Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 38
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Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
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Trying to find an order 38 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
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Ending with final polynomial:
P : 4*t^43 - 13538790826894975698918133043106201220877/8245215608705997557673176628566037678*t^41 + 5023791792361870677802820803790254245787457/16490431217411995115346353257132075356*t^39 - 372469002459309004732526088760107147733226209/10993620811607996743564235504754716904*t^37 + 18512296044115847598350252455393392225511764629/7329080541071997829042823669836477936*t^35 - 980382441175174613373656618407243249627195433575/7329080541071997829042823669836477936*t^33 + 38134282692972321006511099015851214870110432777225/7329080541071997829042823669836477936*t^31 - 2222537707512782775144512388699729710751150702543015/14658161082143995658085647339672955872*t^29 + 98125793794491892210931737999407051502733339600862315/29316322164287991316171294679345911744*t^27 - 6595384843580320032199012139318305705821375425569350015/117265288657151965264685178717383646976*t^25 + 168679028940576238039456860502846413774988645983683796375/234530577314303930529370357434767293952*t^23 - 3267536592708051596862914385435597251301077779264037212125/469061154628607861058740714869534587904*t^21 + 47505015657659265791461917760450352457800901649813670944875/938122309257215722117481429739069175808*t^19 - 63899222459136357344652567135794404148023728985129957864125/234530577314303930529370357434767293952*t^17 + 1996878894183585434068273480712932241394511529114593522525125/1876244618514431444234962859478138351616*t^15 - 11038395946094716623086447532106293222163105582003240115401875/3752489237028862888469925718956276703232*t^13 + 10434108225101370409727275397782870015412941494493299736768125/1876244618514431444234962859478138351616*t^11 - 413033826811243223127466192473359835332333449423217476712923125/60039827792461806215518811503300427251712*t^9 + 630277541799102361891880440491596969650443660214147650712910625/120079655584923612431037623006600854503424*t^7 - 544747462033753238361273889135041681063248387186664572957881875/240159311169847224862075246013201709006848*t^5 + 228698445490860556809413789831786310962768746103255596990228125/480318622339694449724150492026403418013696*t^3 - 15520386894389696408665506786559774420695104982384131697853125/480318622339694449724150492026403418013696*t
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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:   41 out of 43
Indefinite weights: 0 out of 43
Negative weights:   2 out of 43
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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