Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 15 24
-------------------------------------------------
Trying to find an order 15 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P2 : 16*t^19 - 748536/667*t^17 + 226304664/7337*t^15 - 3155515020/7337*t^13 + 24226003620/7337*t^11 - 9496214910/667*t^9 + 1965071745/58*t^7 - 112008278655/2668*t^5 + 250467132825/10672*t^3 - 83438061525/21344*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^43 - 11450711464002921106122836876990392775929972984031283176404763790152761409043531921336/2166156199411436844482862922643225214273207607239388809008659576754806168958898563*t^41 + 131153084696916679457200626998570279279033351255164065795518198534458694220636850414085832/166794027354680637025180445043528341499036985757432938293666787410120075009835189351*t^39 - 11652912509576111009745007295142827976711815905574998635211313057035388660258681900524701612/166794027354680637025180445043528341499036985757432938293666787410120075009835189351*t^37 + 691932055625438372856373168390980063164984895747597051932212714449170119276341867032035248021/166794027354680637025180445043528341499036985757432938293666787410120075009835189351*t^35 - 8317628296930171270984692189004457351063592014243674920571558678699961281967779632825756829635/47655436387051610578622984298150954714010567359266553798190510688605735717095768386*t^33 + 507033919162836808151841042533665328069897432976918443025236426938267495307402416809081127005/94180704322236384542733170549705444098835113358234296043854764206730702998212981*t^31 - 538427529436110721809201944413054524528252897727453222727723031962314738188688231252314580689735/4332312398822873688965725845286450428546415214478777618017319153509612337917797126*t^29 + 37662755626860352468407505929525704815435116881161158764455063878014109193023377899197108842950365/17329249595291494755862903381145801714185660857915110472069276614038449351671188504*t^27 - 1003819409081457181266998518410457027052944129648204797552152057495434828909118088165590881474231665/34658499190582989511725806762291603428371321715830220944138553228076898703342377008*t^25 + 55464797447470690196391039780721808699105065385132608635531781359393521382247749383695841275641375/188361408644472769085466341099410888197670226716468592087709528413461405996425962*t^23 - 3430358168117857528127739072312869660156932035448059183200848042373667532498786542347836046865914625/1506891269155782152683730728795287105581361813731748736701676227307691247971407696*t^21 + 160110629786372521730576703153419573432921513928086484473739280544040736047651098927406544835865995625/12055130153246257221469845830362296844650894509853989893613409818461529983771261568*t^19 - 1392653283686175511076734388651762436909389663094253827612354813408745530731976073849728839061049625625/24110260306492514442939691660724593689301789019707979787226819636923059967542523136*t^17 + 4434196158984583741735256766895060623010324710725257584967256807714487004823402316205993223944692661875/24110260306492514442939691660724593689301789019707979787226819636923059967542523136*t^15 - 20155967072593728208687411478970970163461367604737049422139585825332373327157399418061299500359192204375/48220520612985028885879383321449187378603578039415959574453639273846119935085046272*t^13 + 252537746840512392526138933700580378685839741194736969220298405048598644507041831852651348034621163223125/385764164903880231087035066571593499028828624315327676595629114190768959480680370176*t^11 - 518747662727509553446889293841802271336917439433994539887540069143728887370592831302543697136735504880625/771528329807760462174070133143186998057657248630655353191258228381537918961360740352*t^9 + 325469971083886701603858744593877408739738234923911807729163200404629953150999048230085889604812562393125/771528329807760462174070133143186998057657248630655353191258228381537918961360740352*t^7 - 224579488440968862437042314533602499344052136160224074933020006891748864197915396202178807766808048136875/1543056659615520924348140266286373996115314497261310706382516456763075837922721480704*t^5 + 143900017280366473130504264901414128649710828185688406354676523458370093473575406159627920616298181759375/6172226638462083697392561065145495984461257989045242825530065827052303351690885922816*t^3 - 14826843405512240548442195574920115672724443279500976391303472235554124322313332372759857956701238559375/12344453276924167394785122130290991968922515978090485651060131654104606703381771845632*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:   43 out of 43
