{ "format": "fastandaccurate-result", "formatVersion": 1, "problem": "laplace-dirichlet-2d", "problemVersion": 1, "instance": "flower-15", "spec": { "a": 0.2, "d": 0.25, "instance": "flower-15", "k": 15, "problem": "laplace-dirichlet-2d", "problemVersion": 1 }, "specHash": "0f66b2d599e60ea851124485b5615a6027f9406a1c56bbb7deef269e96079970", "solver": { "id": "mfs-gpu", "version": "1.0.0", "backend": "gpu", "source": "builtin" }, "environment": { "kind": "node", "runtime": "node v24.14.1", "gpu": "Intel open-source Mesa driver: Mesa 25.0.7-2+deb13u1 (node-webgpu (Google Dawn))", "os": "linux 6.12.101+deb13-amd64", "cpu": "13th Gen Intel(R) Core(TM) i7-1355U", "machineLabel": "linux laptop (i7-1355U)", "browserReproducible": true }, "protocol": { "warmupRuns": 2, "minTimedRuns": 5, "timeBudgetSeconds": 0.5, "maxTimedRuns": 50, "statistic": "min", "timer": "host clock around submit and read-back" }, "createdUtc": "2026-08-18T22:32:30.142Z", "points": [ { "n": 8, "solveSeconds": 0.0010730079999993905, "solveSecondsAll": [ 0.0011607960000001186, 0.001150234000000637, 0.0012169009999997797, 0.0011310520000006362, 0.0012135490000000572, 0.0011807860000008076, 0.0013802249999989727, 0.0012404690000003028, 0.0013061440000001312, 0.001435500999999931, 0.00120636100000047, 0.0013070539999989706, 0.0013736009999993257, 0.001176237999998193, 0.0011850059999997029, 0.0012107540000015433, 0.0011502830000008543, 0.001097418999999718, 0.001221267999999327, 0.001166902000000846, 0.0011200129999997443, 0.0011380210000006628, 0.0012290400000001683, 0.0011474679999992077, 0.0010947550000000774, 0.001167250000000422, 0.0011416480000007142, 0.0011824740000010933, 0.0011410739999992074, 0.001170283000001291, 0.0011312870000001567, 0.0010747580000006565, 0.0011605080000008457, 0.0010989190000000235, 0.0011055930000002264, 0.0011753609999996116, 0.0012105389999996987, 0.001091946000000462, 0.0010976510000000417, 0.0011294090000010329, 0.001175307999999859, 0.001075937999999951, 0.0010991900000008172, 0.0011134469999997236, 0.001074296000000686, 0.0011467049999992014, 0.001116027000000031, 0.00118838500000129, 0.0010730079999993905, 0.001079024999999092 ], "coldSeconds": 0.0014721389999995153, "relMax": 0.382047739415996, "relL2": 0.15846663833592162 }, { "n": 12, "solveSeconds": 0.0006388569999999162, "solveSecondsAll": [ 0.0013713349999998172, 0.0013257829999984096, 0.001326736000000892, 0.0013238259999998263, 0.0013835579999995388, 0.0013396749999992608, 0.0013745519999993122, 0.0013811279999990803, 0.0013613669999995182, 0.0013515260000003765, 0.0010702889999993203, 0.0007641869999988558, 0.0006967839999997522, 0.0006696539999993547, 0.0006623800000015763, 0.0006822940000001836, 0.0006756499999992229, 0.0007295979999998963, 0.000673134000000573, 0.0006550509999997303, 0.0006553139999996347, 0.0007259589999994205, 0.0006523760000000039, 0.0006495510000004287, 0.0007307089999994787, 0.0007598139999990962, 0.0007415860000000976, 0.0006863499999999476, 0.0006550029999998515, 0.0006397680000009132, 0.0006852039999994304, 0.0006578190000000177, 0.0006627310000003491, 0.0006974640000007639, 0.0006720230000009905, 0.0006551849999996193, 0.0006654619999990246, 0.0006911479999998847, 0.000648416999998517, 0.0007131219999992026, 0.0006673489999993763, 0.0006820339999994758, 0.0006388569999999162, 0.0006860520000009274, 0.0006738339999992605, 