{ "format": "fastandaccurate-result", "formatVersion": 1, "problem": "laplace-dirichlet-2d", "problemVersion": 1, "instance": "star-hard", "spec": { "a": 0.3, "d": 0.08, "instance": "star-hard", "k": 5, "problem": "laplace-dirichlet-2d", "problemVersion": 1 }, "specHash": "cd0f3e5dc72e88da57eaf0a1696e04c32da1b28b439b79069dcf740b1cb70799", "solver": { "id": "mfs", "version": "1.0.0", "backend": "cpu", "source": "builtin" }, "environment": { "kind": "node", "runtime": "node v24.14.1", "numblVersion": "0.4.18", "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": "numbl tic/toc" }, "createdUtc": "2026-08-18T10:57:07.291Z", "points": [ { "n": 8, "solveSeconds": 0.0002038550000023065, "solveSecondsAll": [ 0.0006836559999925385, 0.0006341950000035013, 0.0006077999999973827, 0.0005217560000048138, 0.0003692530000023453, 0.000254172000005326, 0.00025786399999816467, 0.0002730920000004744, 0.0002957940000030135, 0.00025423099999954957, 0.00024900700000074494, 0.0002248859999909314, 0.00027236900000815467, 0.0002483339999983514, 0.0002433489999944527, 0.0002855759999960128, 0.00029442200000318053, 0.0002651849999963929, 0.0002608959999932381, 0.0002162960000049452, 0.00026888699999716437, 0.0002454560000018091, 0.0002382629999999608, 0.00023873100000315617, 0.00024398899999056312, 0.0002395960000001196, 0.0002038550000023065, 0.00022168200000294291, 0.0003004289999992693, 0.0002653170000073146, 0.0002495929999994928, 0.0002636500000008368, 0.00021290400000140153, 0.00021363300000842855, 0.0002470989999991957, 0.00024752200000222047, 0.00024239300000061803, 0.00025012399999724266, 0.000240924999992842, 0.00023951700000424125, 0.0002380930000001058, 0.00024268100000313098, 0.0002382150000030947, 0.00024013600000216684, 0.00023704899999898998, 0.0002343059999958541, 0.00023954499999945256, 0.0002463529999943148, 0.0002451390000004494, 0.00024087599999944587 ], "coldSeconds": 0.009637144999992131, "relMax": 0.35376829334376525, "relL2": 0.24096365118374863 }, { "n": 12, "solveSeconds": 0.00024089399999382977, "solveSecondsAll": [ 0.0005296730000097227, 0.00032729000000131236, 0.0003489380000019082, 0.00029886400000123103, 0.00027923999999757143, 0.0002686899999986281, 0.00026423499999594924, 0.00026121199999806777, 0.0002546489999986079, 0.0003261450000024979, 0.0002878570000035552, 0.0002607959999991749, 0.0002527790000002028, 0.0002884949999923947, 0.00025306299999527937, 0.00025312499999330385, 0.000251624999997091, 0.0002652699999927677, 0.00024540999999800306, 0.0002492000000060557, 0.00024757900000338395, 0.0002544189999937885, 0.0002525610000034817, 0.00025073000000475076, 0.0002515870000010523, 0.00025870700000041325, 0.00024620399999975007, 0.00024089399999382977, 0.00024957699999816896, 0.0002448510000050419, 0.00024559700000281737, 0.0002540340000081187, 0.0002907390000004284, 0.0003039889999953971, 0.0002978420000019355, 0.0003399219999948855, 0.0003322370000020669, 0.0003214600000092105, 0.0003180089999972324, 0.0003304170000006934, 0.0003181880000013848, 0.0003113599999977623, 0.0003110600000013619, 0.00031240999999226915, 0.0003095769999958975, 0.0003067379999990294, 0.00031882399999005884, 0.0003100580000037212, 0.000280542999995248, 0.0003443080000025134 ], "coldSeconds": 0.005888470000002144, "relMax": 0.5659199117820652, "relL2": 0.23634263160630714 }, { "n": 16, "solveSeconds": 0.0002767120000015666, "solveSecondsAll": [ 0.0004689909999981978, 0.0004123770000035165, 0.0004570280000066873, 0.0003635130000034792, 0.0004007470000004787, 0.0003955980000043269, 0.00031764200000594656, 0.00033029600000133996, 0.0002982370000026435, 0.0003881450000093878, 0.0004555980000020554, 0.00042546599999582213, 0.00044766199999912715, 0.0003868909999980019, 0.00038950000000426144, 0.000392221000005577, 0.000377774999996916, 0.00040516499999654343, 0.00041795500001029495, 0.000390973000001793, 0.0024799510000050873, 0.0006169420000006198, 0.0005311350000027915, 0.0004926330000003531, 0.0003416740000048435, 