Starting with polynomial:
P : 8*t^3 - 12*t
Extension levels are: 3 10 26
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : 8*t^3 - 12*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : 8*t^13 - 629/2*t^11 + 17435/4*t^9 - 105435/4*t^7 + 557865/8*t^5 - 2248785/32*t^3 + 1133055/64*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^39 - 62344019653739501860494948964782623868150229/26776941392753723927870559341744020366902*t^37 + 1233581744529904314609470513581742737711841497885/4070095091698566037036325019945091095769104*t^35 - 190450052906489912692065749584619996195644106830795/8140190183397132074072650039890182191538208*t^33 + 41419600209009034562007305677067523168083740727107195/34595808279437811314808762669533274314037384*t^31 - 175066301769333140233457169580343514664197399121933145/4070095091698566037036325019945091095769104*t^29 + 32656934164920136616048366645889400400865811375206961495/29133312235316051633523168563817494159189376*t^27 - 7967956141139620793661276449581133932940071002880897514625/369021954980669987357960135141688259349732096*t^25 + 114538386211271892544993287568588998740273341104219398430375/369021954980669987357960135141688259349732096*t^23 - 2464033845779568995421369434389334031520340661118437410515875/738043909961339974715920270283376518699464192*t^21 + 1040382453979074178554596810680070099133177055887319055650125/38844416313754735511364224751756658878919168*t^19 - 725689826603055442029691917171482693431296825322208578362375/4569931331029968883689908794324312809284608*t^17 + 3131054153930636782252718342535849163501155239635446349149375/4569931331029968883689908794324312809284608*t^15 - 19212891260161469094091188875725761643023079648839047881258125/9139862662059937767379817588648625618569216*t^13 + 648813938120183219863668890785526731072718353449065117001294375/146237802592959004278077081418378009897107456*t^11 - 1796402629495949352845955540848191923720541892375483071865570625/292475605185918008556154162836756019794214912*t^9 + 1519959679967665559326370237295005468949299028008415630493385625/292475605185918008556154162836756019794214912*t^7 - 702987496567067711634926914145594171816637244913003162088965625/292475605185918008556154162836756019794214912*t^5 + 2331205017591749907313626444424796214669956704613057825904496875/4679609682974688136898466605388096316707438592*t^3 - 274956935804831972811860612795367023122114018353806821174378125/9359219365949376273796933210776192633414877184*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:
| (4.1180864274630133413 - 3.4497662566015261778e-866j)  +/-  (6.02e-246, 6.02e-246j)
| (6.0169129191307612719 + 3.997197167287499997e-874j)  +/-  (5.51e-247, 5.51e-247j)
| (-5.0060083003928503665 + 1.3607391425235137552e-878j)  +/-  (3.12e-246, 3.12e-246j)
| (6.6035767600235451685 + 3.7622473710787502296e-879j)  +/-  (1.3e-247, 1.3e-247j)
| (7.3091823342031220125 - 3.2654286067098244981e-882j)  +/-  (1.34e-248, 1.34e-248j)
| (-7.3091823342031220125 + 1.4381258218795246215e-888j)  +/-  (1.28e-248, 1.28e-248j)
| (4.5496485258910190077 - 5.7236784200865291272e-884j)  +/-  (4.85e-246, 4.85e-246j)
