Starting with polynomial:
P : 2*t
Extension levels are: 1 4 32
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P2 : 2*t^5 - 10*t^3 + 15/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^37 - 58546143341873950838/95149754265757479*t^35 + 112260395072761551226535/1332096559720604706*t^33 - 1510397249094039570452540/222016093286767451*t^31 + 5531610879585775263411275/15311454709432238*t^29 - 29180615900294918512539955/2187350672776034*t^27 + 3089800869190856258172372495/8749402691104136*t^25 - 29793831101313851468212333875/4374701345552068*t^23 + 6741552286776891652982423742375/69995221528833088*t^21 - 69844908123217882268065894674375/69995221528833088*t^19 + 2104047354354544776245230041647625/279980886115332352*t^17 - 2837352316797528128975088988864875/69995221528833088*t^15 + 85699221252513022694669549866070625/559961772230664704*t^13 - 218956513983474245951939792242291875/559961772230664704*t^11 + 1441774273826432756148539635281121875/2239847088922658816*t^9 - 710554838549698803571692201328033125/1119923544461329408*t^7 + 11942582162355816791843849902026575625/35837553422762541056*t^5 - 2714455149602787787643100125575228125/35837553422762541056*t^3 + 664838004747515679748392921831009375/143350213691050164224*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:   37 out of 37
Indefinite weights: 0 out of 37
Negative weights:   0 out of 37
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-7.5508900351331199372 - 1.4042420098533417891e-939j)  +/-  (1.15e-248, 1.15e-248j)
| (-4.3721744177301454185 - 3.7788164485376687703e-954j)  +/-  (1.48e-246, 1.48e-246j)
| (-6.8509889008016275696 - 1.2037218850580552145e-969j)  +/-  (1.02e-247, 1.02e-247j)
| (7.5508900351331199372 + 1.4055057605635690337e-982j)  +/-  (1.08e-248, 1.08e-248j)
| (-4.807601744034108798 + 5.8329139499954479665e-979j)  +/-  (1.94e-246, 1.94e-246j)
| (-5.7469610619721081159 + 6.5833520851452136452e-986j)  +/-  (1.02e-246, 1.02e-246j)
| (6.268799549686576874 - 5.7067471775960000747e-993j)  +/-  (4.47e-247, 4.47e-247j)
| (5.7469610619721081159 + 2.01802490955231437e-992j)  +/-  (1.07e-246, 1.07e-246j)
| (-1.3039614782147112945 - 2.1259873234506316487e-997j)  +/-  (7.38e-251, 7.38e-251j)
| (3.1520618227027751622 + 1.1444647796732370121e-995j)  +/-  (1.97e-247, 1.97e-247j)
| (-6.268799549686576874 + 3.5724859239897133971e-992j)  +/-  (4.16e-247, 4.16e-247j)
| (2.3895545509889844626 + 1.8211806711072627843e-998j)  +/-  (1.72e-248, 1.72e-248j)
| (-1.6582240378081120373 + 8.6975706224977606373e-1000j)  +/-  (5.9e-250, 5.9e-250j)
| (5.263633207528103585 + 2.2666164081019680355e-995j)  +/-  (1.65e-246, 1.65e-246j)
| (2.0201828704560856329 - 1.51286935127575915e-999j)  +/-  (3.44e-249, 3.44e-249j)
| (1.7722089897542826825e-1012 - 4.699413137242556336e-1013j)  +/-  (6.78e-1011, 6.78e-1011j)
| (4.3721744177301454185 + 2.2684765806386306095e-996j)  +/-  (1.52e-246, 1.52e-246j)
| (-2.0201828704560856329 + 1.2768497327909419689e-1000j)  +/-  (3.58e-249, 3.58e-249j)
| (1.3039614782147112945 - 3.6079237859411638023e-1002j)  +/-  (8.23e-251, 8.23e-251j)
| (-2.3895545509889844626 + 1.4477557041749703084e-999j)  +/-  (1.57e-248, 1.57e-248j)
| (-3.1520618227027751622 + 1.5880738979587268308e-997j)  +/-  (1.92e-247, 1.92e-247j)
| (1.6582240378081120373 - 9.6242208925247163628e-1007j)  +/-  (5.85e-250, 5.85e-250j)
| (-2.7666147421064473109 - 4.4813298630820195578e-1003j)  +/-  (6.01e-248, 6.01e-248j)
| (-3.9529802513951788066 + 3.327239442077425972e-1008j)  +/-  (1.07e-246, 1.07e-246j)
| (-0.62463770703891242476 + 1.0113744848057952343e-1030j)  +/-  (8.13e-253, 8.13e-253j)
| (4.807601744034108798 + 2.4324405259734627492e-1020j)  +/-  (1.78e-246, 1.78e-246j)
| (6.8509889008016275696 - 3.9783915300897794168e-1027j)  +/-  (1.1e-247, 1.1e-247j)
| (0.95857246461381850711 - 2.6582927754725655609e-1029j)  +/-  (9.18e-252, 9.18e-252j)
| (-5.263633207528103585 - 6.4626053982404872544e-1026j)  +/-  (1.66e-246, 1.66e-246j)