0.00032147900000722984, 0.00032510300000154757, 0.0003040890000036711, 0.00030359399999468906, 0.0003001639999951067, 0.00029854699999987133, 0.00029567400000019006, 0.0003285490000024538, 0.00031379700000400135, 0.000297450999994453, 0.0003123250000029998, 0.00029132499999917627, 0.0002893639999967945, 0.0003104600000014557, 0.0003023889999980156, 0.00028741199999871014, 0.0002800030000003062, 0.0002786410000084061, 0.0002794939999972712, 0.0002802399999950467, 0.0002767120000015666, 0.00027674800000454525, 0.0002904960000051915, 0.00030313599999942653, 0.0002804249999996955 ], "coldSeconds": 0.006612669000006122, "relMax": 0.11698563456702489, "relL2": 0.049752429398682144 }, { "n": 24, "solveSeconds": 0.00033730900000250585, "solveSecondsAll": [ 0.0005725130000016065, 0.0004226419999966424, 0.00039198000000340016, 0.00040859500000323123, 0.00044641800000277954, 0.0003973760000022253, 0.00038175600000300847, 0.0003724690000055375, 0.000385115000000269, 0.00040459899999945037, 0.0003903859999994097, 0.00038330899999294843, 0.00036769600000496894, 0.0003722040000013749, 0.0003699999999966508, 0.00036066399999867826, 0.0004163869999942449, 0.0005392959999923619, 0.00037181400000463327, 0.00044868100000172717, 0.0004683189999994397, 0.00046986099999912767, 0.00037825599999763426, 0.0003773480000006657, 0.0004801030000010087, 0.0004709279999914884, 0.0004674320000077614, 0.0004648939999967183, 0.0005642220000012799, 0.0005427139999980568, 0.00043306599999937134, 0.00034423500000002605, 0.00033730900000250585, 0.000339060999998253, 0.0004939709999973729, 0.0005417969999967909, 0.0005019060000037712, 0.00048794199999946386, 0.0004854110000067635, 0.00048003999999934877, 0.00047518599999563094, 0.0005021540000029745, 0.0005035699999993426, 0.00047935299999579684, 0.0004799859999948808, 0.0004892040000044062, 0.00047813199999779954, 0.0004734570000053395, 0.00048178299999790397, 0.0004806740000091736 ], "coldSeconds": 0.007365621000005262, "relMax": 0.07109819067618718, "relL2": 0.02847017542467721 }, { "n": 32, "solveSeconds": 0.00042225299999643084, "solveSecondsAll": [ 0.0006310179999999832, 0.0005576900000008322, 0.000520951999995134, 0.0004922000000036064, 0.0004951809999980128, 0.00048623200000008637, 0.00048037399999856234, 0.0004772949999960474, 0.00045248899999705827, 0.0004445590000017319, 0.000440787000002274, 0.00047959999999847014, 0.0004981340000043133, 0.0004462730000014403, 0.0004438509999999951, 0.0004355560000064429, 0.0004393529999902057, 0.0004401160000000459, 0.00043136100000396027, 0.00042877399999952104, 0.0004464450000014608, 0.00042389800000108835, 0.00042225299999643084, 0.0004234729999978981, 0.00042481399999871883, 0.0004309039999910169, 0.0004311929999971653, 0.0004370479999948884, 0.0005782580000044391, 0.00045157899999992424, 0.0004304560000036872, 0.0004449389999976461, 0.0004257189999989919, 0.00044015699999988556, 0.0004474969999961331, 0.00047400900000837964, 0.0004574009999984696, 0.000466523999996582, 0.00047343500000351924, 0.0005369680000057997, 0.0004429270000017027, 0.0004995450000038204, 0.00046179500000675944, 0.0004665850000051819, 0.00048311899999475827, 0.0004594329999960678, 0.00043770500000306356, 0.0005213489999960075, 0.00047321600000316266, 0.00044710799999592155 ], "coldSeconds": 0.01738532000000248, "relMax": 3.7989780950854133, "relL2": 0.8381850553051889 }, { "n": 48, "solveSeconds": 0.000607592999998019, "solveSecondsAll": [ 0.0010221570000013003, 0.0009434239999990268, 0.000840189999998131, 0.0007284139999939043, 0.000700093999995488, 0.0006561679999990133, 0.00100926200000373, 0.0006257960000013441, 0.0007995539999967605, 0.0014751550000013935, 0.0062483620000008955, 0.0011412909999961585, 0.0008749480000034282, 0.0007175560000050041, 0.0007379059999976789, 0.000698720000002595, 0.0006715900000031638, 0.0006802709999931267, 0.0006942310000042085, 0.0007231110000134322, 0.0006351640000019643, 0.0006614430000055904, 0.0006295460000060871, 