0.0006645010000011097, 0.0006515979999985574, 0.0007875709999989339, 0.0008657860000002984, 0.000670031999999992 ], "coldSeconds": 0.0014078379999991739, "relMax": 0.2831351781915817, "relL2": 0.09334531465146015 }, { "n": 16, "solveSeconds": 0.0007651440000008734, "solveSecondsAll": [ 0.000810325999998895, 0.0007854190000016388, 0.0008039820000012697, 0.0007904010000002017, 0.0007895169999992504, 0.0007850489999982528, 0.0007876489999998739, 0.0007799979999999777, 0.0007957409999999072, 0.0007795070000011037, 0.0008029289999994944, 0.0007666250000002038, 0.000783237999999983, 0.0007936430000008841, 0.0007849889999997686, 0.0007695100000000821, 0.0007897790000006352, 0.0007809400000005553, 0.0008077290000001085, 0.0007736469999999827, 0.000777156999998624, 0.0007758200000007492, 0.0008016500000012456, 0.0007960519999996905, 0.0007915179999999964, 0.0007796739999994315, 0.0007749710000007327, 0.0007682289999993373, 0.0008103040000005422, 0.0007749949999997626, 0.0007682960000001913, 0.0007651440000008734, 0.0007870130000010249, 0.0008160680000000866, 0.0008050020000009681, 0.0007776269999994838, 0.0007908079999997427, 0.0007925409999988915, 0.0008197659999987082, 0.000800572000000102, 0.0008525790000003326, 0.000924909999999727, 0.000914282000001549, 0.0009272970000001805, 0.00093500800000038, 0.0009153149999983725, 0.0009445930000001681, 0.0009778470000001108, 0.0011713410000011209, 0.0010624280000010914 ], "coldSeconds": 0.0009114100000006147, "relMax": 4.7270323667902385, "relL2": 2.1491728941516284 }, { "n": 24, "solveSeconds": 0.0010443899999991117, "solveSecondsAll": [ 0.0010894009999992704, 0.0010857619999987947, 0.0010658669999993435, 0.0010841749999999592, 0.0010686359999999694, 0.001052719999999681, 0.0010488270000005287, 0.0011726520000011078, 0.0010695419999992737, 0.001146506999999474, 0.001083441999999195, 0.0011304349999991246, 0.0013973249999999098, 0.001151400000000649, 0.0011018990000011399, 0.0010693609999998443, 0.0011054420000000391, 0.001104525000000649, 0.0010643749999999271, 0.001067246000000523, 0.0010885450000005222, 0.001065864000000147, 0.0010443899999991117, 0.0011166640000010374, 0.0013327740000004269, 0.0011128239999998186, 0.0011028069999993021, 0.0011081340000000637, 0.0011033950000000914, 0.0010737420000004932, 0.001058454999998503, 0.0010636099999992439, 0.0010797550000006596, 0.0010975210000015068, 0.0010904979999995703, 0.0010692959999996673, 0.0010519690000000991, 0.0010578629999999976, 0.0010470800000002781, 0.0010624509999997826, 0.001073097999998936, 0.0010555580000000191, 0.0010610800000013115, 0.0010545750000001135, 0.00106735000000117, 0.0010980920000001788, 0.0010871409999999742, 0.0010524420000001555, 0.0010629810000009456, 0.0011133609999997133 ], "coldSeconds": 0.0012956520000007004, "relMax": 0.18324363300538496, "relL2": 0.04574721751688169 }, { "n": 32, "solveSeconds": 0.0012702580000004673, "solveSecondsAll": [ 0.0013590989999993327, 0.0013602859999991778, 0.0013418579999997745, 0.0015387920000011946, 0.0013702599999996891, 0.0014119689999988624, 0.0013416200000010577, 0.0013247950000004494, 0.001328256999999212, 0.0015511700000006385, 0.0014321359999994456, 0.0014035149999999702, 0.0014057049999992158, 0.0019645290000007663, 0.0020059579999997367, 0.0015084069999993517, 0.0013692119999996067, 0.0013546349999996891, 0.0013483140000007552, 