<reponame>petrovp/networkx-related<gh_stars>0
# see sage worksheet "eval-notebook.ipynb"
planar_graph_evals = dict()
planar_graph_evals[100] = {
 'y': 1.00000000000000,
 'x': 0.03654477051892902919200923409811523110400,
 'x*G_1_dx(x,y)': 0.037992196457707622946696582954948631589741128071633,
 'G_1(x,y)': 0.037248430505369042824973498725034635645401138702917,
 'G_1_dx(x,y)': 1.039606923732857132721102449652881587357,
 'G_1_dx_dx(x,y)': 1.1831386535482450389999321330445312377051882142579,
 'D(x*G_1_dx(x,y),y)': 1.0934784864747254921118423994176960106083344797719,
 'S(x*G_1_dx(x,y),y)': 0.043615154275245713984097428006839582739973031335998,
 'P(x*G_1_dx(x,y),y)': 0.047798636953986932275273557847827380997502556642866,
 'H(x*G_1_dx(x,y),y)': 0.0020646952454928458524714135630290468708588917929978,
 'D_dx(x*G_1_dx(x,y),y)': 3.4510220643480115786480381124523971288897329612804,
 'S_dx(x*G_1_dx(x,y),y)': 1.3720218102112701467662895987957102948727694455662,
 'P_dx(x*G_1_dx(x,y),y)': 1.8025589506146115422873445288228306556638684743230,
 'H_dx(x*G_1_dx(x,y),y)': 0.27644130352212988959440398483385617835309504139118,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.038842683760013258631145523348425252872495951787811,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0509944030396399798033431968899880374175244652148,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.018269821376205136213339189728961087061557977799596,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0041293904909856917049428271260580937417177835859951,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.42678349368229802110658841659708347621419552483258,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.5776552900027292571899978627686055234569248166769,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.51202931170089509779174998138073090222593802515345,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21219384716604521971393935299285233778087622386052,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 15.486584147894426379132756288869747012671665283966
}

planar_graph_evals_n1000_mu2 = {
    'D(x*G_1_dx(x,y),y)': 0.637806651054576543789868114281052782226,
    'D_dx(x*G_1_dx(x,y),y)': 0.696569004272650034553258501901187844797,
    'G_1(x,y)': 0.0371350974110612431577106176437625479004,
    'G_1_dx(x,y)': 1.02349152146425090041372148084962313028,
    'G_1_dx_dx(x,y)': 0.6681252576686826620451319953849912978,
    'G_2_dx(x*G_1_dx(x,y),y)': 0.023219842219972369437856348855081731951,
    'G_2_dx_dx(x*G_1_dx(x,y),y)': 0.622880478267134011353588999105453800863,
    'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.000679173063574668255997920599118410526120,
    'H(x*G_1_dx(x,y),y)': 0.0000823773831520415917684978054015601056388,
    'H_dx(x*G_1_dx(x,y),y)': 0.00510427337050757305444031263634611369205,
    'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0000411886915760208,
    'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.00231559123294228,
    'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.011409175629378519,
    'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.3411352773706396,
    'P(x*G_1_dx(x,y),y)': 0.00938930779484682350336768502426592529014,
    'P_dx(x*G_1_dx(x,y),y)': 0.271262998936713526179079307546743223900,
    'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.04589839549189142,
    'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.4674525884161968,
    'S(x*G_1_dx(x,y),y)': 0.0149266596473254870549308539222398010276,
    'S_dx(x*G_1_dx(x,y),y)': 0.420201731965428935319738881718098507204,
    'x': 0.0367100483755473011833298788754433904407,
    'x*G_1_dx(x,y)': 0.0375724232649151595081505057178980179655,
    'y': 0.61340830622925219163980107752914549580
}

planar_graph_evals[1000] = {
 'y': 1.00000000000000,
 'x': 0.03671004837554730118332987887544339044065,
 'x*G_1_dx(x,y)': 0.038171203376643644932014960539203180819890311777937,
 'G_1(x,y)': 0.037420270675653890807141324989986296689755860699002,
 'G_1_dx(x,y)': 1.039802589910744832755392095781934777504,
 'G_1_dx_dx(x,y)': 1.1846774415007042255080936408349599723174687133972,
 'D(x*G_1_dx(x,y),y)': 1.0941036513737400444294943944658919824857863062393,
 'S(x*G_1_dx(x,y),y)': 0.043861527521017788098635026217455315577374198398717,
 'P(x*G_1_dx(x,y),y)': 0.048125221487014814416805062440615652648842943383894,
 'H(x*G_1_dx(x,y),y)': 0.0021169023657074419140543058078210142595691644566527,
 'D_dx(x*G_1_dx(x,y),y)': 3.5519657293342069199248022890390899314324753074337,
 'S_dx(x*G_1_dx(x,y),y)': 1.3820896025616209150347379553996417363353285344079,
 'P_dx(x*G_1_dx(x,y),y)': 1.8557909831586278129625581473041392395004471367148,
 'H_dx(x*G_1_dx(x,y),y)': 0.31408514361395819192750618633530895559669963631101,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039030877742186944047923311524402278027965185073368,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0517284581204707879884744643796965113901396705080,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.020669113454789829097981966502211822146844042760483,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042338047314148838281086116156420285191383289133057,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.48133832193364833465681132049731034459750131203543,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.7337737924641265514322883004606181310461553271411,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.55930911997651372481201904174329609429936881296714,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21625624230717226596682304599097962863263103886293,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 17.687826318309889133589031505038128365358892695421
}



planar_graph_evals[10000] = {
 'y': 1.00000000000000,
 'x': 0.03672657616120912838246194335317620637431,
 'x*G_1_dx(x,y)': 0.038189108193299681479283219542295950729711490316940,
 'G_1(x,y)': 0.037437456471808779342268850532987352290272558586290,
 'G_1_dx(x,y)': 1.039822171978973895818422608241293242762,
 'G_1_dx_dx(x,y)': 1.1849448438620223820868768620583441284219558133069,
 'D(x*G_1_dx(x,y),y)': 1.0941674910532683943636113933151918469892502370475,
 'S(x*G_1_dx(x,y),y)': 0.043886294604825077239932295043990762516735267629604,
 'P(x*G_1_dx(x,y),y)': 0.048158576187246288974809276848611085808019956479541,
 'H(x*G_1_dx(x,y),y)': 0.0021226202611970281488698214225899986644950129383591,
 'D_dx(x*G_1_dx(x,y),y)': 3.5848049993630618445027588783956899941296455380791,
 'S_dx(x*G_1_dx(x,y),y)': 1.3848915690224881021072526063234671680861320440743,
 'P_dx(x*G_1_dx(x,y),y)': 1.8730006596060386676687907578949963572474461960357,
 'H_dx(x*G_1_dx(x,y),y)': 0.32691277073453507472671551417722646879606729796907,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039049710051328373527902391160990973331014672916284,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0518984761192853005799756361042239051992100802249,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021468305802072359246999714551234962349480746635258,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042452405223940562977396428451799973289900258767183,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.49990616153482210807099478117326916620599397208407,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.7859148613861976484300825888244909204478320575580,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.57493851558207939193703168856805772159925532342481,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21670364168399074747420924986339460290140346238780,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.462969459803365888397738940951942645827212794397
}