0.0006174929999929191, 0.0006175079999977129, 0.0006142510000017865, 0.0006139499999946452, 0.0006258980000026781, 0.0006531300000034435, 0.0006697599999938575, 0.0006239830000041025, 0.0006119679999940786, 0.000607592999998019, 0.000612711999998794, 0.000614478000002805, 0.0006118510000021615, 0.0008306940000082363, 0.000611853999998857, 0.0006114560000014535, 0.0006131509999960372, 0.0006324110000051064, 0.0006166959999944766, 0.0006144810000066059, 0.0006355509999949049, 0.0006087429999936944, 0.0006111559999979477, 0.0006236629999989418, 0.0006158129999960238, 0.0006119140000038215, 0.0006357039999969061 ], "coldSeconds": 0.00911125500000054, "relMax": 0.07663193286783351, "relL2": 0.02271359265222745 }, { "n": 64, "solveSeconds": 0.0008675159999995685, "solveSecondsAll": [ 0.0010511310000040908, 0.0009775109999949905, 0.0016953879999945798, 0.006100134999996953, 0.0014588340000045719, 0.0009742859999946063, 0.0009369839999990859, 0.0009904489999925659, 0.000981997000003787, 0.000937991999997223, 0.0008946079999958556, 0.0009523529999952984, 0.0009985249999999724, 0.0010470960000006357, 0.0010127589999981979, 0.0010289320000040902, 0.0009803879999950027, 0.0009675109999989218, 0.0009524290000086921, 0.0009585279999981822, 0.0009856699999986063, 0.000933097999997301, 0.0009527799999986541, 0.0009185799999968935, 0.000870759000001442, 0.0008909809999977369, 0.0008732059999942976, 0.0008717489999980899, 0.0008910000000028617, 0.0008743570000007139, 0.0009244739999942908, 0.0008713099999937413, 0.0008750069999976517, 0.0008675159999995685, 0.0008864019999919037, 0.000872581000002981, 0.001210851999999818, 0.006155936000006079, 0.0014245839999986742, 0.0009843950000032464, 0.0010223379999985127, 0.0010913850000022762, 0.0009971879999994826, 0.000977999000006946, 0.0010636760000011236, 0.0010345329999950081, 0.000986034000000302, 0.0009398619999956281, 0.0008966949999944518, 0.0009215290000099685 ], "coldSeconds": 0.011561227000001395, "relMax": 0.14348501752299708, "relL2": 0.02971387528791318 }, { "n": 96, "solveSeconds": 0.0015808179999936556, "solveSecondsAll": [ 0.001841491000000417, 0.0017830390000028729, 0.001759059000001173, 0.0017929470000055403, 0.0018010399999965898, 0.0017558529999917027, 0.0016940709999957448, 0.0017140219999944861, 0.0016202099999986785, 0.0016552559999993832, 0.002232567000000074, 0.006386704000007626, 0.00175069800000216, 0.0017305170000057046, 0.0016588720000001445, 0.0016305919999979324, 0.0016849009999972964, 0.001762704000000781, 0.001832616000001508, 0.001778928000000235, 0.0017044760000004544, 0.0017859169999994151, 0.0017077179999986924, 0.001660985999997422, 0.0015906630000017685, 0.001646273000005749, 0.0016087480000024357, 0.001647192999996605, 0.0015893469999994636, 0.0015808179999936556, 0.001970398999993961, 0.006673636000002148, 0.0020198010000029853, 0.0019037899999929664, 0.0019726599999998484, 0.001749314999997864, 0.001877303999997082, 0.0017737140000022578, 0.0018299669999990442, 0.0019381050000006894, 0.0018427420000008965, 0.0016999229999967724, 0.0017623329999949533, 0.001683077999992122, 0.0016706730000066727, 0.001668552999994688, 0.0016978499999993346, 0.0016643770000044356, 0.0016299330000038026, 0.0016296450000012896 ], "coldSeconds": 0.014004628000009234, "relMax": 0.10124475575821881, "relL2": 0.02108958644027326 }, { "n": 128, "solveSeconds": 0.0026128010000050494, "solveSecondsAll": [ 0.003038222000000701, 0.0029844910000065283, 0.0028489009999930204, 0.002795345999999199, 0.002908881000003305, 0.0028216420000077846, 0.0027815260000068065, 0.0027017769999986285, 0.002724492000005796, 0.002765468999996301, 0.0027106009999968705, 0.002814937000003681, 0.004318593999997233, 0.0070412390000029745, 0.0028291520000038872, 0.002784441999992282, 0.0028760190000056696, 0.0027719250000046713, 0.0027785870000016644, 0.002777498999996908, 0.002784894000001259, 0.003054942000005667, 0.002957621000000188, 0.002801694000005739, 