Starting with polynomial:
P : 2*t
Extension levels are: 1 6 40
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : 2*t^7 - 21*t^5 + 105/2*t^3 - 105/4*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^47 - 29489850349848120765366333948308786701/30229520413264054439634042230102181*t^45 + 4374565959746955679221300719564444926465/20153013608842702959756028153401454*t^43 - 20043160977742038095258341406173758391941805/685202462700651900631704957215649436*t^41 + 3662968541530098150486838626595366910225478025/1370404925401303801263409914431298872*t^39 - 481653659978986061803553836561684777603426424505/2740809850802607602526819828862597744*t^37 + 47192752650206445411960224360827302413260671351255/5481619701605215205053639657725195488*t^35 - 207122810427720357384657829975682284471027497934275/644896435482966494712192900908846528*t^33 + 5962999741005285706464697698168906685087043778687075/644896435482966494712192900908846528*t^31 - 8612354109922727189430333365015495510050031084635125/41606221644062354497560832316699776*t^29 + 300782272004148167874046705376097690137947489909974075/83212443288124708995121664633399552*t^27 - 8189138062693759051448999509464623436456236338396612575/166424886576249417990243329266799104*t^25 + 173118765874163818748986855616207441723023864205122914375/332849773152498835980486658533598208*t^23 - 2820729386463628865148301867302806936702121590561673714375/665699546304997671960973317067196416*t^21 + 35034752813126450939111378713000524003705720064827957215625/1331399092609995343921946634134392832*t^19 - 326699583297482540725838206817584755340878846941694105208125/2662798185219990687843893268268785664*t^17 + 4482461486906210681369193956276739006145013661027011303938125/10651192740879962751375573073075142656*t^15 - 22022629004975606999276595757477413491850117269849694717103125/21302385481759925502751146146150285312*t^13 + 74762968223193501667439366939426243898821887981854138786946875/42604770963519851005502292292300570624*t^11 - 167032862720640462540482307669067523742848279352080548936359375/85209541927039702011004584584601141248*t^9 + 229185226256258907389982777205890464948959796456746133861446875/170419083854079404022009169169202282496*t^7 - 173755859918439226628844803263684297895697102090236708301196875/340838167708158808044018338338404564992*t^5 + 60451945614242210330039493030950543969613413108851433618953125/681676335416317616088036676676809129984*t^3 - 6256346681180566489229743524278615609711128802947346644265625/1363352670832635232176073353353618259968*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:
| (6.4068981958197111412 - 8.7777431254614441641e-910j)  +/-  (1.7e-244, 1.7e-244j)
| (-8.5949600817124847035 - 8.5094713175728627833e-915j)  +/-  (3.04e-247, 3.04e-247j)
| (-6.4068981958197111412 - 2.3927266795370331259e-913j)  +/-  (1.63e-244, 1.63e-244j)
| (-5.1617458946519282579 - 5.0738045025803062021e-922j)  +/-  (3.36e-244, 3.36e-244j)
| (3.6825877157643521282 + 1.949718196959294652e-930j)  +/-  (2.84e-245, 2.84e-245j)
| (7.3661495993886168255 - 2.5741847947236131778e-932j)  +/-  (2.33e-245, 2.33e-245j)
| (-7.9234380415904131304 + 5.3088057779447916109e-932j)  +/-  (4.24e-246, 4.24e-246j)
| (7.9234380415904131304 - 2.2538001542466572787e-934j)  +/-  (3.91e-246, 3.91e-246j)
| (-6.8676772096561196135 - 1.5594837568541056595e-932j)  +/-  (7.61e-245, 7.61e-245j)
| (4.0391092709127155717 + 2.0809263349397722987e-932j)  +/-  (7.22e-245, 7.22e-245j)
| (5.9729483059320967043 + 1.2136521870447870837e-934j)  +/-  (2.85e-244, 2.85e-244j)
| (4.4035629178540757918 - 5.2790383458131800406e-934j)  +/-  (1.42e-244, 1.42e-244j)