Indefinite weights: 0 out of 43
Negative weights:   0 out of 43
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-5.795207302042440696 + 2.1469753247856229858e-860j)  +/-  (4.79e-246, 4.79e-246j)
| (-6.8885008047412580463 + 1.9107497642417395558e-867j)  +/-  (3.08e-247, 3.08e-247j)
| (-7.5846655414759826868 - 1.1443778898422104656e-872j)  +/-  (2.85e-248, 2.85e-248j)
| (4.458312741734708521 - 6.2876055121711854202e-871j)  +/-  (1.52e-245, 1.52e-245j)
| (6.310959436223760163 + 4.8347118625234857994e-872j)  +/-  (1.52e-246, 1.52e-246j)
| (3.0788982813861061316 - 1.0732468233983971018e-871j)  +/-  (4.34e-246, 4.34e-246j)
| (-4.0676787766194897745 - 5.1768930873433856919e-874j)  +/-  (1.48e-245, 1.48e-245j)
| (-5.3201716886085721972 - 2.7315911998058176854e-882j)  +/-  (8.24e-246, 8.24e-246j)
| (5.795207302042440696 - 7.3720720973476920684e-886j)  +/-  (4e-246, 4e-246j)
| (7.5846655414759826868 - 4.3077424820864538519e-889j)  +/-  (3.14e-248, 3.14e-248j)
| (1.3498998593245308008 - 1.1675061489726932197e-889j)  +/-  (8.15e-250, 8.15e-250j)
| (5.3201716886085721972 - 2.0168765960507540599e-885j)  +/-  (8e-246, 8e-246j)
| (6.8885008047412580463 + 2.0953864658508229215e-888j)  +/-  (2.91e-247, 2.91e-247j)
| (-1.0392484373427345816 - 1.5964584077079273905e-890j)  +/-  (8.01e-251, 8.01e-251j)
| (-2.4638560979405949251 - 6.5088556114480765025e-887j)  +/-  (6.91e-247, 6.91e-247j)
| (-6.310959436223760163 + 2.9837003915735447939e-890j)  +/-  (1.45e-246, 1.45e-246j)
| (4.0676787766194897745 + 1.0440185424600928863e-888j)  +/-  (1.33e-245, 1.33e-245j)
| (4.8759532376325231043 - 2.5675922162786447274e-890j)  +/-  (1.15e-245, 1.15e-245j)
| (-1.6506801238857845559 + 2.4828481313324029632e-890j)  +/-  (7.6e-249, 7.6e-249j)
| (-2.1888080617024303415 + 1.4722025655279678873e-894j)  +/-  (2.23e-247, 2.23e-247j)
| (2.7676033562166682643 + 1.0496747944334998002e-895j)  +/-  (2.09e-246, 2.09e-246j)
| (1.6506801238857845559 + 2.3297017698039947526e-900j)  +/-  (7.31e-249, 7.31e-249j)
| (-3.7093772333783038526 + 5.0664933829162709113e-903j)  +/-  (1.26e-245, 1.26e-245j)
| (-4.8759532376325231043 + 2.291938473815224518e-912j)  +/-  (1.23e-245, 1.23e-245j)
| (-2.7676033562166682643 + 2.4932037149410197108e-921j)  +/-  (1.78e-246, 1.78e-246j)
| (-1.3498998593245308008 - 3.3512613394836667746e-929j)  +/-  (8.72e-250, 8.72e-250j)
| (1.9300740256285573626 + 4.9640096329812918537e-931j)  +/-  (4.56e-248, 4.56e-248j)
| (2.4638560979405949251 + 2.4275821286715243737e-929j)  +/-  (6.76e-247, 6.76e-247j)
| (-3.3862181400001748776 + 5.9565538583343344031e-936j)  +/-  (8.79e-246, 8.79e-246j)
| (-0.73964741258873689497 + 9.8415836422187363952e-949j)  +/-  (9.18e-252, 9.18e-252j)
| (2.1888080617024303415 + 6.0730396071420330436e-946j)  +/-  (1.93e-247, 1.93e-247j)
| (3.7093772333783038526 - 1.2185423681503479996e-943j)  +/-  (1.24e-245, 1.24e-245j)
| (0.52464762327529031788 - 3.2340635978341538702e-955j)  +/-  (1.45e-252, 1.45e-252j)
| (3.3862181400001748776 - 2.5556197260480321395e-952j)  +/-  (8.65e-246, 8.65e-246j)
| (-3.0436841924342085668e-957 - 3.0389687442837236401e-957j)  +/-  (1.85e-955, 1.85e-955j)
| (-3.0788982813861061316 - 3.5113159952085961707e-963j)  +/-  (4.21e-246, 4.21e-246j)
| (-4.458312741734708521 - 1.7604132877651481184e-982j)  +/-  (1.44e-245, 1.44e-245j)
| (0.73964741258873689497 + 2.546749487793232528e-994j)  +/-  (8.96e-252, 8.96e-252j)
| (1.0392484373427345816 - 7.1964289174891413912e-993j)  +/-  (8.1e-251, 8.1e-251j)
| (-0.30444731057671177329 - 3.1637058155783331819e-995j)  +/-  (1.19e-253, 1.19e-253j)