planar_graph_evals[50000] = {
 'y': 1.00000000000000,
 'x': 0.03672804529771240191127368241786356779064,
 'x*G_1_dx(x,y)': 0.038190699773108873509530429171252310280853555452210,
 'G_1(x,y)': 0.037438984113797324086314477009119583407265518046937,
 'G_1_dx(x,y)': 1.039823912847620120955360847120904431004,
 'G_1_dx_dx(x,y)': 1.1849961181521262606068517879979887027457879813683,
 'D(x*G_1_dx(x,y),y)': 1.0941732024356460244914787065472494641241503501508,
 'S(x*G_1_dx(x,y),y)': 0.043888499248201400365286057364954770384942906108484,
 'P(x*G_1_dx(x,y),y)': 0.048161560292740014966325678032621863722615247690114,
 'H(x*G_1_dx(x,y),y)': 0.0021231428947046091598669711496728300165921963522185,
 'D_dx(x*G_1_dx(x,y),y)': 3.5932766882260278681788920116281659828233600365285,
 'S_dx(x*G_1_dx(x,y),y)': 1.3855773484300057356411944439900801006170238008230,
 'P_dx(x*G_1_dx(x,y),y)': 1.8774316549466235026620084080766345908806819499923,
 'H_dx(x*G_1_dx(x,y),y)': 0.33026768484939862987568915956145129132565428571323,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051384258748716431020261882095876878426215074877,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519370349046177688697971723385554536461622087866,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021675803217681974990258419711013306020080351967756,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042462857894092183197339422993456600331843927044398,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50476105289745452830607345633560529814676000317593,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.7994708206761306095348789296972497375343665353468,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.57898872059396039888336233966277697670890091279202,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21674462484342799740385213646410694327878737323366,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.667830641599664437727287475260498929685853110897
}

planar_graph_evals[100000] = {
 'y': 1.00000000000000,
 'x': 0.03672822893977531110237514980094948796768,
 'x*G_1_dx(x,y)': 0.038190898721171370036003409077460922894948329323323,
 'G_1(x,y)': 0.037439175069225731191235600703417025280975287520611,
 'G_1_dx(x,y)': 1.039824130473275161708604216760604512018,
 'G_1_dx_dx(x,y)': 1.1850554578535207911416157194591322669565462793531,
 'D(x*G_1_dx(x,y),y)': 1.0941739174997540123358794104620695291139630151150,
 'S(x*G_1_dx(x,y),y)': 0.043888774921209258486429356716117393416839850171373,
 'P(x*G_1_dx(x,y),y)': 0.048161933902767186853758267264153508221875464089642,
 'H(x*G_1_dx(x,y),y)': 0.0021232086757775669956917864817986274752477008539804,
 'D_dx(x*G_1_dx(x,y),y)': 3.5952887643261171142881042662646677531690895094872,
 'S_dx(x*G_1_dx(x,y),y)': 1.3857380054161585593744158853666858381895639462827,
 'P_dx(x*G_1_dx(x,y),y)': 1.8784835198894217426392816814488760680533761357176,
 'H_dx(x*G_1_dx(x,y),y)': 0.33106723902053681227440669944910584692614942748686,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051593540414791106018959021390766845221920154889,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519458767903701616940122577561292363355639274885,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021725162017060628499073019168213881084000484681445,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042464173515551339913835729635972549504954017079609,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50591801623486842236093189285303945592018351646883,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8026967055948650570646425832555862585612482729211,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.57995173656414123368385573087388176237130803141858,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21674978614960177385846445830378687994092175112164,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.716784842522454849435194659733062932786401662554
}

planar_graph_evals[250000] = {
    'y': 1.00000000000000,
 'x': 0.03672833912501305661703603023080104007390,
 'x*G_1_dx(x,y)': 0.038191018090034020416353153879059722304716963179510,
 'G_1(x,y)': 0.037439289642501954256693879561294382140226496548842,
 'G_1_dx(x,y)': 1.039824261045350437805489806315216626191,
 'G_1_dx_dx(x,y)': 1.1850473408426527569397329917878349690717240977446,
 'D(x*G_1_dx(x,y),y)': 1.0941743464370849901995330267107297776230186756442,
 'S(x*G_1_dx(x,y),y)': 0.043888940317328065160857962509606209448058957975442,
 'P(x*G_1_dx(x,y),y)': 0.048162158015998568622505850461567763012273255864109,
 'H(x*G_1_dx(x,y),y)': 0.0021232481037583564161692137395558051626864618046090,
 'D_dx(x*G_1_dx(x,y),y)': 3.5970752322133744547320773326574091139424270205223,
 'S_dx(x*G_1_dx(x,y),y)': 1.3858799352055289439351609184396503636350578834434,
 'P_dx(x*G_1_dx(x,y),y)': 1.8794172739190978697657970021524154952610301453428,
 'H_dx(x*G_1_dx(x,y),y)': 0.33177802308874764103111941206534325504633899173602,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051719109047455040629844215285093700987632114158,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519796100298503936874129312736387859493811759234,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021769010889320911635500394993886683145476668091136,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042464964540334347388910712900241235038182264866599,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50694650637797629131766965185833077089686344073414,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8055628934751694369394922737772429788885548316093,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58080711419917215277047606276208277278683756177902,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675288991091215069633592809739866468874563850075,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.760346312150425912676283639298555019699070920628
}

planar_graph_evals[500000] = {
 'y': 1.00000000000000,
 'x': 0.03672837585342563845525632370741822410931,
 'x*G_1_dx(x,y)': 0.038191057879744342317118132117778249714245678459553,
 'G_1(x,y)': 0.037439327833597230254701804813180182599854293887189,
 'G_1_dx(x,y)': 1.039824304569233676695923563089636964038,
 'G_1_dx_dx(x,y)': 1.1850216354604716146090077338203157555353491994519,
 'D(x*G_1_dx(x,y),y)': 1.0941744899074149114003134944524332488702587430545,
 'S(x*G_1_dx(x,y),y)': 0.043888995488122579071683973580629397076174594104219,
 'P(x*G_1_dx(x,y),y)': 0.048162232977073159305672898111607933227553969354129,
 'H(x*G_1_dx(x,y),y)': 0.0021232614422191730229566227601959185665301795961171,
 'D_dx(x*G_1_dx(x,y),y)': 3.5979767715532305688212961973655679402761525418098,
 'S_dx(x*G_1_dx(x,y),y)': 1.3859513062594264607438872193319384362605793575528,
 'P_dx(x*G_1_dx(x,y),y)': 1.8798884322609780259413771275947762179966341622597,
 'H_dx(x*G_1_dx(x,y),y)': 0.33213703303282608213603185043885328601893902199728,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051760967429282777476030792224093844509787194606,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519575003480250253956253193689802265826736181742,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021791147801272383840341714356263542874658937250948,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465228844383460459132455203918371330603591922331,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50746597883672958348263946124515501365436581247884,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8070100261901544182874170473806321496924746159617,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58123889973412499480722953125387768692119323325942,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675392725165312728074916592615600998168387245132,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.782363964449614892434122893479290012706232280611
}