0.0013492780000015046, 0.0013141259999993053, 0.001329278000001068, 0.00133837400000084, 0.0013047719999995024, 0.001311788000000888, 0.0013553690000007918, 0.0013123489999998128, 0.0013444730000010169, 0.0013978139999999257, 0.0013445639999990818, 0.0012953680000009626, 0.0013004650000002585, 0.0012707900000004883, 0.0012702580000004673, 0.0012785950000015873, 0.0013190140000006068, 0.002076492000000144, 0.0021199140000007903, 0.002030327999998917, 0.0015941509999993287, 0.0013807379999998374, 0.0013254740000011225, 0.001316512999999759, 0.001278533000000607, 0.001274865999999747, 0.0013015619999987393, 0.0012857899999999063, 0.0012819220000001223, 0.0012893929999991088, 0.0012862569999997505 ], "coldSeconds": 0.0014158879999995406, "relMax": 0.044776724100491036, "relL2": 0.018212037546808252 }, { "n": 48, "solveSeconds": 0.001790005000000747, "solveSecondsAll": [ 0.001999340000000302, 0.0019089550000007875, 0.001867251000001488, 0.001961404000001494, 0.0018637130000006437, 0.0018131259999991016, 0.0017919050000000424, 0.0018168920000007347, 0.0018242350000000442, 0.00181194399999913, 0.0019124019999999292, 0.0020647890000000187, 0.0019155859999991662, 0.0018205470000011701, 0.0018306090000005497, 0.0018168580000001383, 0.0022387849999995525, 0.0019081249999999272, 0.001876035999999658, 0.0018181539999986853, 0.0018468820000016421, 0.001886028000000806, 0.0018844069999995553, 0.001791320000000269, 0.0018310270000001766, 0.001790005000000747, 0.0018221430000012332, 0.0018235659999991185, 0.0019973950000003243, 0.0018438069999992877, 0.0018196289999996224, 0.0020400620000000343, 0.002341645000000426, 0.002252833999998984, 0.001973005000001649, 0.0019268199999987702, 0.0019038230000005569, 0.002061237000001711, 0.0022224159999987025, 0.0021247650000004795, 0.0019868989999995393, 0.0024991279999994733, 0.0027123050000009245, 0.0020299030000005586, 0.0021008529999999156, 0.0021526619999985997, 0.0021536949999990613, 0.002274209000001065, 0.0021535210000001824, 0.001898456000000806 ], "coldSeconds": 0.0028467000000000553, "relMax": 0.030952687242778262, "relL2": 0.006685239204563405 }, { "n": 64, "solveSeconds": 0.0022983299999996235, "solveSecondsAll": [ 0.003073080000000118, 0.0029336100000000444, 0.0031250879999988684, 0.002692653000000064, 0.002517614999998841, 0.0025646500000002562, 0.0026124439999985045, 0.002626046999999744, 0.0025845819999995, 0.002541164000000208, 0.002512408000000505, 0.0030207080000000134, 0.002991009999999733, 0.0029344920000003187, 0.002707067999999708, 0.0026748330000009447, 0.0027133580000008807, 0.0025599309999997785, 0.0026213370000004945, 0.002560454000000391, 0.002540479000001142, 0.0025277210000003835, 0.0024147049999992303, 0.002455283999999665, 0.0023416679999991173, 0.002442541000000347, 0.0023570440000003144, 0.0023210779999990336, 0.002319233999998687, 0.0024644559999997, 0.002503738000001249, 0.0024371879999998784, 0.002459585999999035, 0.0023594769999999697, 0.0023402640000003885, 0.0023554459999995743, 0.0024905870000002323, 0.0023314940000000207, 0.002330855000000156, 0.0024310239999995246, 0.002305177000000185, 0.0023119950000000246, 0.0023899810000002617, 0.0023381229999995413, 0.0023123539999996864, 0.0023473919999996724, 0.0023290930000002845, 0.0022983299999996235, 0.0023764329999994517, 0.0023048240000007355 ], "coldSeconds": 0.002662376000000222, "relMax": 