| (-0.52464762327529031788 + 4.2210874953735636822e-994j)  +/-  (1.32e-252, 1.32e-252j)
| (-1.9300740256285573626 + 7.4360773385561719293e-992j)  +/-  (4.79e-248, 4.79e-248j)
| (0.30444731057671177329 - 9.4353387169786993113e-999j)  +/-  (1.19e-253, 1.19e-253j)
-------------------------------------------------
The weights are:
| (7.225131976684944849e-16 + 1.1440981362994386258e-874j)  +/-  (1.46e-87, 7.31e-210j)
| (8.6473027846687455268e-22 - 3.3215468144307271462e-879j)  +/-  (6.22e-91, 3.11e-213j)
| (4.7043261512871328935e-26 + 6.5290471157062490252e-882j)  +/-  (7.03e-93, 3.51e-215j)
| (5.3235398179856483802e-10 - 1.6374712244369512983e-872j)  +/-  (5.82e-86, 2.91e-208j)
| (1.5415298659017301458e-18 - 2.7398955073146476361e-878j)  +/-  (2.53e-92, 1.27e-214j)
| (1.3306432140639873106e-05 - 9.3853580166647938358e-869j)  +/-  (1.76e-80, 8.77e-203j)
| (1.3817122942128870063e-08 + 1.2930689474599044477e-870j)  +/-  (6.76e-85, 3.37e-207j)
| (1.319536400489237753e-13 - 9.7769748858214278816e-874j)  +/-  (2.53e-88, 1.26e-210j)
| (7.225131976684944849e-16 + 1.33836286191785851e-876j)  +/-  (3.41e-91, 1.7e-213j)
| (4.7043261512871328935e-26 - 8.7321138526809587852e-883j)  +/-  (6.87e-97, 3.43e-219j)
| (0.028056574867324452603 - 5.7067146937235626761e-866j)  +/-  (1.05e-72, 5.23e-195j)
| (1.319536400489237753e-13 - 4.1783653327543959662e-875j)  +/-  (1.79e-90, 8.94e-213j)
| (8.6473027846687455268e-22 + 2.8630630679241433044e-880j)  +/-  (7.77e-95, 3.88e-217j)
| (0.059601437328317600529 + 1.7738727782175889639e-865j)  +/-  (2.65e-72, 1.32e-194j)
| (0.00038038749338131967538 - 4.76963110535534466e-867j)  +/-  (2.19e-83, 1.09e-205j)
| (1.5415298659017301458e-18 + 6.4313124448544588183e-877j)  +/-  (1.97e-94, 9.84e-217j)
| (1.3817122942128870063e-08 + 2.2648679121132945048e-871j)  +/-  (3.15e-88, 1.57e-210j)
| (1.1486439150779746199e-11 + 9.4052052980066361068e-874j)  +/-  (7.44e-90, 3.71e-212j)
| (0.010804270123665277568 + 5.3036091759862827154e-866j)  +/-  (1.49e-80, 7.43e-203j)
| (0.0012180490482103254577 + 1.4233695764348621326e-866j)  +/-  (2.08e-83, 1.04e-205j)
| (8.282343582093548421e-05 + 4.4425472986769044128e-868j)  +/-  (1.93e-85, 9.65e-208j)
| (0.010804270123665277568 + 2.9520929965368414918e-866j)  +/-  (3.89e-81, 1.94e-203j)
| (2.0282722145068402221e-07 - 1.086969750571383052e-869j)  +/-  (9.94e-90, 4.96e-212j)
| (1.1486439150779746199e-11 + 1.091803162318655957e-872j)  +/-  (9.07e-93, 4.53e-215j)
| (8.282343582093548421e-05 + 1.2564620125220338303e-867j)  +/-  (8.78e-87, 4.39e-209j)
| (0.028056574867324452603 - 9.1726137941129165293e-866j)  +/-  (1.09e-81, 5.45e-204j)
| (0.0036138448239454114995 - 1.5144339758637848038e-866j)  +/-  (1.6e-84, 7.99e-207j)
| (0.00038038749338131967538 - 1.9238641347095368351e-867j)  +/-  (1.44e-86, 7.21e-209j)
| (1.832365193531886366e-06 + 6.6441958295505378691e-869j)  +/-  (4.01e-90, 2e-212j)
| (0.089578587796453691233 - 4.165275821062797623e-865j)  +/-  (2.25e-83, 1.12e-205j)
| (0.0012180490482103254577 + 6.4293950126730285192e-867j)  +/-  (6.01e-86, 3e-208j)
| (2.0282722145068402221e-07 - 2.3854111506899942409e-870j)  +/-  (1.29e-90, 6.46e-213j)
| (0.073754463745153469765 + 5.4568484431282560628e-865j)  +/-  (5.78e-86, 2.88e-208j)
| (1.832365193531886366e-06 + 1.7432801053858051388e-869j)  +/-  (1e-89, 5e-212j)
| (0.17741280887892413482 + 4.5716015188278340451e-865j)  +/-  (4.13e-86, 2.06e-208j)
| (1.3306432140639873106e-05 - 3.0661704776215719101e-868j)  +/-  (2.26e-90, 1.13e-212j)
| (5.3235398179856483802e-10 - 1.2558840923529258184e-871j)  +/-  (4.81e-94, 2.4e-216j)
| (0.089578587796453691233 - 3.2223824711305846177e-865j)  +/-  (7.5e-87, 3.74e-209j)
| (0.059601437328317600529 + 1.2344020117295001218e-865j)  +/-  (3.1e-87, 1.55e-209j)
| (0.14418780091261378556 - 5.9095690599334577187e-865j)  +/-  (2.19e-87, 1.1e-209j)
| (0.073754463745153469765 + 6.5432312143455114656e-865j)  +/-  (2.04e-87, 1.02e-209j)
| (0.0036138448239454114995 - 3.026914689634306033e-866j)  +/-  (3.08e-89, 1.54e-211j)
| (0.14418780091261378556 - 5.3196496145423034058e-865j)  +/-  (1.54e-87, 7.53e-210j)
