Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 7 30
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : 16*t^11 - 328*t^9 + 2112*t^7 - 5040*t^5 + 4095*t^3 - 1575/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^41 - 301619649563088778451063682584623628227711427092/57830037255501682299341379350291112494566129*t^39 + 44061305853941326460364601899747100471036453899078/57830037255501682299341379350291112494566129*t^37 - 7647591851050245487772550298960785271800510345290055/115660074511003364598682758700582224989132258*t^35 + 881464923656760669869764509446166657228558145369620315/231320149022006729197365517401164449978264516*t^33 - 35727243596735122112718429580841754905696535158630580585/231320149022006729197365517401164449978264516*t^31 + 2104823836693513233598697785245541707616262719986696418785/462640298044013458394731034802328899956529032*t^29 - 91855992354996593084129608758600633298412187385203353773605/925280596088026916789462069604657799913058064*t^27 + 230754895997319292233267389472872505500961880845022941006825/142350860936619525659917241477639661525085856*t^25 - 5659754491512560780947804267276082902768415864275852087678875/284701721873239051319834482955279323050171712*t^23 + 104058237383178305630928517588328108284510911168176570052636375/569403443746478102639668965910558646100343424*t^21 - 355991337644633448265667356636768853667201452526198016383192375/284701721873239051319834482955279323050171712*t^19 + 3580517635529124833097150854801221901273855431437012254858932125/569403443746478102639668965910558646100343424*t^17 - 103901980781688889994547379957039133772327885722338548928788939375/4555227549971824821117351727284469168802747392*t^15 + 529494610732702750468692707285708007136491436693248552928420404375/9110455099943649642234703454568938337605494784*t^13 - 44573745360403046508031797859857973624496269664322603978573699375/444412443899690226450473339247265284761243648*t^11 + 4058812807181001805489168367567995808065253357541727152644427718125/36441820399774598568938813818275753350421979136*t^9 - 335714989384443816763483715637146745412192634737560103898186998125/4555227549971824821117351727284469168802747392*t^7 + 1850274792794892752720147218629515661490573153795278481984996509375/72883640799549197137877627636551506700843958272*t^5 - 1931897254351260203101924567934088034292611995922782025371552553125/583069126396393577103021021092412053606751666176*t^3 + 25578653615964767992711550028943631712038314741116762820425140625/1166138252792787154206042042184824107213503332352*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:
| (-5.3454150686706009778 - 4.1437207582038439244e-915j)  +/-  (4.28e-246, 4.28e-246j)
| (5.8289390914859695704 + 1.7618898675155637018e-920j)  +/-  (2.52e-246, 2.52e-246j)
| (-7.632926147887064725 - 1.0850823208768226539e-922j)  +/-  (1.86e-248, 1.86e-248j)
| (7.632926147887064725 + 4.2912791666397357679e-924j)  +/-  (1.86e-248, 1.86e-248j)
| (-6.9331899232707743961 - 4.1172929159805740473e-921j)  +/-  (2.18e-247, 2.18e-247j)
| (-6.3509513895489115742 - 6.509940180132920553e-920j)  +/-  (9.53e-247, 9.53e-247j)
| (6.3509513895489115742 + 1.0914339796287300029e-922j)  +/-  (8.75e-247, 8.75e-247j)
| (4.4545529053254709119 + 2.711342986978786812e-921j)  +/-  (5.46e-246, 5.46e-246j)