| (-6.0169129191307612719 + 3.9043545827182701018e-888j)  +/-  (5.97e-247, 5.97e-247j)
| (-6.6035767600235451685 - 2.4222877511650456391e-888j)  +/-  (1.33e-247, 1.33e-247j)
| (1.5418704662959449562 + 2.2964548183574134916e-891j)  +/-  (8.87e-250, 8.87e-250j)
| (1.2247448713915890491 + 1.0063079847263681217e-891j)  +/-  (1.23e-250, 1.23e-250j)
| (-4.1180864274630133413 + 1.8032426039315589165e-886j)  +/-  (5.45e-246, 5.45e-246j)
| (-2.8913250801809129717 - 2.5586462932405017958e-889j)  +/-  (6.25e-247, 6.25e-247j)
| (5.0060083003928503665 - 1.9437577231773597588e-895j)  +/-  (3.06e-246, 3.06e-246j)
| (3.7214884612847426714 + 4.4523298715185984932e-904j)  +/-  (9.06e-246, 9.06e-246j)
| (5.4915977749095938054 + 4.3796513302743162495e-910j)  +/-  (1.6e-246, 1.6e-246j)
| (-2.5296025834934300893 - 4.9331398246634701682e-910j)  +/-  (1.51e-247, 1.51e-247j)
| (-1.2247448713915890491 + 5.1269652406270001915e-917j)  +/-  (1.11e-250, 1.11e-250j)
| (-0.91243895624192680585 + 5.1451905729618235948e-918j)  +/-  (1.25e-251, 1.25e-251j)
| (-2.186308246417625265 + 4.8511823311772222829e-913j)  +/-  (3.36e-248, 3.36e-248j)
| (-5.4915977749095938054 - 1.2062072452253715881e-913j)  +/-  (1.51e-246, 1.51e-246j)
| (2.186308246417625265 + 2.4784198097212078852e-914j)  +/-  (3.31e-248, 3.31e-248j)
| (3.5038956294253926917 + 3.6491150719851838174e-917j)  +/-  (8.69e-246, 8.69e-246j)
| (-3.5038956294253926917 + 2.9668960798574642487e-926j)  +/-  (8.28e-246, 8.28e-246j)
| (-0.30581534164478753897 - 5.8083396993959631376e-943j)  +/-  (7.25e-254, 7.25e-254j)
| (-4.5496485258910190077 + 3.4312250306237028333e-935j)  +/-  (4.77e-246, 4.77e-246j)
| (1.8602834494799461889 + 9.4864194284539100648e-942j)  +/-  (7.17e-249, 7.17e-249j)
| (-3.7214884612847426714 + 9.1924120745530022216e-939j)  +/-  (9.07e-246, 9.07e-246j)
| (-3.2595330824338197843 - 2.1697157921527961279e-944j)  +/-  (3.69e-246, 3.69e-246j)
| (-0.60808265691331281929 - 2.3230676679788983698e-950j)  +/-  (1.17e-252, 1.17e-252j)
| (-1.5418704662959449562 - 6.9344780529287210674e-948j)  +/-  (9.22e-250, 9.22e-250j)
| (2.5296025834934300893 + 5.6528738142935761386e-944j)  +/-  (1.39e-247, 1.39e-247j)
| (0.91243895624192680585 - 1.5553983276095681889e-958j)  +/-  (1.34e-251, 1.34e-251j)
| (2.8913250801809129717 - 3.4151142003615752239e-961j)  +/-  (6.46e-247, 6.46e-247j)
| (-1.8602834494799461889 - 1.1500999573440697869e-977j)  +/-  (6.24e-249, 6.24e-249j)
| (0.30581534164478753897 + 1.8372393670631784276e-985j)  +/-  (7.25e-254, 7.25e-254j)
| (-5.2512315533042508669e-986 - 2.7314245462160225855e-986j)  +/-  (2.31e-984, 2.31e-984j)
| (0.60808265691331281929 + 5.1080560627183637243e-986j)  +/-  (1.17e-252, 1.17e-252j)
| (3.2595330824338197843 + 2.4788398931711728039e-994j)  +/-  (3.43e-246, 3.43e-246j)
-------------------------------------------------
The weights are:
| (1.0193716827880236299e-08 + 2.421186175451120427e-873j)  +/-  (7.44e-83, 9.32e-205j)
| (5.8831429424407611893e-17 - 5.6468273846769844817e-880j)  +/-  (2.33e-89, 2.92e-211j)
| (3.4660998644675557483e-12 + 1.1474658390690524033e-877j)  +/-  (2.51e-88, 3.15e-210j)