planar_graph_evals[750000] = {
 'y': 1.00000000000000,
 'x': 0.03672838809622983240132975486629061878778,
 'x*G_1_dx(x,y)': 0.038191071142965097242108233957034880622426256327925,
 'G_1(x,y)': 0.037439340563962666436246107645998975608670692338710,
 'G_1_dx(x,y)': 1.039824319077159290804138378219261588595,
 'G_1_dx_dx(x,y)': 1.1850226901372243632934706431974170352946809121526,
 'D(x*G_1_dx(x,y),y)': 1.0941745376307340417585316178517025962930547390441,
 'S(x*G_1_dx(x,y),y)': 0.043889013870502976357555604370678550699573541277599,
 'P(x*G_1_dx(x,y),y)': 0.048162257911785697147269890426711001884590817660245,
 'H(x*G_1_dx(x,y),y)': 0.0021232658484453682537061230543130437088903801062250,
 'D_dx(x*G_1_dx(x,y),y)': 3.5983760999506990408320300103419514036566421921899,
 'S_dx(x*G_1_dx(x,y),y)': 1.3859828647042288777677481280047605032091603405158,
 'P_dx(x*G_1_dx(x,y),y)': 1.8800971144647237658649122444770539431863954215655,
 'H_dx(x*G_1_dx(x,y),y)': 0.33229612078174639719936963786013695726108643010863,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051774919784787570201947282866377250416970446582,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519592087510525717957340497223446595088049776321,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021800955023507586301071586230174756151044785112570,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465316968907365074122461086260874177807602124490,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50769617053811313695668587063727851939441816575898,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8076511746078155944017553592260221865844119595500,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58143018145065348069900433231240238673771005376624,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675427311241257711437682967878241714057150706617,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.792123879975436604847196299230235835769934543175
}

planar_graph_evals[1000000] = {
 'y': 1.00000000000000,
 'x': 0.03672839421763192937436647044572681612702,
 'x*G_1_dx(x,y)': 0.038191077774575980199233776473627298116040760198882,
 'G_1(x,y)': 0.037439346929145453210329006137985768748760785299583,
 'G_1_dx(x,y)': 1.039824326331215200224472935739271445235,
 'G_1_dx_dx(x,y)': 1.1850243037682476125388043144957046596224483119359,
 'D(x*G_1_dx(x,y),y)': 1.0941745614945346701067169348224595014477948478899,
 'S(x*G_1_dx(x,y),y)': 0.043889023061862874084965131596885982815610016583877,
 'P(x*G_1_dx(x,y),y)': 0.048162270380260833963667922443117642631759644436441,
 'H(x*G_1_dx(x,y),y)': 0.0021232680524109620580838807824558760004251868695519,
 'D_dx(x*G_1_dx(x,y),y)': 3.5986141807781736569594438177171178934290657817242,
 'S_dx(x*G_1_dx(x,y),y)': 1.3860016640301035836808601038338424609790679497884,
 'P_dx(x*G_1_dx(x,y),y)': 1.8802215276795817897910575551632388091802322193130,
 'H_dx(x*G_1_dx(x,y),y)': 0.33239098906848828348752615872003662326976561262274,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051781895972214810606008773492308888543276220349,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519602250452591914715757217380906972078302979230,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021806802662437626172763517358004458010986237556229,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465361048219241161677615649117520008503737391040,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50783343954001801840451642387874400654998441680617,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8080334741318986368488713806629003473626011059865,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58154423177953332734330572940287234329162265560945,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675444611547729199604936938584138876249204090791,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.797944931407955456090405190770294626189440399056
}

planar_graph_evals[2000000] = {
 'y': 1.00000000000000,
 'x': 0.03672840339973507483392154381488111213587,
 'x*G_1_dx(x,y)': 0.038191087721993046034176487947816671634008731241562,
 'G_1(x,y)': 0.037439356476919723695090632715432156226498138775643,
 'G_1_dx(x,y)': 1.039824337212246165906267025185587897180,
 'G_1_dx_dx(x,y)': 1.1850237469004464960241885948360847672155172070526,
 'D(x*G_1_dx(x,y),y)': 1.0941745972935647471789317376312591303457341018159,
 'S(x*G_1_dx(x,y),y)': 0.043889036849166285292107677786519706093891627425951,
 'P(x*G_1_dx(x,y),y)': 0.048162289084713205183546376064814726782398190551129,
 'H(x*G_1_dx(x,y),y)': 0.0021232713596852567032776837799246974694442838388027,
 'D_dx(x*G_1_dx(x,y),y)': 3.5990650062715062781184871381043538856327587478748,
 'S_dx(x*G_1_dx(x,y),y)': 1.3860372295201077843762780264296336222635956325920,
 'P_dx(x*G_1_dx(x,y),y)': 1.8804571065659099617184659400651921842801018463056,
 'H_dx(x*G_1_dx(x,y),y)': 0.33257067018548853202374317160952807908906126897717,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051792360268317188640761377130425519689865302160,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519621448554507988168272847445351590602815248547,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021817876753847893378334350741951863258321290580720,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465427193705134065553675598493949388885676776082,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50809342689914002521015157960213927780159485541176,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8087574812761005533790597860348754404625402574366,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58176021088845417337621938451036447891112866757851,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675470573313946242346180991912795990829489312808,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.808971988728386506139150041458824383364669888835
}

planar_graph_evals[5000000] = {
 'y': 1.00000000000000,
 'x': 0.03672840890899696210965458783637368974118,
 'x*G_1_dx(x,y)': 0.038191093690443201640296295669494871867553821954360,
 'G_1(x,y)': 0.037439362205584337687780167500169050274878294284694,
 'G_1_dx(x,y)': 1.039824343740823442143349600465277922753,
 'G_1_dx_dx(x,y)': 1.1850380782584510846504518916514101152958358995846,
 'D(x*G_1_dx(x,y),y)': 1.0941746187755092082947171737094168758804010472449,
 'S(x*G_1_dx(x,y),y)': 0.043889045121747444642565987083390192081271832831325,
 'P(x*G_1_dx(x,y),y)': 0.048162300308704781808285144819439457316303485529883,
 'H(x*G_1_dx(x,y),y)': 0.0021232733450569818438660418065872264828257288837201,
 'D_dx(x*G_1_dx(x,y),y)': 3.5994651133285070219539063207961026978209169347505,
 'S_dx(x*G_1_dx(x,y),y)': 1.3860687581503519583739457812966525625949053640216,
 'P_dx(x*G_1_dx(x,y),y)': 1.8806661740914530957428787069181992514738408773424,
 'H_dx(x*G_1_dx(x,y),y)': 0.33273018108670196783708183258125088375217069338643,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051798638856635582570100119083171433598758765061,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519638436149689017782455813305813129131732392961,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021827706211008428999222549454688360349154656010633,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465466901139636877320836131744529656514577674398,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50832422815238631268395919671319411110675060462899,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8094001372791800460729016247631120473561344848378,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58195190904963682687451072951546161075808170746264,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675486158963428079929853353755259280925419833015,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.818763336005659090479539746631618588356597613027
}