| (5.3454150686706009778 - 1.9738681503312732936e-921j)  +/-  (4.31e-246, 4.31e-246j)
| (-4.0378255176410156961 + 5.9044934365752259669e-920j)  +/-  (4.29e-246, 4.29e-246j)
| (2.019905816376567721 - 2.6772119985283981411e-928j)  +/-  (1.2e-248, 1.2e-248j)
| (3.2759416955673464603 - 2.1055495568774953202e-926j)  +/-  (2.52e-246, 2.52e-246j)
| (-1.6506801238857845559 + 3.4932479690129244563e-928j)  +/-  (1.63e-249, 1.63e-249j)
| (-4.8893639034570378423 - 5.8163990062086001927e-925j)  +/-  (5.56e-246, 5.56e-246j)
| (1.0362802085752798674 - 3.9824740524910320765e-934j)  +/-  (9.48e-251, 9.48e-251j)
| (2.7300048516244558441 - 4.3304615024975338736e-931j)  +/-  (4.72e-247, 4.72e-247j)
| (6.9331899232707743961 - 2.5530688011249013034e-931j)  +/-  (2.11e-247, 2.11e-247j)
| (-5.8289390914859695704 + 1.1206360842342457871e-928j)  +/-  (2.21e-246, 2.21e-246j)
| (-1.0362802085752798674 + 1.4289023397357924515e-936j)  +/-  (9.27e-251, 9.27e-251j)
| (-2.3862793919737297977 + 1.5472848308672718791e-933j)  +/-  (8.28e-248, 8.28e-248j)
| (-2.996577359655941383 - 4.272884663377392899e-951j)  +/-  (1.47e-246, 1.47e-246j)
| (1.2854478856052658339 - 5.1076292202999144278e-963j)  +/-  (3.21e-250, 3.21e-250j)
| (-4.4545529053254709119 - 4.4727283724863083504e-967j)  +/-  (5.18e-246, 5.18e-246j)
| (-1.2854478856052658339 + 1.5453440662672783325e-975j)  +/-  (2.91e-250, 2.91e-250j)
| (-2.7300048516244558441 - 1.6767122719369753199e-983j)  +/-  (4.98e-247, 4.98e-247j)
| (3.6400756006897818823 - 3.6096055319073307006e-995j)  +/-  (3.39e-246, 3.39e-246j)
| (0.083585766328673793598 + 5.4561573220657398487e-1003j)  +/-  (8.96e-255, 8.96e-255j)
| (1.6506801238857845559 - 1.2178200212181066941e-1005j)  +/-  (1.64e-249, 1.64e-249j)
| (-3.2759416955673464603 + 4.1587794125353394055e-1017j)  +/-  (2.43e-246, 2.43e-246j)
| (-0.88671360272745058574 + 1.1446937641648886527e-1035j)  +/-  (2.4e-251, 2.4e-251j)
| (-3.6400756006897818823 + 8.3975187686401286302e-1035j)  +/-  (3.31e-246, 3.31e-246j)
| (-0.083585766328673793598 + 9.3051711907486706751e-1048j)  +/-  (8.96e-255, 8.96e-255j)
| (0.88671360272745058574 + 5.9331044112736534584e-1045j)  +/-  (2.38e-251, 2.38e-251j)
| (4.0378255176410156961 + 3.777448346715361601e-1039j)  +/-  (4.84e-246, 4.84e-246j)
| (6.5549972219449646905e-1052 + 9.9249496979992435778e-1052j)  +/-  (4.88e-1050, 4.88e-1050j)
| (-2.019905816376567721 + 1.0967376255724304019e-1042j)  +/-  (1.24e-248, 1.24e-248j)
| (4.8893639034570378423 + 1.5354604392962270373e-1041j)  +/-  (5.71e-246, 5.71e-246j)
| (0.52464762327529031788 - 8.5800337381127237418e-1049j)  +/-  (4.58e-253, 4.58e-253j)
| (2.996577359655941383 + 3.6934566455443546189e-1042j)  +/-  (1.44e-246, 1.44e-246j)
| (2.3862793919737297977 + 1.7458696394713138812e-1048j)  +/-  (8.33e-248, 8.33e-248j)
| (-0.52464762327529031788 - 3.1489767501395746105e-1053j)  +/-  (4.47e-253, 4.47e-253j)
-------------------------------------------------
The weights are:
| (1.0298881979425620158e-13 - 2.7563156323038904381e-927j)  +/-  (2.55e-93, 6.55e-215j)
| (4.9531734403279346169e-16 + 1.5972159167876262202e-930j)  +/-  (1.14e-95, 2.93e-217j)
| (2.2658902265777001132e-26 + 1.1808929880720947348e-935j)  +/-  (5.85e-100, 1.5e-221j)
| (2.2658902265777001132e-26 - 2.0822588747862630173e-936j)  +/-  (5.49e-101, 1.41e-222j)
