Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 5 38
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P2 : 16*t^9 - 168*t^7 + 432*t^5 - 270*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^47 - 1210416446467091249886306809359296099379668383310420190068827328/157281009354020553361820686714156147142188786633746890875247*t^45 + 644948692286679587164282900115025437322952400269161771830862525096/381968165574049915307278810591522071631029910396242449268457*t^43 - 599805336707917101998550398985104093884576320067771173306090300221754/2673777159018349407150951674140654501417209372773697144879199*t^41 + 270139225865718160195108344281932513837801800623180891113104471174502761/13368885795091747035754758370703272507086046863868485724395995*t^39 - 17504377904101596324033875460615292446178822651324970164047245890301448738/13368885795091747035754758370703272507086046863868485724395995*t^37 + 241417111308022751864593268607034332250795315103703849454133955564304569447/3819681655740499153072788105915220716310299103962424492684570*t^35 - 417461700998832535888013611098024544562877467942324143962594819500204690781/179749724976023489556366499101892739591072899009996446714568*t^33 + 11833124815712400135842891392595595983654814682158272437444748426823268990941/179749724976023489556366499101892739591072899009996446714568*t^31 - 65165868115924387729781881637135629235178218465798489454766856472128902988721/44937431244005872389091624775473184897768224752499111678642*t^29 + 8950788662231343960452674223015799328490570268347831181034833114831557404985109/359499449952046979112732998203785479182145798019992893429136*t^27 - 478704604960351410779604889112841913775000825638222055051857637740032525024761199/1437997799808187916450931992815141916728583192079971573716544*t^25 + 9925205754099903992553488640215308858331468615839994274306524619215335991007244275/2875995599616375832901863985630283833457166384159943147433088*t^23 - 39574139335929622090218291359111702868526202003796846493389357737827545370563481575/1437997799808187916450931992815141916728583192079971573716544*t^21 + 959679939494772111300095491567779447971265584280337997759441524927235123645790698775/5751991199232751665803727971260567666914332768319886294866176*t^19 - 17407759974371305510851577309773201151358368218183300079338711488876167728387966689925/23007964796931006663214911885042270667657331073279545179464704*t^17 + 231107909475706326627691901134502903421125973185867597809021172619011327743453198028925/92031859187724026652859647540169082670629324293118180717858816*t^15 - 136357013049767876297511486299289011288401698361873891793964289604094336648170198164125/23007964796931006663214911885042270667657331073279545179464704*t^13 + 1761418209594722333901829030194948916548460194532685593063371761972011537125645409598625/184063718375448053305719295080338165341258648586236361435717632*t^11 - 7387857336351549913771532876087718967575365919608623360960897960220381728355933207166375/736254873501792213222877180321352661365034594344945445742870528*t^9 + 9356886813252807854531678472081294769264238391312320572101476127424066279255908821256375/1472509747003584426445754360642705322730069188689890891485741056*t^7 - 1609825480084081931092000503540531282857440951522146126162858258795233268719628996693375/736254873501792213222877180321352661365034594344945445742870528*t^5 + 1013703806628898957584380458829141478411679999112634787026078637511327054721251963544375/2945019494007168852891508721285410645460138377379781782971482112*t^3 - 198168884362339221527978734021707856831204359536056833247274128392041896735597582655625/11780077976028675411566034885141642581840553509519127131885928448*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:   47 out of 47
Indefinite weights: 0 out of 47
Negative weights:   0 out of 47
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.5389963507141392893 + 4.0149407094036314786e-916j)  +/-  (3.04e-247, 3.04e-247j)
| (-7.3151523238197611842 - 7.2967195635408180146e-912j)  +/-  (2.38e-245, 2.38e-245j)
| (-5.9311918447409056993 + 5.129836179918164534e-929j)  +/-  (2.7e-244, 2.7e-244j)
| (-4.7467953392194056957 + 4.7373203390380309171e-948j)  +/-  (2.32e-244, 2.32e-244j)
| (-7.8698767527613642502 - 4.4356824356284916536e-959j)  +/-  (4.5e-246, 4.5e-246j)
| (-2.9752102451344114199 - 1.1839850537079916299e-960j)  +/-  (2.98e-246, 2.98e-246j)
| (-6.3617891767179658652 + 4.0338603228705525689e-968j)  +/-  (1.64e-244, 1.64e-244j)
| (4.0163739878065864688 - 3.9928199412961924962e-985j)  +/-  (6.98e-245, 6.98e-245j)
| (-5.1273956985061984368 - 1.0994087799806306238e-985j)  +/-  (2.93e-244, 2.93e-244j)
| (5.1273956985061984368 - 1.196308374480659506e-997j)  +/-  (2.9e-244, 2.9e-244j)
| (6.3617891767179658652 - 5.4397847612616802679e-998j)  +/-  (1.62e-244, 1.62e-244j)
| (5.5211692449790154422 - 1.5222857898507883752e-999j)  +/-  (3.25e-244, 3.25e-244j)
| (5.9311918447409056993 + 2.4287202986917067288e-1000j)  +/-  (2.57e-244, 2.57e-244j)
| (-1.6506801238857845559 - 3.0602349255048102088e-1004j)  +/-  (3.63e-249, 3.63e-249j)
| (-1.9763368797891283895 + 1.4197237487977696402e-1002j)  +/-  (2.53e-248, 2.53e-248j)
| (-5.5211692449790154422 + 1.1390291397647331988e-999j)  +/-  (3.26e-244, 3.26e-244j)
| (0.73395630342256598469 + 7.4099393664632435235e-1012j)  +/-  (8.02e-252, 8.02e-252j)
| (-6.8194883339465765459 - 1.3319474817588297384e-1004j)  +/-  (8.1e-245, 8.1e-245j)
| (2.6384291054842239697 - 5.5708701762931882835e-1012j)  +/-  (6.73e-247, 6.73e-247j)
| (-8.5389963507141392893 - 5.8654143345077541709e-1013j)  +/-  (3.58e-247, 3.58e-247j)
| (7.3151523238197611842 + 3.6141040270566653103e-1011j)  +/-  (2.57e-245, 2.57e-245j)
| (3.6632761601337692471 + 2.9270032133956837766e-1009j)  +/-  (3.18e-245, 3.18e-245j)
| (7.8698767527613642502 - 7.4578741643948956695e-1012j)  +/-  (4.36e-246, 4.36e-246j)
| (4.3770583951540816154 - 7.1848637531384411736e-1009j)  +/-  (1.5e-244, 1.5e-244j)
| (2.9752102451344114199 + 4.0829438753731633761e-1011j)  +/-  (2.86e-246, 2.86e-246j)
| (2.3055955199768363935 + 8.8647057038771704626e-1014j)  +/-  (1.47e-247, 1.47e-247j)
