Starting with polynomial:
P : t
Extension levels are: 1 2 4 36
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : t^3 - 3/4*t
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P3 : t^7 - 2*t^5 + 19/16*t^3 - 3/16*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 11*t^41 + 901/16*t^39 - 1425/8*t^37 + 99789/256*t^35 - 160293/256*t^33 + 391391/512*t^31 - 5797/8*t^29 + 8850655/16384*t^27 - 5224089/16384*t^25 + 156547365/1048576*t^23 - 29004495/524288*t^21 + 270405135/16777216*t^19 - 61256475/16777216*t^17 + 42456735/67108864*t^15 - 1374365/16777216*t^13 + 32947615/4294967296*t^11 - 2129501/4294967296*t^9 + 1418065/68719476736*t^7 - 17017/34359738368*t^5 + 6181/1099511627776*t^3 - 21/1099511627776*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (-0.99720379718118014823 + 5.5169816287978318479e-852j)  +/-  (8.34e-240, 8.34e-240j)
| (-1 - 2.595932048753656683e-878j)  +/-  (4.26e-240, 4.26e-240j)
| (-0.93087374864420425564 - 4.6783204997719922173e-899j)  +/-  (7.88e-241, 7.88e-241j)
| (1 + 3.6552035149436133127e-909j)  +/-  (4.14e-240, 4.14e-240j)
| (0.90096886790241912624 - 3.9666300640497518636e-913j)  +/-  (3.69e-241, 3.69e-241j)
| (0.95557280578614073281 - 2.5388549146449117594e-912j)  +/-  (1.81e-240, 1.81e-240j)
| (-0.98883082622512854507 + 4.7308629168179895371e-913j)  +/-  (6.02e-240, 6.02e-240j)
| (-0.90096886790241912624 + 1.2688524099549955714e-923j)  +/-  (3.22e-241, 3.22e-241j)
| (-0.97492791218182360702 - 1.2903246996521064845e-926j)  +/-  (3.33e-240, 3.33e-240j)
| (0.99720379718118014823 + 3.6073954790029428035e-939j)  +/-  (6.56e-240, 6.56e-240j)
| (0.82623877431599487195 - 5.8942725209274074179e-945j)  +/-  (3.07e-242, 3.07e-242j)
| (0.98883082622512854507 - 1.0403434121942699311e-941j)  +/-  (5.2e-240, 5.2e-240j)
| (-0.95557280578614073281 - 2.9817186584748706482e-944j)  +/-  (1.97e-240, 1.97e-240j)
| (-0.82623877431599487195 - 1.2495186264394579934e-952j)  +/-  (3.41e-242, 3.41e-242j)
| (0.97492791218182360702 + 6.1804136671400638507e-955j)  +/-  (3.69e-240, 3.69e-240j)
| (0.86602540378443864676 + 1.1947647088670673043e-958j)  +/-  (1.26e-241, 1.26e-241j)
| (0.93087374864420425564 + 9.3448106027958686564e-960j)  +/-  (8.69e-241, 8.69e-241j)
| (-0.36534102436639501454 - 1.3343409645750171414e-968j)  +/-  (1.5e-249, 1.5e-249j)
| (-0.78183148246802980871 - 3.5876641158923005914e-960j)  +/-  (7.87e-243, 7.87e-243j)
| (-0.86602540378443864676 - 1.5506419180812230294e-963j)  +/-  (1.19e-241, 1.19e-241j)
| (0.73305187182982632852 + 1.8274742386610493849e-972j)  +/-  (1.72e-243, 1.72e-243j)
| (0.78183148246802980871 + 7.8609798979028333677e-976j)  +/-  (6.91e-243, 6.91e-243j)
| (0.22252093395631440429 - 1.1563788906505144036e-985j)  +/-  (5.77e-252, 5.77e-252j)