0.029123528324601657, "relL2": 0.007406658677829612 }, { "n": 96, "solveSeconds": 0.003358973000000333, "solveSecondsAll": [ 0.003445096999999805, 0.0034195059999983643, 0.0035025839999998426, 0.00349035399999957, 0.0035082629999997153, 0.0034005489999999554, 0.003358973000000333, 0.0036779029999997872, 0.003596050999998624, 0.003584687999999005, 0.003535597999998572, 0.0038495439999987864, 0.0037863560000005237, 0.003696422999999413, 0.0035761839999995573, 0.003527766999999585, 0.003615658999999141, 0.003580195000000458, 0.0035546269999995276, 0.00363172300000042, 0.003632939000000988, 0.003549666000000798, 0.0038310610000007726, 0.003860058999998728, 0.003782427000000098, 0.003614342000000761, 0.0034512340000001133, 0.003519383000000744, 0.003537414999998873, 0.003435688999999911, 0.0033836179999998423, 0.003396114999999554, 0.00344803900000079, 0.0036306880000011007, 0.003496062999998685, 0.0035352900000016232, 0.004012649000000238, 0.004039683000000877, 0.0038590190000013535, 0.0036488799999988258, 0.003528716999999233, 0.003949818999999479, 0.0038205340000004072, 0.0037533340000009048, 0.003584403000000748, 0.0035268860000014684, 0.0035075230000002192, 0.003435452000001533, 0.023660160999999787, 0.0038230590000002847 ], "coldSeconds": 0.0036326850000004923, "relMax": 1.6485144842228963, "relL2": 0.37551918923414745 }, { "n": 128, "solveSeconds": 0.004236602000000858, "solveSecondsAll": [ 0.004605610999999044, 0.004552659000000858, 0.004716866999999183, 0.005321858000001157, 0.0047099670000006885, 0.0045655380000007425, 0.004547422000001461, 0.004583114999999452, 0.004572017999998934, 0.0045156829999996265, 0.004504554000001008, 0.004475099999999657, 0.0044747850000003385, 0.004539652999999816, 0.00458721499999956, 0.0044697909999995315, 0.0044869330000001355, 0.004531153999998423, 0.0042726220000004105, 0.0043514350000004925, 0.0042989469999993165, 0.00435131199999887, 0.004363116000000446, 0.0044065739999987275, 0.004344164000000091, 0.00441162599999916, 0.004394797999999355, 0.0042843049999992215, 0.004236602000000858, 0.004337195000000065, 0.004268047999999908, 0.004257420999998431, 0.004283903000001373, 0.0043586669999986045, 0.004422790000000532, 0.004293354999999792, 0.00426778000000013, 0.004459734000000026, 0.004290973000001031, 0.00436679600000025, 0.005278882999999041, 0.0045554250000004685, 0.004543646000000081, 0.004534074999999575, 0.004438987999999881, 0.004493385999998281, 0.004432698999999048, 0.004398510000000897, 0.004536305999999967, 0.004434229000000414 ], "coldSeconds": 0.004667235999999321, "relMax": 0.0021428418374378837, "relL2": 0.0004698956186799177 }, { "n": 192, "solveSeconds": 0.006828176000000894, "solveSecondsAll": [ 0.0071696809999994005, 0.0072270969999990485, 0.007850736999998845, 0.007969473999999536, 0.007352247000000716, 0.007502663000001121, 0.00761475099999916, 0.007788259000000835, 0.007316385000000082, 0.007297609999999622, 0.007274489999999787, 0.00732477899999867, 0.007256955000000744, 0.007210089000000153, 0.007038162000000739, 0.007159937999998874, 0.007288387000000512, 0.007271641000001182, 0.007384706000000733, 0.007150180000000546, 0.0071509689999984406, 0.00695458999999937, 0.0069939439999998285, 0.007039700000001176, 0.006883499999999912, 0.006971433000000616, 0.00754051199999958, 0.007096895999999106, 0.007204585000001316, 0.006981697999999596, 