| (1.3295840337517418916 - 2.178493882371618085e-1016j)  +/-  (5.26e-250, 5.26e-250j)
| (6.8194883339465765459 + 8.3685449666439718996e-1012j)  +/-  (7.46e-245, 7.46e-245j)
| (-4.0163739878065864688 - 4.9733768190308461119e-1009j)  +/-  (7.09e-245, 7.09e-245j)
| (-0.52464762327529031788 - 1.4646786629971278986e-1026j)  +/-  (1.33e-252, 1.33e-252j)
| (-3.3165552718448806113 - 1.0629140132438111444e-1017j)  +/-  (1.05e-245, 1.05e-245j)
| (3.3165552718448806113 + 6.3658532990889258146e-1023j)  +/-  (1.13e-245, 1.13e-245j)
| (-4.3770583951540816154 + 6.6708258973598293758e-1023j)  +/-  (1.55e-244, 1.55e-244j)
| (-1.3295840337517418916 - 5.2795855625079333221e-1036j)  +/-  (4.48e-250, 4.48e-250j)
| (4.7467953392194056957 + 4.8768276412888498451e-1030j)  +/-  (2.39e-244, 2.39e-244j)
| (-3.6632761601337692471 - 9.9341474919099169625e-1032j)  +/-  (2.96e-245, 2.96e-245j)
| (1.9763368797891283895 + 2.1103726210521272253e-1040j)  +/-  (2.38e-248, 2.38e-248j)
| (0.52464762327529031788 + 7.0302529841487735757e-1046j)  +/-  (1.19e-252, 1.19e-252j)
| (1.6506801238857845559 - 1.9361438740095355496e-1042j)  +/-  (3.85e-249, 3.85e-249j)
| (-0.73395630342256598469 + 7.6636078190937766104e-1044j)  +/-  (9.42e-252, 9.42e-252j)
| (-1.0172391775067136497 - 5.6150311435266145093e-1043j)  +/-  (5.89e-251, 5.89e-251j)
| (-2.6384291054842239697 - 1.9750050068995447065e-1040j)  +/-  (6.71e-247, 6.71e-247j)
| (3.2985002444620424157e-1063 - 2.5437930696788900781e-1062j)  +/-  (1.21e-1060, 1.21e-1060j)
| (0.29044493834141554852 + 1.7670981430028685829e-1047j)  +/-  (9.5e-254, 9.5e-254j)
| (1.0172391775067136497 + 1.7062268443884245735e-1045j)  +/-  (6.23e-251, 6.23e-251j)
| (-0.29044493834141554852 - 2.339585287451910152e-1047j)  +/-  (9.5e-254, 9.5e-254j)
| (-2.3055955199768363935 + 1.3268667203434615695e-1044j)  +/-  (1.45e-247, 1.45e-247j)
-------------------------------------------------
The weights are:
| (9.39614761588446441e-33 - 3.2798857906946293698e-941j)  +/-  (2.69e-80, 6.28e-202j)
| (1.6900836567097555006e-24 - 9.6297930314835460282e-935j)  +/-  (1.73e-77, 4.04e-199j)
| (1.2475064379081781241e-16 + 1.5884965666336245263e-931j)  +/-  (1.08e-73, 2.52e-195j)
| (3.465050660947275382e-11 - 9.1010612544306956482e-929j)  +/-  (3.77e-70, 8.82e-192j)
| (4.2592175938471911794e-28 - 2.7031299481835505029e-937j)  +/-  (1.02e-79, 2.38e-201j)
| (2.736725773248018462e-05 + 1.6274620974979676206e-925j)  +/-  (2.04e-63, 4.78e-185j)
| (6.6177683010230741702e-19 - 1.3246994473695503956e-932j)  +/-  (2.74e-75, 6.39e-197j)
| (1.9859796877259149877e-08 - 7.9153498462487132669e-928j)  +/-  (1.34e-71, 3.13e-193j)
| (8.3401137562291704819e-13 + 1.3123899406521461519e-929j)  +/-  (7.2e-72, 1.68e-193j)
| (8.3401137562291704819e-13 + 2.3075577889190108084e-930j)  +/-  (3.4e-76, 7.94e-198j)
| (6.6177683010230741702e-19 - 9.2339335591132209433e-934j)  +/-  (1.4e-80, 3.28e-202j)
| (1.3066634478431745126e-14 - 2.2165497980986131681e-931j)  +/-  (4.45e-78, 1.04e-199j)