| (-0.73305187182982632852 - 1.2218104229904380062e-977j)  +/-  (1.32e-243, 1.32e-243j)
| (-0.68017273777091939019 - 7.8548773351728703474e-982j)  +/-  (2.3e-244, 2.3e-244j)
| (0.14904226617617444693 + 1.6075520117755734388e-988j)  +/-  (2.81e-253, 2.81e-253j)
| (0.62348980185873353053 - 7.8849434002621704173e-983j)  +/-  (2.6e-245, 2.6e-245j)
| (0.5 + 9.4622417181097178377e-986j)  +/-  (2.61e-247, 2.61e-247j)
| (-0.074730093586424254291 - 1.6376044896656641075e-988j)  +/-  (1.4e-254, 1.4e-254j)
| (-0.62348980185873353053 - 1.0182010252620051553e-984j)  +/-  (2.74e-245, 2.74e-245j)
| (-0.29475517441090421683 - 7.5123711152294425441e-989j)  +/-  (9.58e-251, 9.58e-251j)
| (0.29475517441090421683 + 2.5042604438262897132e-990j)  +/-  (9.15e-251, 9.15e-251j)
| (0.68017273777091939019 - 9.6583571323659647941e-987j)  +/-  (2.22e-244, 2.22e-244j)
| (0.074730093586424254291 + 1.1632496697097023486e-997j)  +/-  (1.4e-254, 1.4e-254j)
| (-0.56332005806362202775 - 9.8031497093669114602e-991j)  +/-  (2.8e-246, 2.8e-246j)
| (-0.43388373911755812048 + 8.9436167810948597673e-992j)  +/-  (2.27e-248, 2.27e-248j)
| (1.0430030144293828604e-996 + 1.4535540994460064692e-996j)  +/-  (7.69e-995, 7.69e-995j)
| (0.56332005806362202775 + 2.574830258227261202e-991j)  +/-  (3.12e-246, 3.12e-246j)
| (0.36534102436639501454 - 1.1061671638206287029e-994j)  +/-  (1.65e-249, 1.65e-249j)
| (-0.22252093395631440429 + 9.5531979949460166853e-996j)  +/-  (5.84e-252, 5.84e-252j)
| (-0.5 + 1.5767670043472890766e-991j)  +/-  (3.17e-247, 3.17e-247j)
| (-0.14904226617617444693 + 1.2465008846196323489e-997j)  +/-  (2.53e-253, 2.53e-253j)
| (0.43388373911755812048 - 1.612534909855020187e-994j)  +/-  (2.17e-248, 2.17e-248j)
-------------------------------------------------
The weights are:
| (0.023809523809523809524 - 1.1727761434979696504e-851j)  +/-  (3.09e-68, 2.7e-183j)
| (0.011904761904761904762 + 2.3488408023100239743e-851j)  +/-  (2.41e-68, 2.11e-183j)
| (0.023809523809523809524 + 1.9803499069406261554e-852j)  +/-  (7.74e-70, 6.77e-185j)
| (0.011904761904761904762 - 3.2885153140846735309e-854j)  +/-  (1.52e-70, 1.32e-185j)
| (0.023809523809523809524 - 6.9201663191047067425e-854j)  +/-  (1.09e-70, 9.56e-186j)
| (0.023809523809523809524 - 6.726663216261693362e-854j)  +/-  (8.19e-71, 7.16e-186j)
| (0.023809523809523809524 - 1.5688183577494528834e-851j)  +/-  (4.55e-69, 3.97e-184j)
| (0.023809523809523809524 - 1.3649587154272243342e-852j)  +/-  (4.98e-71, 4.35e-186j)
| (0.023809523809523809524 + 5.8968119763305377302e-852j)  +/-  (1.09e-69, 9.52e-185j)
| (0.023809523809523809524 + 6.5862517681378956641e-854j)  +/-  (7.98e-72, 6.97e-187j)
| (0.023809523809523809524 - 7.2037752930005522879e-854j)  +/-  (5.53e-74, 4.84e-189j)