| (-3.3330129961213830973 + 5.8865041834149869532e-938j)  +/-  (1.04e-245, 1.04e-245j)
| (6.8676772096561196135 + 5.6026235304420254069e-940j)  +/-  (7.27e-245, 7.27e-245j)
| (8.5949600817124847035 - 2.9819224294991969716e-946j)  +/-  (3.02e-247, 3.02e-247j)
| (-5.9729483059320967043 + 4.3825102141477933376e-942j)  +/-  (2.6e-244, 2.6e-244j)
| (1.9932224439880046727 + 1.4970828888366970377e-950j)  +/-  (3.03e-248, 3.03e-248j)
| (4.7772232533009290124 - 2.3441471514692103979e-946j)  +/-  (2.33e-244, 2.33e-244j)
| (-7.3661495993886168255 + 7.3325228897052392713e-949j)  +/-  (2.38e-245, 2.38e-245j)
| (5.5593228729827483689 - 1.0887203335388405769e-948j)  +/-  (3.1e-244, 3.1e-244j)
| (3.3330129961213830973 + 5.0107840190286351234e-954j)  +/-  (9.84e-246, 9.84e-246j)
| (1.673551628767471445 - 1.5181194688950648115e-960j)  +/-  (4.73e-249, 4.73e-249j)
| (-2.9896410716993094583 - 3.0250767163643583045e-955j)  +/-  (2.98e-246, 2.98e-246j)
| (-0.81628788285896466304 + 2.6496356284360469462e-965j)  +/-  (1.48e-251, 1.48e-251j)
| (2.9896410716993094583 + 4.8210305666078296664e-960j)  +/-  (3.01e-246, 3.01e-246j)
| (-3.6825877157643521282 - 2.5167711555955519168e-960j)  +/-  (3.02e-245, 3.02e-245j)
| (1.0745022198605765791 + 3.7326738907218175492e-980j)  +/-  (1.03e-250, 1.03e-250j)
| (-1.9932224439880046727 + 9.7359598229693641585e-974j)  +/-  (2.98e-248, 2.98e-248j)
| (-4.7772232533009290124 + 7.5096494574136558008e-979j)  +/-  (2.53e-244, 2.53e-244j)
| (-1.3642330701496096562 + 1.80761290393811614e-999j)  +/-  (7.79e-250, 7.79e-250j)
| (-2.3197465717736434472 - 3.1277188873587945118e-996j)  +/-  (1.78e-247, 1.78e-247j)
| (5.1617458946519282579 - 2.5952670137615007675e-993j)  +/-  (3.02e-244, 3.02e-244j)
| (0.81628788285896466304 - 4.7347150217022049289e-1008j)  +/-  (1.64e-251, 1.64e-251j)
| (-4.4035629178540757918 - 7.9892556057885327999e-1001j)  +/-  (1.32e-244, 1.32e-244j)
| (-1.0745022198605765791 + 4.8423577101590069616e-1020j)  +/-  (1.07e-250, 1.07e-250j)
| (-1.673551628767471445 + 7.224287280224971806e-1018j)  +/-  (4.92e-249, 4.92e-249j)
| (2.3197465717736434472 + 2.7841397530728893838e-1016j)  +/-  (1.54e-247, 1.54e-247j)
| (0.5668118702723686868 - 5.9620120401462823653e-1022j)  +/-  (1.42e-252, 1.42e-252j)
| (-5.5593228729827483689 - 9.8306048443422799959e-1016j)  +/-  (3.2e-244, 3.2e-244j)
| (-0.29175812799828760619 - 6.3454306977921771814e-1034j)  +/-  (9.62e-254, 9.62e-254j)
| (-0.5668118702723686868 - 4.187295398503327449e-1033j)  +/-  (1.55e-252, 1.55e-252j)
| (0.29175812799828760619 + 6.0847532885936136998e-1034j)  +/-  (9.62e-254, 9.62e-254j)
| (-5.4706116129343912728e-1040 - 2.347164936171036112e-1040j)  +/-  (2.8e-1038, 2.8e-1038j)
| (1.3642330701496096562 - 5.6686835550008778741e-1031j)  +/-  (7.01e-250, 7.01e-250j)
| (-2.6519613568352334924 - 1.8269059216158493234e-1028j)  +/-  (7.8e-247, 7.8e-247j)
| (2.6519613568352334924 + 1.3451724562336093422e-1033j)  +/-  (8.02e-247, 8.02e-247j)
| (-4.0391092709127155717 - 4.0823608785011429057e-1040j)  +/-  (7.06e-245, 7.06e-245j)
-------------------------------------------------
The weights are:
| (3.7472269444432170123e-19 + 2.2508212861563867847e-927j)  +/-  (9.45e-88, 1.2e-208j)
| (3.6129001663297951564e-33 + 9.3772675989341395959e-937j)  +/-  (6.64e-94, 8.45e-215j)
| (3.7472269444432170123e-19 + 2.5055806412771115042e-929j)  +/-  (2.48e-88, 3.16e-209j)
| (5.9157813333696771303e-13 - 6.4682969601242108203e-926j)  +/-  (1.83e-84, 2.33e-205j)
| (2.5669592555479535792e-07 - 4.4502986759546445644e-922j)  +/-  (2.1e-79, 2.67e-200j)
| (8.0348872417117790948e-25 - 3.3903490408102589336e-931j)  +/-  (2.79e-92, 3.55e-213j)