planar_graph_evals[10000000] = {
 'y': 1.00000000000000,
 'x': 0.03672841074541759120156560251020454894295,
 'x*G_1_dx(x,y)': 0.038191095679927525946179627438553089511816521689602,
 'G_1(x,y)': 0.037439364115139215003818748536060148142108244505674,
 'G_1_dx(x,y)': 1.039824345917289498683965498869179567476,
 'G_1_dx_dx(x,y)': 1.1850404367416613362787806906663648549420010371043,
 'D(x*G_1_dx(x,y),y)': 1.0941746259367777706128031133590973829544113341583,
 'S(x*G_1_dx(x,y),y)': 0.043889047879324405471001570039881591702980397725496,
 'P(x*G_1_dx(x,y),y)': 0.048162304050359484867115514038870448674381696101020,
 'H(x*G_1_dx(x,y),y)': 0.0021232740070938802746860292803453425770492403318060,
 'D_dx(x*G_1_dx(x,y),y)': 3.5996667938576622171537494965895828080195501987504,
 'S_dx(x*G_1_dx(x,y),y)': 1.3860846379505853996155774872194357493144305028471,
 'P_dx(x*G_1_dx(x,y),y)': 1.8807715550007596475409510393402039661117015777091,
 'H_dx(x*G_1_dx(x,y),y)': 0.33281060090631716999722097002994309259341811819419,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051800731723013755678013356384239088237087868651,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519646980958717459656263640755861225033278155920,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021832661342921557767866380019158437958437714998511,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465480141877605493720585606906851540984806636081,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50844058969732520832532819646178574873247863258153,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8097241144302011040891789078218574697670027073702,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58204854370090537988257674957016397324719903780239,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675491356280849326308440649098100350667271150354,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.823700553939293956470100703330197223999793620904
}

planar_graph_evals[20000000] = {
 'y': 1.00000000000000,
 'x': 0.03672841166362790574752110984711997854383,
 'x*G_1_dx(x,y)': 0.038191096674669413691666094515429179809904982424512,
 'G_1(x,y)': 0.037439365069916659318386060369958479620910615471318,
 'G_1_dx(x,y)': 1.039824347005208075100426676292054270417,
 'G_1_dx_dx(x,y)': 1.1851032701478478161189712119925785633868144549138,
 'D(x*G_1_dx(x,y),y)': 1.0941746295175839901037182149917860234237106827719,
 'S(x*G_1_dx(x,y),y)': 0.043889049258126118518109516606551528515387842680713,
 'P(x*G_1_dx(x,y),y)': 0.048162305921276675964451242253358308049259260404692,
 'H(x*G_1_dx(x,y),y)': 0.0021232743381811956211574561318761868590635796865263,
 'D_dx(x*G_1_dx(x,y),y)': 3.5998094144201099167165353729358575475809785647870,
 'S_dx(x*G_1_dx(x,y),y)': 1.3860958623755534796866599999275839864734834985573,
 'P_dx(x*G_1_dx(x,y),y)': 1.8808460750307079201587035596436049980381917936782,
 'H_dx(x*G_1_dx(x,y),y)': 0.33286747701384851687117181336466856306930327255156,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051801778156646436437879447328211277743434847025,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519653016204305992337954308858107773655083629198,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021836165592865796363128113182705520815727756131438,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465486763623912423149122637523737181271593730531,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50852288507562748435189788815109527159441369829122,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8099532328682937939188281863966829951813512989510,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58211688238250726857851462500990649851134711594850,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675493955527111241196177404062488936121713008948,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.827192660398022647061594621178742553469807013142
}


# N = 100
# J_a and J_a_dx are wrong.
reference_evals = {
    'D(x*G_1_dx(x,y),y)': 1.09347848647472549211184239941769601061,
    'D_dx(x*G_1_dx(x,y),y)': 3.45102206434801157864803811245239712851,

    #'Fusy_K': 0.00206469524549284585247141356302904687086,
    'G_3_arrow(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.00206469524549284585247141356302904687086,

    'Fusy_K_dx': 0.213391746841149010553294208298541737991,
    'Fusy_K_dy': 0.0182698213762051362133391897289610870537,
    'G_1(x,y)': 0.0372484305053690456202661877963311349072,
    'G_1_dx(x,y)': 1.03960692373287371278312170556092216601,
    'G_1_dx_dx(x,y)': 1.1831386535487874823112196643179832576,
    'G_2_dx(x*G_1_dx(x,y),y)': 0.038842683760013258631145523348425252874,
    'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.05099440303963997980334319688998807042,
    'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0182698213762051362133391897289610870537,
    'H(x*G_1_dx(x,y),y)': 0.00206469524549284585247141356302904687086,
    'H_dx(x*G_1_dx(x,y),y)': 0.276441303522129889594403984833856178203,
    'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.00103234762274642,
    'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.106695873420575,
    'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21219385343653063,
    'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 15.48657625114519,
    'K_dx_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 5592.386366298111,
    'K_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 1.729773462783172,
    'K_dy_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 539.8558558558559,
    'K_dy_dx_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 1183895.1899970463,
    'K_snake(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 1.254888507718696,
    'K_snake_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 543.8610354223433,
    'K_snake_dx_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 1277786.7614037835,
    'P(x*G_1_dx(x,y),y)': 0.0477986369539869322752735578478273809975,
    'P_dx(x*G_1_dx(x,y),y)': 1.80255895061461154228734452882283065547,
    'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.5120292887029289,
    'R_b_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 129.2273161413563,
    'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.577655310621243,
    'R_w_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 414.9509202453988,
    'S(x*G_1_dx(x,y),y)': 0.0436151542752457139840974280068395827400,
    'S_dx(x*G_1_dx(x,y),y)': 1.37202181021127014676628959879571029484,
    'x': 0.0365447705189290291920092340981152311040,
    'x*G_1_dx(x,y)': 0.0379921964577076229466965829549486315897,
    'y': 1.00000000000000}

all_evaluations = [
    reference_evals,
    # planar_graph_evals_n100,
    # planar_graph_evals_n1000
    # planar_graph_evals_n10000
]