0.00695937000000049, 0.006828176000000894, 0.008633969000000434, 0.007507137000000511, 0.008057893000001058, 0.007218032000000676, 0.0072598760000000765, 0.007383696000000782, 0.007259036999999808, 0.007223550000000614, 0.007199934999998731, 0.0071798570000009936, 0.006938384999999471, 0.0070511690000003, 0.006964771000000838, 0.016626296000000367, 0.007390349000001152, 0.0072627259999990205, 0.007043895000000702, 0.006914037999998982 ], "coldSeconds": 0.006984538000000612, "relMax": 0.003072064497482915, "relL2": 0.0008973609148210924 }, { "n": 256, "solveSeconds": 0.009570208999999523, "solveSecondsAll": [ 0.009719441000001097, 0.009570208999999523, 0.010023473999999623, 0.010387705999999525, 0.00994250699999975, 0.010519635000000561, 0.011338391999999657, 0.010473159999999553, 0.010175803000000087, 0.01010794099999839, 0.00992899099999886, 0.00984952599999997, 0.009921247000000221, 0.009815255999999863, 0.010033383999998478, 0.010862299999998867, 0.010671016000000236, 0.010174693000000843, 0.010032264999999825, 0.010190533000000869, 0.010269227999999202, 0.010182286000001112, 0.010058952999999747, 0.010192041000000245, 0.010572091, 0.01211986600000091, 0.010175505000001066, 0.010168797000000267, 0.01066974300000038, 0.010285485000000335, 0.010758003999999346, 0.010248460999999225, 0.010101400999999895, 0.010050256000000445, 0.009981244999999035, 0.01006876899999952, 0.009989509000000908, 0.010859387000000425, 0.010044572000000699, 0.010032414999999673, 0.009863682999999582, 0.009862655999999333, 0.01012897300000077, 0.011106491000000461, 0.022676868000000468, 0.010658110000000305, 0.010796019999999771, 0.01053771500000039 ], "coldSeconds": 0.009620523999999932, "relMax": 0.0129963711856114, "relL2": 0.003576935051437422 }, { "n": 384, "solveSeconds": 0.016864677999999914, "solveSecondsAll": [ 0.017252746000000117, 0.01720638600000166, 0.01712425599999915, 0.017162902000000032, 0.01717475999999988, 0.01716297399999894, 0.017564198000000034, 0.017267227999998795, 0.017325072999999976, 0.017320983000001434, 0.01707891600000039, 0.017633352999999262, 0.01742506499999945, 0.017587736000001315, 0.017492474000000584, 0.01746393099999841, 0.01740606999999909, 0.017248818000000027, 0.017577299999999012, 0.017234667000000627, 0.016931274000000485, 0.0169846579999994, 0.016864677999999914, 0.02018042500000047, 0.0175749880000003, 0.01750636400000076, 0.01792478800000026, 0.017404162999999244, 0.018011441000000558 ], "coldSeconds": 0.017697377000000417, "relMax": 0.11131653977428344, "relL2": 0.023736910975235573 }, { "n": 512, "solveSeconds": 0.026412011999998868, "solveSecondsAll": [ 0.026412011999998868, 0.23686775300000046, 0.02712995899999987, 0.027444640000001526, 0.027369195000001127, 0.027541807999999945, 0.027464005000001634, 0.02733605400000124, 0.027468156999999337, 0.027457624999999097, 0.027585239 ], "coldSeconds": 0.026784612999999808, "relMax": 0.22737045410686543, "relL2": 0.047908249457924525 }, { "n": 768, "solveSeconds": 0.04210458300000028, "solveSecondsAll": [ 0.04504818499999965, 0.04545006300000023, 0.04210458300000028, 0.043346230999999534, 0.04471259999999893, 0.045398246000000655, 0.04872148000000016, 0.048524790999999824, 0.04751915699999881, 0.04798601300000155, 0.04839203000000271 ], "coldSeconds": 0.0567881260000031, "relMax": 0.0703167976398978, "relL2": 0.01927952559460133 } ] }