0.0027677439999962417, 0.0027672739999999862, 0.0031270200000008685, 0.006792209999993304, 0.0028138499999954547, 0.0027499920000053635, 0.002818381000004422, 0.0026866980000050944, 0.0027050349999981904, 0.0027543679999908477, 0.002740857000006258, 0.0026694319999975846, 0.00267565600000097, 0.0026812610000064296, 0.0026840700000008155, 0.002630621999998084, 0.003112735999998506, 0.009210152000001415, 0.004007715000000189, 0.002754965999997694, 0.002746066000000269, 0.002700054000001728, 0.002701349000005848, 0.0026128010000050494, 0.0026744829999927333, 0.002685507000002474 ], "coldSeconds": 0.022540327000001525, "relMax": 0.07797844016265722, "relL2": 0.02062145013848051 }, { "n": 192, "solveSeconds": 0.006268391999995515, "solveSecondsAll": [ 0.007025810999998328, 0.011658071999995911, 0.006445689999999615, 0.00649687900000373, 0.006503917999999942, 0.006591831000001491, 0.0065999509999983275, 0.006323363999996445, 0.007189240999998958, 0.01075196999999406, 0.006814796000000456, 0.006432905999993466, 0.006634768000004954, 0.0065540530000021135, 0.0065679499999973245, 0.007131311000001972, 0.00636752300000154, 0.007100895999997192, 0.01110707700000546, 0.006404201000002274, 0.006283753000005277, 0.006343832000005989, 0.006349959999994326, 0.006444090999998764, 0.006643567999994104, 0.00659271900000391, 0.010279390000000888, 0.006407139000003781, 0.006650999999997964, 0.006696306999998569, 0.006438187000000539, 0.006291015999998706, 0.0066048320000007266, 0.006889389999997775, 0.011074819000000957, 0.006442155000002003, 0.0063403019999981325, 0.0062837749999999915, 0.006523076999997102, 0.006556832999997653, 0.006286891000002015, 0.006476963000004332, 0.006907141000006334, 0.010237540000005652, 0.006424039000002324, 0.006268391999995515, 0.006472753000004161, 0.006817368000007207, 0.006953535000000954, 0.006787205999998491 ], "coldSeconds": 0.02192342400000058, "relMax": 0.0005808046861575829, "relL2": 0.00018640613251259583 }, { "n": 256, "solveSeconds": 0.012667440999997837, "solveSecondsAll": [ 0.014435350999995933, 0.013557629999993992, 0.01316064599999578, 0.016306965999994816, 0.01804958900000031, 0.013651622000004693, 0.013122312999996666, 0.012976750999996511, 0.013205261000003077, 0.013464123000005657, 0.017066571000000863, 0.013106201999995903, 0.013451490000001343, 0.013198506000001942, 0.012836907000000508, 0.016781428999998127, 0.012667440999997837, 0.013443773999995301, 0.012997078000005047, 0.012883266000002891, 0.013788226999999154, 0.015897834000000444, 0.01357635699999804, 0.013091963999997347, 0.013055196999999907, 0.012914757999993753, 0.013697403000001884, 0.017529000999999766, 0.013301235000000133, 0.012857886999995571, 0.013007303999998499, 0.013169255000001101, 0.0167227510000032, 0.012799856000000887, 0.01294180600000061, 0.012731518000002495 ], "coldSeconds": 0.03854879600000771, "relMax": 0.0007199753684606416, "relL2": 0.00022167207232277986 }, { "n": 384, "solveSeconds": 0.038414482999996835, "solveSecondsAll": [ 0.038414482999996835, 0.04179160600000387, 0.04097667799999982, 0.04089557200000371, 0.04066232499999245, 0.04243911900000086, 0.039088623999994354, 0.03960488500000281, 0.04260250699999801, 0.03856245800000124, 0.0392699629999953, 0.044632405999990965, 0.03968511600000113 ], "coldSeconds": 0.07065423299999907, "relMax": 0.0000066385581709322546, "relL2": 0.000004133137928663183 }, { "n": 512, "solveSeconds": 0.08500106700000032, "solveSecondsAll": [ 0.0860081180000023, 0.09305599399999664, 0.08610516999999618, 0.08989734200000044, 0.08500106700000032, 0.09060736200000719 ], "coldSeconds": 0.12663970799999902, "relMax": 0.000006968577923121953, "relL2": 0.000006186731319051547 }, { "n": 768, "solveSeconds": 0.2674002000000044, "solveSecondsAll": [ 0.274606894999998, 0.27479459899999625, 0.2674002000000044, 0.2689096840000005, 0.27382437100000345 ], "coldSeconds": 0.33026680599999736, "relMax": 0.000003992015804376783, "relL2": 0.00000378141873397912 } ] }