# see sage worksheet "eval-notebook.ipynb"
planar_graph_evals = dict()
planar_graph_evals[100] = {
 'y': 1.00000000000000,
 'x': 0.03654477051892902919200923409811523110400,
 'x*G_1_dx(x,y)': 0.037992196457707622946696582954948631589741128071633,
 'G_1(x,y)': 0.037248430505369042824973498725034635645401138702917,
 'G_1_dx(x,y)': 1.039606923732857132721102449652881587357,
 'G_1_dx_dx(x,y)': 1.1831386535482450389999321330445312377051882142579,
 'D(x*G_1_dx(x,y),y)': 1.0934784864747254921118423994176960106083344797719,
 'S(x*G_1_dx(x,y),y)': 0.043615154275245713984097428006839582739973031335998,
 'P(x*G_1_dx(x,y),y)': 0.047798636953986932275273557847827380997502556642866,
 'H(x*G_1_dx(x,y),y)': 0.0020646952454928458524714135630290468708588917929978,
 'D_dx(x*G_1_dx(x,y),y)': 3.4510220643480115786480381124523971288897329612804,
 'S_dx(x*G_1_dx(x,y),y)': 1.3720218102112701467662895987957102948727694455662,
 'P_dx(x*G_1_dx(x,y),y)': 1.8025589506146115422873445288228306556638684743230,
 'H_dx(x*G_1_dx(x,y),y)': 0.27644130352212988959440398483385617835309504139118,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.038842683760013258631145523348425252872495951787811,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0509944030396399798033431968899880374175244652148,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.018269821376205136213339189728961087061557977799596,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0041293904909856917049428271260580937417177835859951,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.42678349368229802110658841659708347621419552483258,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.5776552900027292571899978627686055234569248166769,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.51202931170089509779174998138073090222593802515345,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21219384716604521971393935299285233778087622386052,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 15.486584147894426379132756288869747012671665283966
}

planar_graph_evals_n1000_mu2 = {
    'D(x*G_1_dx(x,y),y)': 0.637806651054576543789868114281052782226,
    'D_dx(x*G_1_dx(x,y),y)': 0.696569004272650034553258501901187844797,
    'G_1(x,y)': 0.0371350974110612431577106176437625479004,
    'G_1_dx(x,y)': 1.02349152146425090041372148084962313028,
    'G_1_dx_dx(x,y)': 0.6681252576686826620451319953849912978,
    'G_2_dx(x*G_1_dx(x,y),y)': 0.023219842219972369437856348855081731951,
    'G_2_dx_dx(x*G_1_dx(x,y),y)': 0.622880478267134011353588999105453800863,
    'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.000679173063574668255997920599118410526120,
    'H(x*G_1_dx(x,y),y)': 0.0000823773831520415917684978054015601056388,
    'H_dx(x*G_1_dx(x,y),y)': 0.00510427337050757305444031263634611369205,
    'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0000411886915760208,
    'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.00231559123294228,
    'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.011409175629378519,
    'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.3411352773706396,
    'P(x*G_1_dx(x,y),y)': 0.00938930779484682350336768502426592529014,
    'P_dx(x*G_1_dx(x,y),y)': 0.271262998936713526179079307546743223900,
    'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.04589839549189142,
    'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.4674525884161968,
    'S(x*G_1_dx(x,y),y)': 0.0149266596473254870549308539222398010276,
    'S_dx(x*G_1_dx(x,y),y)': 0.420201731965428935319738881718098507204,
    'x': 0.0367100483755473011833298788754433904407,
    'x*G_1_dx(x,y)': 0.0375724232649151595081505057178980179655,
    'y': 0.61340830622925219163980107752914549580
}

planar_graph_evals[1000] = {
 'y': 1.00000000000000,
 'x': 0.03671004837554730118332987887544339044065,
 'x*G_1_dx(x,y)': 0.038171203376643644932014960539203180819890311777937,
 'G_1(x,y)': 0.037420270675653890807141324989986296689755860699002,
 'G_1_dx(x,y)': 1.039802589910744832755392095781934777504,
 'G_1_dx_dx(x,y)': 1.1846774415007042255080936408349599723174687133972,
 'D(x*G_1_dx(x,y),y)': 1.0941036513737400444294943944658919824857863062393,
 'S(x*G_1_dx(x,y),y)': 0.043861527521017788098635026217455315577374198398717,
 'P(x*G_1_dx(x,y),y)': 0.048125221487014814416805062440615652648842943383894,
 'H(x*G_1_dx(x,y),y)': 0.0021169023657074419140543058078210142595691644566527,
 'D_dx(x*G_1_dx(x,y),y)': 3.5519657293342069199248022890390899314324753074337,
 'S_dx(x*G_1_dx(x,y),y)': 1.3820896025616209150347379553996417363353285344079,
 'P_dx(x*G_1_dx(x,y),y)': 1.8557909831586278129625581473041392395004471367148,
 'H_dx(x*G_1_dx(x,y),y)': 0.31408514361395819192750618633530895559669963631101,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039030877742186944047923311524402278027965185073368,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0517284581204707879884744643796965113901396705080,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.020669113454789829097981966502211822146844042760483,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042338047314148838281086116156420285191383289133057,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.48133832193364833465681132049731034459750131203543,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.7337737924641265514322883004606181310461553271411,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.55930911997651372481201904174329609429936881296714,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21625624230717226596682304599097962863263103886293,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 17.687826318309889133589031505038128365358892695421
}



planar_graph_evals[10000] = {
 'y': 1.00000000000000,
 'x': 0.03672657616120912838246194335317620637431,
 'x*G_1_dx(x,y)': 0.038189108193299681479283219542295950729711490316940,
 'G_1(x,y)': 0.037437456471808779342268850532987352290272558586290,
 'G_1_dx(x,y)': 1.039822171978973895818422608241293242762,
 'G_1_dx_dx(x,y)': 1.1849448438620223820868768620583441284219558133069,
 'D(x*G_1_dx(x,y),y)': 1.0941674910532683943636113933151918469892502370475,
 'S(x*G_1_dx(x,y),y)': 0.043886294604825077239932295043990762516735267629604,
 'P(x*G_1_dx(x,y),y)': 0.048158576187246288974809276848611085808019956479541,
 'H(x*G_1_dx(x,y),y)': 0.0021226202611970281488698214225899986644950129383591,
 'D_dx(x*G_1_dx(x,y),y)': 3.5848049993630618445027588783956899941296455380791,
 'S_dx(x*G_1_dx(x,y),y)': 1.3848915690224881021072526063234671680861320440743,
 'P_dx(x*G_1_dx(x,y),y)': 1.8730006596060386676687907578949963572474461960357,
 'H_dx(x*G_1_dx(x,y),y)': 0.32691277073453507472671551417722646879606729796907,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039049710051328373527902391160990973331014672916284,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0518984761192853005799756361042239051992100802249,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021468305802072359246999714551234962349480746635258,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042452405223940562977396428451799973289900258767183,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.49990616153482210807099478117326916620599397208407,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.7859148613861976484300825888244909204478320575580,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.57493851558207939193703168856805772159925532342481,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21670364168399074747420924986339460290140346238780,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.462969459803365888397738940951942645827212794397
}