| (-0.95857246461381850711 - 2.8236702925740005372e-1044j)  +/-  (9.19e-252, 9.19e-252j)
| (3.9529802513951788066 - 2.3884865902862924634e-1038j)  +/-  (1.02e-246, 1.02e-246j)
| (2.7666147421064473109 + 2.3594999737534318339e-1040j)  +/-  (6.06e-248, 6.06e-248j)
| (0.62463770703891242476 - 1.1626840729667221643e-1046j)  +/-  (8.08e-253, 8.08e-253j)
| (3.5469965369475930447 + 3.46328517981107072e-1047j)  +/-  (4.6e-247, 4.6e-247j)
| (-3.5469965369475930447 - 4.3743121366582195407e-1057j)  +/-  (4.92e-247, 4.92e-247j)
| (-0.3056050656203917202 - 9.0563748607557052663e-1074j)  +/-  (6.26e-254, 6.26e-254j)
| (0.3056050656203917202 - 1.8428239433039667682e-1075j)  +/-  (6.26e-254, 6.26e-254j)
-------------------------------------------------
The weights are:
| (7.8773309820135630015e-26 - 8.6297384755243090869e-964j)  +/-  (2.1e-95, 5.03e-219j)
| (1.2012415319038830317e-09 - 1.1617137463018800085e-956j)  +/-  (1.59e-87, 3.81e-211j)
| (1.457397100652228159e-21 + 2.5816154674005399635e-962j)  +/-  (3.76e-94, 8.99e-218j)
| (7.8773309820135630015e-26 - 7.3247529504796166424e-966j)  +/-  (2.07e-98, 4.95e-222j)
| (2.3002624493696673753e-11 + 1.5781153645328685436e-957j)  +/-  (2.27e-89, 5.44e-213j)
| (1.2788987657373754545e-15 + 1.2986048501957601115e-959j)  +/-  (5.69e-92, 1.36e-215j)
| (2.6453806545913565752e-18 - 6.5713613011275635345e-962j)  +/-  (2.45e-96, 5.86e-220j)
| (1.2788987657373754545e-15 + 1.7616317502083340123e-960j)  +/-  (2.28e-95, 5.44e-219j)
| (0.03607503156114633023 - 1.7247868108327890591e-952j)  +/-  (2.22e-78, 5.31e-202j)
| (1.065439070232153041e-05 + 5.5751680668260304611e-955j)  +/-  (5.01e-89, 1.2e-212j)
| (2.6453806545913565752e-18 - 7.0832872030498053186e-961j)  +/-  (4.21e-95, 1.01e-218j)
| (0.00069739586801630010896 + 7.3211897732076731504e-954j)  +/-  (3.45e-86, 8.25e-210j)
| (0.012923754709752242437 + 8.4675619865961184924e-953j)  +/-  (3.45e-82, 8.25e-206j)
| (2.4516168481765435741e-13 - 2.9677288993500528531e-959j)  +/-  (7.17e-95, 1.72e-218j)
| (0.0034840548902827873177 - 2.1284826906251154226e-953j)  +/-  (2.17e-85, 5.19e-209j)
| (0.1707260709924944956 - 7.3232388761767902244e-952j)  +/-  (2.9e-81, 6.93e-205j)
| (1.2012415319038830317e-09 - 3.0971495484224188329e-957j)  +/-  (3.4e-93, 8.12e-217j)
| (0.0034840548902827873177 - 3.6834105554389485685e-953j)  +/-  (9.04e-86, 2.16e-209j)
| (0.03607503156114633023 - 1.2168040691029569041e-952j)  +/-  (2.51e-83, 5.99e-207j)
| (0.00069739586801630010896 + 1.4100205577798114429e-953j)  +/-  (8.06e-88, 1.93e-211j)
| (1.065439070232153041e-05 + 1.3565151569391399565e-954j)  +/-  (4.79e-91, 1.14e-214j)
| (0.012923754709752242437 + 5.4181662049862556778e-953j)  +/-  (2.71e-87, 6.48e-211j)
| (0.00010193207697849650373 - 4.7078513495802228636e-954j)  +/-  (9.24e-90, 2.21e-213j)
| (3.8035676395521828403e-08 + 6.8583726652648629304e-956j)  +/-  (3.12e-93, 7.46e-217j)
| (0.12488078397886620065 - 4.9723254225115805638e-952j)  +/-  (4.36e-86, 1.04e-209j)
| (2.3002624493696673753e-11 + 3.5030402965712073311e-958j)  +/-  (1.41e-96, 3.36e-220j)
| (1.457397100652228159e-21 + 1.2546112558002751653e-963j)  +/-  (1.04e-101, 2.5e-225j)
| (0.076584258355598676076 + 2.4180180778845128634e-952j)  +/-  (5.66e-89, 1.35e-212j)
| (2.4516168481765435741e-13 - 1.6626909706144595659e-958j)  +/-  (5.93e-97, 1.42e-220j)
| (0.076584258355598676076 + 3.1212141685229201758e-952j)  +/-  (8.64e-89, 2.07e-212j)
| (3.8035676395521828403e-08 + 2.1449984792596216723e-956j)  +/-  (1.75e-95, 4.19e-219j)
| (0.00010193207697849650373 - 2.1830523108692001249e-954j)  +/-  (1.59e-93, 3.79e-217j)
| (0.12488078397886620065 - 4.2125206741447146796e-952j)  +/-  (7.84e-91, 1.86e-214j)
| (7.7573710539917525809e-07 - 1.2015173196701083613e-955j)  +/-  (5.8e-95, 1.39e-218j)
| (7.7573710539917525809e-07 - 3.3303354822724391619e-955j)  +/-  (4.96e-95, 1.19e-218j)
| (0.15987828367513700302 + 6.7330946629022666864e-952j)  +/-  (2.24e-91, 5.6e-215j)
| (0.15987828367513700302 + 6.2092814061946589105e-952j)  +/-  (1.63e-91, 3.53e-215j)