| (1.2475064379081781241e-16 + 1.6596402153576993162e-932j)  +/-  (2.39e-79, 5.58e-201j)
| (0.011972510815218026062 + 9.887863567234871649e-924j)  +/-  (6.48e-62, 1.51e-183j)
| (0.0037182307918566135314 - 3.9036285002096284762e-924j)  +/-  (2.07e-64, 4.84e-186j)
| (1.3066634478431745126e-14 - 1.5859873744394803152e-930j)  +/-  (3.26e-77, 7.62e-199j)
| (0.082358491827898504725 - 1.3437939642812705449e-922j)  +/-  (2.12e-63, 4.95e-185j)
| (1.7000240016462269709e-21 + 1.0137585119166523416e-933j)  +/-  (3.61e-81, 8.44e-203j)
| (0.00017899958985304406843 - 2.398487927718541482e-925j)  +/-  (2.5e-72, 5.83e-194j)
| (9.39614761588446441e-33 + 4.2488864670072617528e-940j)  +/-  (3.51e-87, 8.21e-209j)
| (1.6900836567097555006e-24 - 8.4291256050158218781e-937j)  +/-  (1.44e-86, 3.35e-208j)
| (2.9315572109669786154e-07 + 3.9972366916408105886e-927j)  +/-  (6.19e-77, 1.45e-198j)
| (4.2592175938471911794e-28 + 9.8748079871659311982e-939j)  +/-  (2.39e-88, 5.58e-210j)
| (9.8436576765782592013e-10 + 1.3472958685539918546e-928j)  +/-  (5.64e-79, 1.32e-200j)
| (2.736725773248018462e-05 + 6.863792472351453114e-926j)  +/-  (8.56e-76, 2e-197j)
| (0.00091760359389756927408 + 7.6245403209360720525e-925j)  +/-  (3.9e-74, 9.1e-196j)
| (0.030623559958487136856 - 1.7043432405127248238e-923j)  +/-  (1.07e-70, 2.51e-192j)
| (1.7000240016462269709e-21 + 3.554979789011426374e-935j)  +/-  (1.87e-85, 4.37e-207j)
| (1.9859796877259149877e-08 - 2.7189760709263064691e-927j)  +/-  (5.13e-81, 1.2e-202j)
| (0.0830130629252693536 + 2.5351473079352944929e-922j)  +/-  (1.38e-73, 3.22e-195j)
| (3.2418701260421270076e-06 - 4.6826970334567123681e-926j)  +/-  (9.37e-80, 2.19e-201j)
| (3.2418701260421270076e-06 - 1.7611675843711593819e-926j)  +/-  (2.05e-78, 4.8e-200j)
| (9.8436576765782592013e-10 + 5.3615940413538640853e-928j)  +/-  (7.07e-82, 1.65e-203j)
| (0.030623559958487136856 - 2.4615203101350411582e-923j)  +/-  (2.06e-75, 4.83e-197j)
| (3.465050660947275382e-11 - 1.9378938957199787715e-929j)  +/-  (3.92e-82, 9.17e-204j)
| (2.9315572109669786154e-07 + 1.2016666109167759961e-926j)  +/-  (9.77e-81, 2.28e-202j)
| (0.0037182307918566135314 - 2.2429937553910072006e-924j)  +/-  (1.51e-77, 3.55e-199j)
| (0.0830130629252693536 + 2.1958378856450871831e-922j)  +/-  (5.36e-76, 1.33e-197j)
| (0.011972510815218026062 + 6.2469970215294092966e-924j)  +/-  (3.44e-77, 8.05e-199j)
| (0.082358491827898504725 - 1.6435224740878305085e-922j)  +/-  (1.33e-76, 3.24e-198j)
| (0.06097149712321006287 + 6.3421816616307828017e-923j)  +/-  (4.63e-77, 1.06e-198j)
| (0.00017899958985304406843 - 5.1047589437091466806e-925j)  +/-  (1.33e-80, 3e-202j)
| (0.16780369902047428483 + 2.0615917024493849887e-922j)  +/-  (3.46e-77, 9.57e-199j)
| (0.14231327070083257264 - 2.217659818367795765e-922j)  +/-  (3.2e-77, 8.78e-199j)
| (0.06097149712321006287 + 4.7936429039326951044e-923j)  +/-  (7.78e-78, 2.06e-199j)
| (0.14231327070083257264 - 2.4010434174634566429e-922j)  +/-  (1.45e-77, 4.46e-199j)
| (0.00091760359389756927408 + 1.4642768242648779045e-924j)  +/-  (3.4e-80, 7.07e-202j)