planar_graph_evals[50000] = {
 'y': 1.00000000000000,
 'x': 0.03672804529771240191127368241786356779064,
 'x*G_1_dx(x,y)': 0.038190699773108873509530429171252310280853555452210,
 'G_1(x,y)': 0.037438984113797324086314477009119583407265518046937,
 'G_1_dx(x,y)': 1.039823912847620120955360847120904431004,
 'G_1_dx_dx(x,y)': 1.1849961181521262606068517879979887027457879813683,
 'D(x*G_1_dx(x,y),y)': 1.0941732024356460244914787065472494641241503501508,
 'S(x*G_1_dx(x,y),y)': 0.043888499248201400365286057364954770384942906108484,
 'P(x*G_1_dx(x,y),y)': 0.048161560292740014966325678032621863722615247690114,
 'H(x*G_1_dx(x,y),y)': 0.0021231428947046091598669711496728300165921963522185,
 'D_dx(x*G_1_dx(x,y),y)': 3.5932766882260278681788920116281659828233600365285,
 'S_dx(x*G_1_dx(x,y),y)': 1.3855773484300057356411944439900801006170238008230,
 'P_dx(x*G_1_dx(x,y),y)': 1.8774316549466235026620084080766345908806819499923,
 'H_dx(x*G_1_dx(x,y),y)': 0.33026768484939862987568915956145129132565428571323,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051384258748716431020261882095876878426215074877,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519370349046177688697971723385554536461622087866,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021675803217681974990258419711013306020080351967756,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042462857894092183197339422993456600331843927044398,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50476105289745452830607345633560529814676000317593,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.7994708206761306095348789296972497375343665353468,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.57898872059396039888336233966277697670890091279202,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21674462484342799740385213646410694327878737323366,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.667830641599664437727287475260498929685853110897
}

planar_graph_evals[100000] = {
 'y': 1.00000000000000,
 'x': 0.03672822893977531110237514980094948796768,
 'x*G_1_dx(x,y)': 0.038190898721171370036003409077460922894948329323323,
 'G_1(x,y)': 0.037439175069225731191235600703417025280975287520611,
 'G_1_dx(x,y)': 1.039824130473275161708604216760604512018,
 'G_1_dx_dx(x,y)': 1.1850554578535207911416157194591322669565462793531,
 'D(x*G_1_dx(x,y),y)': 1.0941739174997540123358794104620695291139630151150,
 'S(x*G_1_dx(x,y),y)': 0.043888774921209258486429356716117393416839850171373,
 'P(x*G_1_dx(x,y),y)': 0.048161933902767186853758267264153508221875464089642,
 'H(x*G_1_dx(x,y),y)': 0.0021232086757775669956917864817986274752477008539804,
 'D_dx(x*G_1_dx(x,y),y)': 3.5952887643261171142881042662646677531690895094872,
 'S_dx(x*G_1_dx(x,y),y)': 1.3857380054161585593744158853666858381895639462827,
 'P_dx(x*G_1_dx(x,y),y)': 1.8784835198894217426392816814488760680533761357176,
 'H_dx(x*G_1_dx(x,y),y)': 0.33106723902053681227440669944910584692614942748686,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051593540414791106018959021390766845221920154889,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519458767903701616940122577561292363355639274885,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021725162017060628499073019168213881084000484681445,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042464173515551339913835729635972549504954017079609,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50591801623486842236093189285303945592018351646883,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8026967055948650570646425832555862585612482729211,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.57995173656414123368385573087388176237130803141858,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21674978614960177385846445830378687994092175112164,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.716784842522454849435194659733062932786401662554
}

planar_graph_evals[250000] = {
    'y': 1.00000000000000,
 'x': 0.03672833912501305661703603023080104007390,
 'x*G_1_dx(x,y)': 0.038191018090034020416353153879059722304716963179510,
 'G_1(x,y)': 0.037439289642501954256693879561294382140226496548842,
 'G_1_dx(x,y)': 1.039824261045350437805489806315216626191,
 'G_1_dx_dx(x,y)': 1.1850473408426527569397329917878349690717240977446,
 'D(x*G_1_dx(x,y),y)': 1.0941743464370849901995330267107297776230186756442,
 'S(x*G_1_dx(x,y),y)': 0.043888940317328065160857962509606209448058957975442,
 'P(x*G_1_dx(x,y),y)': 0.048162158015998568622505850461567763012273255864109,
 'H(x*G_1_dx(x,y),y)': 0.0021232481037583564161692137395558051626864618046090,
 'D_dx(x*G_1_dx(x,y),y)': 3.5970752322133744547320773326574091139424270205223,
 'S_dx(x*G_1_dx(x,y),y)': 1.3858799352055289439351609184396503636350578834434,
 'P_dx(x*G_1_dx(x,y),y)': 1.8794172739190978697657970021524154952610301453428,
 'H_dx(x*G_1_dx(x,y),y)': 0.33177802308874764103111941206534325504633899173602,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051719109047455040629844215285093700987632114158,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519796100298503936874129312736387859493811759234,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021769010889320911635500394993886683145476668091136,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042464964540334347388910712900241235038182264866599,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50694650637797629131766965185833077089686344073414,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8055628934751694369394922737772429788885548316093,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58080711419917215277047606276208277278683756177902,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675288991091215069633592809739866468874563850075,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.760346312150425912676283639298555019699070920628
}

planar_graph_evals[500000] = {
 'y': 1.00000000000000,
 'x': 0.03672837585342563845525632370741822410931,
 'x*G_1_dx(x,y)': 0.038191057879744342317118132117778249714245678459553,
 'G_1(x,y)': 0.037439327833597230254701804813180182599854293887189,
 'G_1_dx(x,y)': 1.039824304569233676695923563089636964038,
 'G_1_dx_dx(x,y)': 1.1850216354604716146090077338203157555353491994519,
 'D(x*G_1_dx(x,y),y)': 1.0941744899074149114003134944524332488702587430545,
 'S(x*G_1_dx(x,y),y)': 0.043888995488122579071683973580629397076174594104219,
 'P(x*G_1_dx(x,y),y)': 0.048162232977073159305672898111607933227553969354129,
 'H(x*G_1_dx(x,y),y)': 0.0021232614422191730229566227601959185665301795961171,
 'D_dx(x*G_1_dx(x,y),y)': 3.5979767715532305688212961973655679402761525418098,
 'S_dx(x*G_1_dx(x,y),y)': 1.3859513062594264607438872193319384362605793575528,
 'P_dx(x*G_1_dx(x,y),y)': 1.8798884322609780259413771275947762179966341622597,
 'H_dx(x*G_1_dx(x,y),y)': 0.33213703303282608213603185043885328601893902199728,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051760967429282777476030792224093844509787194606,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519575003480250253956253193689802265826736181742,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021791147801272383840341714356263542874658937250948,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465228844383460459132455203918371330603591922331,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50746597883672958348263946124515501365436581247884,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8070100261901544182874170473806321496924746159617,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58123889973412499480722953125387768692119323325942,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675392725165312728074916592615600998168387245132,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.782363964449614892434122893479290012706232280611
}