| (4.0994110572300105079e-20 + 5.9251701783217722564e-882j)  +/-  (3.55e-91, 4.45e-213j)
| (2.8829694358882658258e-24 - 1.9428349460187820215e-884j)  +/-  (3.18e-93, 3.99e-215j)
| (2.8829694358882658258e-24 + 5.4254194709480888562e-885j)  +/-  (1.13e-95, 1.42e-217j)
| (2.5641585872180455458e-10 + 4.7299328396511239229e-875j)  +/-  (8.05e-87, 1.01e-208j)
| (5.8831429424407611893e-17 + 1.0579522565121987754e-880j)  +/-  (7.79e-93, 9.76e-215j)
| (4.0994110572300105079e-20 - 1.3735698408501122473e-882j)  +/-  (3.54e-94, 4.44e-216j)
| (0.016631643221151782379 + 2.3335685764192429692e-870j)  +/-  (2.91e-76, 3.65e-198j)
| (0.039749694585546572318 - 3.8724750725764548494e-870j)  +/-  (8.64e-74, 1.08e-195j)
| (1.0193716827880236299e-08 + 4.2696943059576143592e-875j)  +/-  (9.19e-89, 1.15e-210j)
| (4.8721421566208093662e-05 + 1.8250146402448925634e-872j)  +/-  (4.46e-85, 5.59e-207j)
| (3.4660998644675557483e-12 - 1.1791112858231322175e-876j)  +/-  (3.63e-90, 4.55e-212j)
| (1.940978491598060731e-07 - 1.6595853402892886911e-872j)  +/-  (1.32e-87, 1.65e-209j)
| (2.2686464302295133322e-14 + 2.9961467037589756336e-878j)  +/-  (1.81e-91, 2.27e-213j)
| (0.00033141923472824957548 - 5.8407661201347501215e-872j)  +/-  (8.85e-86, 1.11e-207j)
| (0.039749694585546572318 - 2.0970890573890488481e-870j)  +/-  (2.06e-80, 2.58e-202j)
| (0.075612120173501171656 + 3.6808398021111220975e-870j)  +/-  (1.19e-79, 1.5e-201j)
| (0.0015802422327212488275 + 1.7907207041334472205e-871j)  +/-  (8.68e-85, 1.09e-206j)
| (2.2686464302295133322e-14 - 4.2823899404483929741e-879j)  +/-  (3.15e-94, 3.95e-216j)
| (0.0015802422327212488275 + 5.8440509269557084767e-871j)  +/-  (4.75e-86, 5.96e-208j)
| (3.2372870299540589205e-07 + 4.2510726084780643409e-872j)  +/-  (6.85e-89, 8.58e-211j)
| (3.2372870299540589205e-07 + 3.4255783579627762331e-873j)  +/-  (4.41e-90, 5.53e-212j)
| (0.1561557961819257768 + 7.2519247934629500592e-870j)  +/-  (9.46e-84, 1.19e-205j)
| (2.5641585872180455458e-10 - 2.3550094143861152225e-876j)  +/-  (7.69e-93, 9.63e-215j)
| (0.0056767835575515835062 - 1.2524691167305858571e-870j)  +/-  (6.02e-87, 7.55e-209j)
| (1.940978491598060731e-07 - 8.3957125225471634405e-874j)  +/-  (7.92e-91, 9.93e-213j)
| (4.8725200648561680686e-06 - 7.2128532475475806918e-873j)  +/-  (6.29e-90, 7.88e-212j)
| (0.11763123469753732583 - 5.5885888302090576478e-870j)  +/-  (8.07e-87, 1.01e-208j)
| (0.016631643221151782379 + 1.0621594344041137054e-870j)  +/-  (5.47e-88, 6.89e-210j)
| (0.00033141923472824957548 - 2.444318014316556762e-871j)  +/-  (6.14e-91, 7.85e-213j)
| (0.075612120173501171656 + 5.7762303010996409843e-870j)  +/-  (1.43e-88, 1.74e-210j)
| (4.8721421566208093662e-05 + 1.0427683142610749466e-871j)  +/-  (6.66e-92, 8.33e-214j)
| (0.0056767835575515835062 - 4.7300996087230515543e-871j)  +/-  (3.66e-89, 4.27e-211j)
| (0.1561557961819257768 + 8.415404414078825715e-870j)  +/-  (3.94e-89, 4.58e-211j)
| (0.17315388778706307568 - 8.2565214657973245965e-870j)  +/-  (5.26e-89, 6.29e-211j)
| (0.11763123469753732583 - 7.524953669928745252e-870j)  +/-  (1.98e-89, 2.18e-211j)
| (4.8725200648561680686e-06 - 6.1980641214408459821e-872j)  +/-  (7.15e-93, 1.07e-214j)