| (1.8354485894362492387e-28 - 2.7947389759733992652e-934j)  +/-  (2.93e-93, 3.72e-214j)
| (1.8354485894362492387e-28 + 2.6341415974630005557e-933j)  +/-  (4.59e-94, 5.84e-215j)
| (8.8449058863044020409e-22 - 9.9853289039738309087e-931j)  +/-  (1.4e-90, 1.78e-211j)
| (1.6704584124661042161e-08 + 1.0261418417365836254e-922j)  +/-  (9.9e-83, 1.26e-203j)
| (7.6516995713374044417e-17 - 1.3165902399390181666e-926j)  +/-  (3.12e-89, 3.97e-210j)
| (7.8826500035564676314e-10 - 2.0963382538267026061e-923j)  +/-  (1.08e-84, 1.37e-205j)
| (2.9268223997300351842e-06 + 5.4302969300567396528e-922j)  +/-  (1.4e-83, 1.78e-204j)
| (8.8449058863044020409e-22 + 2.854284243613027632e-929j)  +/-  (1.23e-91, 1.57e-212j)
| (3.6129001663297951564e-33 - 6.4175331490095010181e-936j)  +/-  (2.74e-97, 3.49e-218j)
| (7.6516995713374044417e-17 - 4.5791892882438942078e-928j)  +/-  (5.34e-92, 6.79e-213j)
| (0.0034336786376143764177 + 1.477711345411808561e-919j)  +/-  (4.69e-78, 5.97e-199j)
| (2.6205979103981148928e-11 + 3.7780966415183197442e-924j)  +/-  (4.7e-87, 5.98e-208j)
| (8.0348872417117790948e-25 + 2.3704730074691965758e-932j)  +/-  (7.39e-96, 9.4e-217j)
| (8.6409552401172028829e-15 + 8.7323728189178041161e-926j)  +/-  (4.25e-89, 5.41e-210j)
| (2.9268223997300351842e-06 + 1.7219829276516525738e-921j)  +/-  (5.45e-84, 6.94e-205j)
| (0.010812556122187590302 - 3.7474510980176247948e-919j)  +/-  (9.65e-79, 1.23e-199j)
| (2.5222545551333817779e-05 - 2.1782363211587826569e-921j)  +/-  (8.57e-87, 1.09e-207j)
| (0.071133610836144728144 + 2.6299073268415434143e-918j)  +/-  (2.25e-79, 2.86e-200j)
| (2.5222545551333817779e-05 - 5.9934634659203599769e-921j)  +/-  (6.63e-84, 8.43e-205j)
| (2.5669592555479535792e-07 - 1.200521746902893442e-922j)  +/-  (4.57e-89, 5.81e-210j)
| (0.048882967308989196546 - 1.9873605890757650934e-918j)  +/-  (9.05e-80, 1.15e-200j)
| (0.0034336786376143764177 + 7.7614229186614701382e-920j)  +/-  (2.13e-84, 2.71e-205j)
| (2.6205979103981148928e-11 + 5.4951078838120282178e-925j)  +/-  (3.3e-92, 4.19e-213j)
| (0.026474197852329798139 + 5.8582425109822450521e-919j)  +/-  (1.24e-82, 1.57e-203j)
| (0.00085544556145507123385 - 2.5696133702656589573e-920j)  +/-  (4.15e-86, 5.28e-207j)
| (5.9157813333696771303e-13 - 6.0247423629017880656e-925j)  +/-  (2.58e-91, 3.28e-212j)
| (0.071133610836144728144 + 3.3983755592466532388e-918j)  +/-  (1.96e-82, 2.48e-203j)
| (7.8826500035564676314e-10 - 3.8793004841349279697e-924j)  +/-  (1.07e-91, 1.35e-212j)
| (0.048882967308989196546 - 1.4162320773610112978e-918j)  +/-  (3.26e-83, 4.11e-204j)
| (0.010812556122187590302 - 2.1945018339997929728e-919j)  +/-  (5.91e-85, 7.45e-206j)
| (0.00085544556145507123385 - 5.4889809426949341333e-920j)  +/-  (4.4e-87, 5.53e-208j)
| (0.10673301796354118969 - 4.1649385108220499745e-918j)  +/-  (1.84e-83, 2.32e-204j)
| (8.6409552401172028829e-15 + 6.1615125035535965079e-927j)  +/-  (3.53e-94, 4.46e-215j)
| (0.14846788519676983462 + 3.7472351353993644621e-918j)  +/-  (4.27e-84, 5.39e-205j)
| (0.10673301796354118969 - 3.4875604002181841309e-918j)  +/-  (5.06e-84, 6.38e-205j)
| (0.14846788519676983462 + 4.1050064888247340523e-918j)  +/-  (1.18e-84, 1.49e-205j)
| (0.16602295313626237113 - 3.8842961855484117038e-918j)  +/-  (1.27e-84, 1.6e-205j)
| (0.026474197852329798139 + 9.0301946933778696857e-919j)  +/-  (2.52e-86, 3.17e-207j)
| (0.00016674036930501058982 + 7.8452619643761231643e-921j)  +/-  (4.17e-89, 5.4e-210j)
| (0.00016674036930501058982 + 1.8937165062527335569e-920j)  +/-  (5.18e-89, 5.98e-210j)
| (1.6704584124661042161e-08 + 2.3232946568770476283e-923j)  +/-  (6e-92, 8.04e-213j)