planar_graph_evals[750000] = {
 'y': 1.00000000000000,
 'x': 0.03672838809622983240132975486629061878778,
 'x*G_1_dx(x,y)': 0.038191071142965097242108233957034880622426256327925,
 'G_1(x,y)': 0.037439340563962666436246107645998975608670692338710,
 'G_1_dx(x,y)': 1.039824319077159290804138378219261588595,
 'G_1_dx_dx(x,y)': 1.1850226901372243632934706431974170352946809121526,
 'D(x*G_1_dx(x,y),y)': 1.0941745376307340417585316178517025962930547390441,
 'S(x*G_1_dx(x,y),y)': 0.043889013870502976357555604370678550699573541277599,
 'P(x*G_1_dx(x,y),y)': 0.048162257911785697147269890426711001884590817660245,
 'H(x*G_1_dx(x,y),y)': 0.0021232658484453682537061230543130437088903801062250,
 'D_dx(x*G_1_dx(x,y),y)': 3.5983760999506990408320300103419514036566421921899,
 'S_dx(x*G_1_dx(x,y),y)': 1.3859828647042288777677481280047605032091603405158,
 'P_dx(x*G_1_dx(x,y),y)': 1.8800971144647237658649122444770539431863954215655,
 'H_dx(x*G_1_dx(x,y),y)': 0.33229612078174639719936963786013695726108643010863,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051774919784787570201947282866377250416970446582,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519592087510525717957340497223446595088049776321,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021800955023507586301071586230174756151044785112570,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465316968907365074122461086260874177807602124490,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50769617053811313695668587063727851939441816575898,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8076511746078155944017553592260221865844119595500,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58143018145065348069900433231240238673771005376624,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675427311241257711437682967878241714057150706617,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.792123879975436604847196299230235835769934543175
}

planar_graph_evals[1000000] = {
 'y': 1.00000000000000,
 'x': 0.03672839421763192937436647044572681612702,
 'x*G_1_dx(x,y)': 0.038191077774575980199233776473627298116040760198882,
 'G_1(x,y)': 0.037439346929145453210329006137985768748760785299583,
 'G_1_dx(x,y)': 1.039824326331215200224472935739271445235,
 'G_1_dx_dx(x,y)': 1.1850243037682476125388043144957046596224483119359,
 'D(x*G_1_dx(x,y),y)': 1.0941745614945346701067169348224595014477948478899,
 'S(x*G_1_dx(x,y),y)': 0.043889023061862874084965131596885982815610016583877,
 'P(x*G_1_dx(x,y),y)': 0.048162270380260833963667922443117642631759644436441,
 'H(x*G_1_dx(x,y),y)': 0.0021232680524109620580838807824558760004251868695519,
 'D_dx(x*G_1_dx(x,y),y)': 3.5986141807781736569594438177171178934290657817242,
 'S_dx(x*G_1_dx(x,y),y)': 1.3860016640301035836808601038338424609790679497884,
 'P_dx(x*G_1_dx(x,y),y)': 1.8802215276795817897910575551632388091802322193130,
 'H_dx(x*G_1_dx(x,y),y)': 0.33239098906848828348752615872003662326976561262274,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051781895972214810606008773492308888543276220349,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519602250452591914715757217380906972078302979230,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021806802662437626172763517358004458010986237556229,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465361048219241161677615649117520008503737391040,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50783343954001801840451642387874400654998441680617,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8080334741318986368488713806629003473626011059865,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58154423177953332734330572940287234329162265560945,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675444611547729199604936938584138876249204090791,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.797944931407955456090405190770294626189440399056
}

planar_graph_evals[2000000] = {
 'y': 1.00000000000000,
 'x': 0.03672840339973507483392154381488111213587,
 'x*G_1_dx(x,y)': 0.038191087721993046034176487947816671634008731241562,
 'G_1(x,y)': 0.037439356476919723695090632715432156226498138775643,
 'G_1_dx(x,y)': 1.039824337212246165906267025185587897180,
 'G_1_dx_dx(x,y)': 1.1850237469004464960241885948360847672155172070526,
 'D(x*G_1_dx(x,y),y)': 1.0941745972935647471789317376312591303457341018159,
 'S(x*G_1_dx(x,y),y)': 0.043889036849166285292107677786519706093891627425951,
 'P(x*G_1_dx(x,y),y)': 0.048162289084713205183546376064814726782398190551129,
 'H(x*G_1_dx(x,y),y)': 0.0021232713596852567032776837799246974694442838388027,
 'D_dx(x*G_1_dx(x,y),y)': 3.5990650062715062781184871381043538856327587478748,
 'S_dx(x*G_1_dx(x,y),y)': 1.3860372295201077843762780264296336222635956325920,
 'P_dx(x*G_1_dx(x,y),y)': 1.8804571065659099617184659400651921842801018463056,
 'H_dx(x*G_1_dx(x,y),y)': 0.33257067018548853202374317160952807908906126897717,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051792360268317188640761377130425519689865302160,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519621448554507988168272847445351590602815248547,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021817876753847893378334350741951863258321290580720,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465427193705134065553675598493949388885676776082,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50809342689914002521015157960213927780159485541176,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8087574812761005533790597860348754404625402574366,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58176021088845417337621938451036447891112866757851,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675470573313946242346180991912795990829489312808,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.808971988728386506139150041458824383364669888835
}

planar_graph_evals[5000000] = {
 'y': 1.00000000000000,
 'x': 0.03672840890899696210965458783637368974118,
 'x*G_1_dx(x,y)': 0.038191093690443201640296295669494871867553821954360,
 'G_1(x,y)': 0.037439362205584337687780167500169050274878294284694,
 'G_1_dx(x,y)': 1.039824343740823442143349600465277922753,
 'G_1_dx_dx(x,y)': 1.1850380782584510846504518916514101152958358995846,
 'D(x*G_1_dx(x,y),y)': 1.0941746187755092082947171737094168758804010472449,
 'S(x*G_1_dx(x,y),y)': 0.043889045121747444642565987083390192081271832831325,
 'P(x*G_1_dx(x,y),y)': 0.048162300308704781808285144819439457316303485529883,
 'H(x*G_1_dx(x,y),y)': 0.0021232733450569818438660418065872264828257288837201,
 'D_dx(x*G_1_dx(x,y),y)': 3.5994651133285070219539063207961026978209169347505,
 'S_dx(x*G_1_dx(x,y),y)': 1.3860687581503519583739457812966525625949053640216,
 'P_dx(x*G_1_dx(x,y),y)': 1.8806661740914530957428787069181992514738408773424,
 'H_dx(x*G_1_dx(x,y),y)': 0.33273018108670196783708183258125088375217069338643,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051798638856635582570100119083171433598758765061,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519638436149689017782455813305813129131732392961,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021827706211008428999222549454688360349154656010633,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465466901139636877320836131744529656514577674398,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50832422815238631268395919671319411110675060462899,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8094001372791800460729016247631120473561344848378,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58195190904963682687451072951546161075808170746264,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675486158963428079929853353755259280925419833015,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.818763336005659090479539746631618588356597613027
}