| (4.6931324421205303252e-22 - 4.1305334202471315443e-933j)  +/-  (2.17e-98, 5.57e-220j)
| (9.3829349984674299655e-19 + 4.743719508096638799e-931j)  +/-  (4.6e-97, 1.18e-218j)
| (9.3829349984674299655e-19 - 4.0806426025617894819e-932j)  +/-  (2.14e-98, 5.49e-220j)
| (5.7888280647478814456e-10 - 1.0246188653845104465e-926j)  +/-  (3.55e-94, 9.13e-216j)
| (1.0298881979425620158e-13 - 3.9953741903673941453e-929j)  +/-  (3.81e-96, 9.79e-218j)
| (1.9109331238736606182e-08 + 8.7963896326715684004e-925j)  +/-  (6.01e-94, 1.54e-215j)
| (0.0035206318336198982101 + 1.0253896187165099367e-921j)  +/-  (2.7e-85, 6.95e-207j)
| (4.0929502023251814493e-06 + 1.1953108794408913885e-923j)  +/-  (3.94e-91, 1.01e-212j)
| (0.013634047796733383347 - 7.0426757262721868199e-921j)  +/-  (2.94e-84, 7.55e-206j)
| (1.0405628178801487776e-11 + 1.6177740706085906691e-926j)  +/-  (2.24e-96, 5.77e-218j)
| (0.013071513082927356596 - 7.4328013811433887345e-920j)  +/-  (3.21e-80, 8.25e-202j)
| (0.00010269506296304976796 + 1.3815831134023685759e-922j)  +/-  (1.07e-89, 2.74e-211j)
| (4.6931324421205303252e-22 + 5.3439444446228889008e-934j)  +/-  (3.14e-101, 8.06e-223j)
| (4.9531734403279346169e-16 - 3.6886227936286788614e-929j)  +/-  (1.34e-98, 3.45e-220j)
| (0.013071513082927356596 - 1.1009503733010612036e-919j)  +/-  (2.61e-83, 6.72e-205j)
| (0.00068566719961643448273 - 8.9381916245382464094e-922j)  +/-  (1.44e-90, 3.71e-212j)
| (1.6913907798949436385e-05 - 1.9387314568829159445e-922j)  +/-  (5.25e-93, 1.35e-214j)
| (0.038652487310247853782 + 1.9911163405470049845e-920j)  +/-  (1.14e-86, 2.94e-208j)
| (5.7888280647478814456e-10 - 1.1224612069778017006e-925j)  +/-  (1.72e-96, 4.41e-218j)
| (0.038652487310247853782 + 3.252621315071376504e-920j)  +/-  (2.57e-87, 6.61e-209j)
| (0.00010269506296304976796 + 4.2689366895359804144e-922j)  +/-  (1.87e-92, 4.8e-214j)
| (3.8308938403127385709e-07 - 1.2921894399219717479e-924j)  +/-  (4.48e-97, 1.15e-218j)
| (0.65243156875552588383 + 8.6934470844040018316e-919j)  +/-  (1.11e-88, 2.84e-210j)
| (0.013634047796733383347 - 3.7182733709898610491e-921j)  +/-  (5.84e-91, 1.5e-212j)
| (4.0929502023251814493e-06 + 4.9866502419617632066e-923j)  +/-  (1.74e-94, 4.47e-216j)
| (0.084847411000489141741 + 1.2238355373608626008e-919j)  +/-  (1.5e-89, 3.86e-211j)
| (3.8308938403127385709e-07 - 6.8284155331386398844e-924j)  +/-  (1.63e-95, 4.2e-217j)
| (0.65243156875552588383 + 8.9697508803154969729e-919j)  +/-  (1.11e-89, 2.84e-211j)
| (0.084847411000489141741 + 8.7546122431858578773e-920j)  +/-  (2.07e-90, 5.31e-212j)
| (1.9109331238736606182e-08 + 1.2184188951901816294e-925j)  +/-  (5.67e-99, 1.46e-220j)
| (-0.93683045261524107081 - 1.6701074826999524356e-918j)  +/-  (6.77e-90, 1.74e-211j)
| (0.0035206318336198982101 + 2.2719107766608263185e-921j)  +/-  (8.68e-94, 2.23e-215j)
| (1.0405628178801487776e-11 + 7.2178452991910140523e-928j)  +/-  (4.01e-101, 1.03e-222j)
| (0.16144779461938906929 - 7.4772999195472122303e-920j)  +/-  (4.59e-92, 1.18e-213j)
| (1.6913907798949436385e-05 - 5.4535325243482542657e-923j)  +/-  (8.62e-97, 2.23e-218j)
| (0.00068566719961643448273 - 3.4190807294449037241e-922j)  +/-  (5.65e-96, 1.43e-217j)
| (0.16144779461938906929 - 9.1055175794374232069e-920j)  +/-  (1.58e-93, 5.06e-215j)