| (0.023809523809523809524 - 6.614018904779893717e-854j)  +/-  (2.07e-72, 1.81e-187j)
| (0.023809523809523809524 - 3.1552624870523590608e-852j)  +/-  (7.18e-72, 6.28e-187j)
| (0.023809523809523809524 - 7.6832502488622454025e-853j)  +/-  (7.33e-75, 6.41e-190j)
| (0.023809523809523809524 + 6.6606456771589301097e-854j)  +/-  (8.5e-73, 7.42e-188j)
| (0.023809523809523809524 + 7.0499488404052380625e-854j)  +/-  (9.54e-75, 8.34e-190j)
| (0.023809523809523809524 + 6.8128331109906351298e-854j)  +/-  (1e-73, 8.74e-189j)
| (0.023809523809523809524 - 2.0788802743103110168e-853j)  +/-  (2.7e-79, 2.36e-194j)
| (0.023809523809523809524 + 6.0990524999705063689e-853j)  +/-  (5.27e-77, 4.6e-192j)
| (0.023809523809523809524 + 1.0013593096104373603e-852j)  +/-  (1.56e-75, 1.37e-190j)
| (0.023809523809523809524 - 7.591751196090538029e-854j)  +/-  (1.23e-78, 1.08e-193j)
| (0.023809523809523809524 + 7.3835919360445921163e-854j)  +/-  (9.35e-78, 8.17e-193j)
| (0.023809523809523809524 - 1.076937296541215444e-853j)  +/-  (7.25e-82, 6.34e-197j)
| (0.023809523809523809524 - 4.9727710775852651344e-853j)  +/-  (4.95e-79, 4.32e-194j)
| (0.023809523809523809524 + 4.1433386902821561644e-853j)  +/-  (6.23e-80, 5.44e-195j)
| (0.023809523809523809524 + 1.1459730126603327121e-853j)  +/-  (9.45e-83, 8.25e-198j)
| (0.023809523809523809524 - 8.1049684854300725763e-854j)  +/-  (6.26e-82, 5.47e-197j)
| (0.023809523809523809524 - 8.7734686283107016115e-854j)  +/-  (7.15e-83, 6.25e-198j)
| (0.023809523809523809524 - 1.4239615171217132728e-853j)  +/-  (2.41e-84, 2.11e-199j)
| (0.023809523809523809524 - 3.5148992837217853292e-853j)  +/-  (1.02e-82, 8.93e-198j)
| (0.023809523809523809524 + 1.8699831018179024544e-853j)  +/-  (2.91e-84, 2.54e-199j)
| (0.023809523809523809524 + 1.0167250534720635813e-853j)  +/-  (2.65e-84, 2.31e-199j)
| (0.023809523809523809524 + 7.831080422936675254e-854j)  +/-  (7.02e-83, 6.14e-198j)
| (0.023809523809523809524 - 1.225417971937651882e-853j)  +/-  (1.2e-84, 1.05e-199j)
| (0.023809523809523809524 + 3.0274632028092008435e-853j)  +/-  (1.11e-84, 9.73e-200j)
| (0.023809523809523809524 + 2.3318307872632478612e-853j)  +/-  (2.15e-85, 1.88e-200j)
| (0.023809523809523809524 + 1.3172503536275791328e-853j)  +/-  (2.71e-85, 2.37e-200j)
| (0.023809523809523809524 + 8.4174750040563310054e-854j)  +/-  (3.13e-85, 2.72e-200j)
| (0.023809523809523809524 - 9.6405419748594245722e-854j)  +/-  (7.86e-86, 6.9e-201j)
| (0.023809523809523809524 - 1.6956190937379591945e-853j)  +/-  (1.69e-86, 1.5e-201j)
| (0.023809523809523809524 - 2.6419087342509028213e-853j)  +/-  (2.4e-86, 2.1e-201j)
| (0.023809523809523809524 + 1.5487227449695803358e-853j)  +/-  (1.42e-86, 1.27e-201j)
| (0.023809523809523809524 + 9.1788029813535339068e-854j)  +/-  (9.11e-87, 7.16e-202j)