planar_graph_evals[10000000] = {
 'y': 1.00000000000000,
 'x': 0.03672841074541759120156560251020454894295,
 'x*G_1_dx(x,y)': 0.038191095679927525946179627438553089511816521689602,
 'G_1(x,y)': 0.037439364115139215003818748536060148142108244505674,
 'G_1_dx(x,y)': 1.039824345917289498683965498869179567476,
 'G_1_dx_dx(x,y)': 1.1850404367416613362787806906663648549420010371043,
 'D(x*G_1_dx(x,y),y)': 1.0941746259367777706128031133590973829544113341583,
 'S(x*G_1_dx(x,y),y)': 0.043889047879324405471001570039881591702980397725496,
 'P(x*G_1_dx(x,y),y)': 0.048162304050359484867115514038870448674381696101020,
 'H(x*G_1_dx(x,y),y)': 0.0021232740070938802746860292803453425770492403318060,
 'D_dx(x*G_1_dx(x,y),y)': 3.5996667938576622171537494965895828080195501987504,
 'S_dx(x*G_1_dx(x,y),y)': 1.3860846379505853996155774872194357493144305028471,
 'P_dx(x*G_1_dx(x,y),y)': 1.8807715550007596475409510393402039661117015777091,
 'H_dx(x*G_1_dx(x,y),y)': 0.33281060090631716999722097002994309259341811819419,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051800731723013755678013356384239088237087868651,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519646980958717459656263640755861225033278155920,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021832661342921557767866380019158437958437714998511,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465480141877605493720585606906851540984806636081,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50844058969732520832532819646178574873247863258153,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8097241144302011040891789078218574697670027073702,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58204854370090537988257674957016397324719903780239,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675491356280849326308440649098100350667271150354,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.823700553939293956470100703330197223999793620904
}

planar_graph_evals[20000000] = {
 'y': 1.00000000000000,
 'x': 0.03672841166362790574752110984711997854383,
 'x*G_1_dx(x,y)': 0.038191096674669413691666094515429179809904982424512,
 'G_1(x,y)': 0.037439365069916659318386060369958479620910615471318,
 'G_1_dx(x,y)': 1.039824347005208075100426676292054270417,
 'G_1_dx_dx(x,y)': 1.1851032701478478161189712119925785633868144549138,
 'D(x*G_1_dx(x,y),y)': 1.0941746295175839901037182149917860234237106827719,
 'S(x*G_1_dx(x,y),y)': 0.043889049258126118518109516606551528515387842680713,
 'P(x*G_1_dx(x,y),y)': 0.048162305921276675964451242253358308049259260404692,
 'H(x*G_1_dx(x,y),y)': 0.0021232743381811956211574561318761868590635796865263,
 'D_dx(x*G_1_dx(x,y),y)': 3.5998094144201099167165353729358575475809785647870,
 'S_dx(x*G_1_dx(x,y),y)': 1.3860958623755534796866599999275839864734834985573,
 'P_dx(x*G_1_dx(x,y),y)': 1.8808460750307079201587035596436049980381917936782,
 'H_dx(x*G_1_dx(x,y),y)': 0.33286747701384851687117181336466856306930327255156,
 'G_2_dx(x*G_1_dx(x,y),y)': 0.039051801778156646436437879447328211277743434847025,
 'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.0519653016204305992337954308858107773655083629198,
 'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.021836165592865796363128113182705520815727756131438,
 'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0042465486763623912423149122637523737181271593730531,
 'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.50852288507562748435189788815109527159441369829122,
 'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.8099532328682937939188281863966829951813512989510,
 'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.58211688238250726857851462500990649851134711594850,
 'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21675493955527111241196177404062488936121713008948,
 'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 18.827192660398022647061594621178742553469807013142
}


# N = 100
# J_a and J_a_dx are wrong.
reference_evals = {
    'D(x*G_1_dx(x,y),y)': 1.09347848647472549211184239941769601061,
    'D_dx(x*G_1_dx(x,y),y)': 3.45102206434801157864803811245239712851,

    #'Fusy_K': 0.00206469524549284585247141356302904687086,
    'G_3_arrow(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.00206469524549284585247141356302904687086,

    'Fusy_K_dx': 0.213391746841149010553294208298541737991,
    'Fusy_K_dy': 0.0182698213762051362133391897289610870537,
    'G_1(x,y)': 0.0372484305053690456202661877963311349072,
    'G_1_dx(x,y)': 1.03960692373287371278312170556092216601,
    'G_1_dx_dx(x,y)': 1.1831386535487874823112196643179832576,
    'G_2_dx(x*G_1_dx(x,y),y)': 0.038842683760013258631145523348425252874,
    'G_2_dx_dx(x*G_1_dx(x,y),y)': 1.05099440303963997980334319688998807042,
    'G_3_arrow_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.0182698213762051362133391897289610870537,
    'H(x*G_1_dx(x,y),y)': 0.00206469524549284585247141356302904687086,
    'H_dx(x*G_1_dx(x,y),y)': 0.276441303522129889594403984833856178203,
    'J_a(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.00103234762274642,
    'J_a_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.106695873420575,
    'K(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.21219385343653063,
    'K_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 15.48657625114519,
    'K_dx_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 5592.386366298111,
    'K_dy(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 1.729773462783172,
    'K_dy_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 539.8558558558559,
    'K_dy_dx_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 1183895.1899970463,
    'K_snake(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 1.254888507718696,
    'K_snake_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 543.8610354223433,
    'K_snake_dx_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 1277786.7614037835,
    'P(x*G_1_dx(x,y),y)': 0.0477986369539869322752735578478273809975,
    'P_dx(x*G_1_dx(x,y),y)': 1.80255895061461154228734452882283065547,
    'R_b(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 0.5120292887029289,
    'R_b_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 129.2273161413563,
    'R_w(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 2.577655310621243,
    'R_w_dx(x*G_1_dx(x,y),D(x*G_1_dx(x,y),y))': 414.9509202453988,
    'S(x*G_1_dx(x,y),y)': 0.0436151542752457139840974280068395827400,
    'S_dx(x*G_1_dx(x,y),y)': 1.37202181021127014676628959879571029484,
    'x': 0.0365447705189290291920092340981152311040,
    'x*G_1_dx(x,y)': 0.0379921964577076229466965829549486315897,
    'y': 1.00000000000000}

all_evaluations = [
    reference_evals,
    # planar_graph_evals_n100,
    # planar_graph_evals_n1000
    # planar_graph_evals_n10000
]
# see sage worksheet "eval-notebook.ipynb" # N = 100 # J_a and J_a_dx are wrong. #'Fusy_K': 0.00206469524549284585247141356302904687086, # planar_graph_evals_n100, # planar_graph_evals_n1000 # planar_graph_evals_n10000