Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 5 30
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 30 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^39 - 4054133533663046530151764713664689659180736096/845539399497391266332019985565096931719317*t^37 + 7023031957800301457157822188923678108203167577792/10992012193466086462316259812346260112351121*t^35 - 551028601925426430966690807090096301755031092114990/10992012193466086462316259812346260112351121*t^33 + 28417359252958387656608830349226950037051580644050790/10992012193466086462316259812346260112351121*t^31 - 1018637537094272337153959713516617541811907066560662185/10992012193466086462316259812346260112351121*t^29 + 52360852535354521421543673746556571828123593861406333635/21984024386932172924632519624692520224702242*t^27 - 151014182718084970298872877634976968081580988099364068985/3382157597989565065328079942260387726877268*t^25 + 1040854391549818612415399457333198011798167567474015417125/1691078798994782532664039971130193863438634*t^23 - 84521705696773165991418370592913404572374974569648610215125/13528630391958260261312319769041550907509072*t^21 + 1258263711542387363536960206931767222811528413861758925238875/27057260783916520522624639538083101815018144*t^19 - 3402052799052889226532561688833328002894648630886648439866125/13528630391958260261312319769041550907509072*t^17 + 105336772061017272862371670991159509336962047285376324149546625/108229043135666082090498558152332407260072576*t^15 - 571018262494109043336039626319764962494729314260903114789794375/216458086271332164180997116304664814520145152*t^13 + 2100722041199728944394008291122124133751396379653976519087298125/432916172542664328361994232609329629040290304*t^11 - 5008989108836112745761702006183010664472881073219548361995424375/865832345085328656723988465218659258080580608*t^9 + 14462380397535414513503124333658476281847856340206058957955751875/3463329380341314626895953860874637032322322432*t^7 - 5728439596622854641284299259043482469763140394825136645014160625/3463329380341314626895953860874637032322322432*t^5 + 2174499594116370881128893693681099296900937308817535855397540625/6926658760682629253791907721749274064644644864*t^3 - 598452682048084449352711595522475942733186027630331044574053125/27706635042730517015167630886997096258578579456*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
Sufficient bits for target precision reached
Positive weights:   35 out of 39
Indefinite weights: 0 out of 39
Negative weights:   4 out of 39
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
