179743989486e-911j)  +/-  (4.04e-84, 2.5e-205j)
| (3.0160795556688670445e-08 + 1.6871120418129356049e-910j)  +/-  (5.06e-86, 3.14e-207j)
| (3.5639359957775766053e-28 + 1.9887158503344916191e-920j)  +/-  (2.21e-95, 1.37e-216j)
| (4.8475757898551032512e-11 + 9.0434376460953888921e-912j)  +/-  (1.82e-88, 1.13e-209j)
| (4.3195471605151203201e-05 + 2.9285337860324637231e-909j)  +/-  (1.75e-82, 1.09e-203j)
| (4.5653852144989224857e-07 + 3.5933441699269003979e-910j)  +/-  (1.51e-84, 9.34e-206j)
| (0.016736925057110421657 - 8.9603985080572412755e-908j)  +/-  (2.8e-76, 1.73e-197j)
| (4.5653852144989224857e-07 - 5.9597366611989787278e-910j)  +/-  (6.1e-86, 3.78e-207j)
| (4.3195471605151203201e-05 - 5.073500548490888198e-909j)  +/-  (5.6e-84, 3.47e-205j)
| (0.040707909449555950833 - 4.0742209095355428321e-908j)  +/-  (1.54e-75, 9.53e-197j)
| (7.0496588321346598955e-33 + 6.5811983096377486641e-923j)  +/-  (3.94e-100, 2.44e-221j)
| (1.4522368609504203839e-16 - 5.2222818959298482937e-914j)  +/-  (1.34e-92, 8.33e-214j)
| (0.07870134468680223335 - 1.9115977985955616921e-907j)  +/-  (3.27e-77, 2.02e-198j)
| (4.8475757898551032512e-11 - 5.8898537678511354031e-912j)  +/-  (7.06e-90, 4.37e-211j)
| (0.00027899403592489461415 + 1.2339620882064966536e-908j)  +/-  (1.28e-84, 7.93e-206j)
| (0.12167637440839641486 + 1.1361536367149810659e-908j)  +/-  (1.49e-78, 9.25e-200j)
| (1.1050079023313890567e-12 + 1.0384914931336411803e-912j)  +/-  (4.07e-91, 2.53e-212j)
| (0.040707909449555950833 + 1.3884454234499127672e-907j)  +/-  (1.35e-79, 8.34e-201j)
| (0.0013945736559458281146 + 1.3671469901110400569e-908j)  +/-  (1.45e-84, 9e-206j)
| (0.16370301375788249464 + 1.7339725232033990599e-907j)  +/-  (9.29e-79, 5.76e-200j)
| (0.0054458926723527906258 + 5.1725774118230987042e-908j)  +/-  (1.02e-82, 6.3e-204j)
| (0.15315768044041834177 - 8.6871312035153345981e-908j)  +/-  (6.47e-79, 4.01e-200j)
| (0.15315768044041834177 - 2.2791321126312593801e-907j)  +/-  (2.88e-79, 1.79e-200j)
| (1.1050079023313890567e-12 - 1.7169728641569715029e-912j)  +/-  (6.6e-92, 4.09e-213j)
| (5.115052176989434617e-06 + 1.8504031176890388879e-909j)  +/-  (3.1e-87, 1.92e-208j)
| (0.0054458926723527906258 - 2.3786395998223779388e-908j)  +/-  (1.49e-85, 9.26e-207j)
| (0.07870134468680223335 + 2.9814500696388782508e-908j)  +/-  (3.13e-82, 1.94e-203j)
| (1.6278091606361898758e-14 + 2.9433484082864931804e-913j)  +/-  (6.8e-93, 4.21e-214j)
| (0.00027899403592489461415 - 6.7829709173458755936e-909j)  +/-  (1.69e-87, 1.05e-208j)
| (0.12167637440839641486 + 2.2907446532017321994e-907j)  +/-  (5.25e-83, 3.25e-204j)
| (5.115052176989434617e-06 - 1.1015124883002441171e-909j)  +/-  (4.39e-89, 2.72e-210j)
| (0.016736925057110421657 + 3.4938126802640145475e-908j)  +/-  (4.55e-86, 2.82e-207j)
| (1.4522368609504203839e-16 + 2.1385728746354052923e-914j)  +/-  (2.12e-96, 1.31e-217j)
| (0.0013945736559458281146 - 2.6728417693632727891e-908j)  +/-  (5.82e-89, 3.49e-210j)
| (7.1590329599101369508e-19 - 2.8352747821536043313e-915j)  +/-  (1.07e-97, 6.63e-219j)
| (1.4418555397992200922e-09 - 4.1798295198597223464e-911j)  +/-  (7.82e-93, 4.66e-214j)
