files / problems / smale-tau / compute / q1 / certificate.json

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{
 "problem": "smale-tau",
 "quest": "q1",
 "definition": "tau(N) = least k with x_0 = 1, x_k = N, x_i = x_j o x_l (j, l < i), o in {+, -, *}",
 "reached_within_k_steps": [
  1,
  2,
  4,
  9,
  26,
  102,
  562,
  4363,
  46154,
  652227
 ],
 "nodes_per_depth_to_9": [
  1,
  2,
  8,
  59,
  663,
  10609,
  225219,
  6057298,
  199290037
 ],
 "targets": {
  "13!": {
   "value": "6227020800",
   "shortest_found": 11,
   "no_program_of_length_at_most": null,
   "program": [
    "1",
    "2",
    "3",
    "4",
    "9",
    "36",
    "39",
    "324",
    "12636",
    "492804",
    "492800",
    "6227020800"
   ],
   "tau_range": [
    1,
    11
   ]
  },
  "14!": {
   "value": "87178291200",
   "shortest_found": 11,
   "no_program_of_length_at_most": null,
   "program": [
    "1",
    "2",
    "4",
    "6",
    "12",
    "144",
    "140",
    "840",
    "120960",
    "725760",
    "120120",
    "87178291200"
   ],
   "tau_range": [
    1,
    11
   ]
  },
  "15!": {
   "value": "1307674368000",
   "shortest_found": 12,
   "no_program_of_length_at_most": 11,
   "program": [
    "1",
    "2",
    "3",
    "6",
    "8",
    "36",
    "28",
    "1008",
    "1000",
    "36000",
    "36036",
    "36288000",
    "1307674368000"
   ],
   "tau": 12
  },
  "16!": {
   "value": "20922789888000",
   "shortest_found": 12,
   "no_program_of_length_at_most": 11,
   "program": [
    "1",
    "2",
    "3",
    "4",
    "7",
    "12",
    "144",
    "143",
    "1008",
    "144144",
    "144000",
    "145297152",
    "20922789888000"
   ],
   "tau": 12
  },
  "17!": {
   "value": "355687428096000",
   "shortest_found": 12,
   "no_program_of_length_at_most": 11,
   "program": [
    "1",
    "2",
    "4",
    "6",
    "12",
    "144",
    "140",
    "156",
    "20160",
    "936",
    "18869760",
    "18849600",
    "355687428096000"
   ],
   "tau": 12
  },
  "18!": {
   "value": "6402373705728000",
   "shortest_found": null,
   "no_program_of_length_at_most": 12,
   "program": null,
   "tau_at_least": 13
  },
  "19!": {
   "value": "121645100408832000",
   "shortest_found": null,
   "no_program_of_length_at_most": 12,
   "program": null,
   "tau_at_least": 13
  },
  "20!": {
   "value": "2432902008176640000",
   "shortest_found": null,
   "no_program_of_length_at_most": 12,
   "program": null,
   "tau_at_least": 13
  },
  "21!": {
   "value": "51090942171709440000",
   "shortest_found": null,
   "no_program_of_length_at_most": 12,
   "program": null,
   "tau_at_least": 13
  },
  "22!": {
   "value": "1124000727777607680000",
   "shortest_found": null,
   "no_program_of_length_at_most": 12,
   "program": null,
   "tau_at_least": 13
  },
  "29#": {
   "value": "6469693230",
   "shortest_found": 12,
   "no_program_of_length_at_most": 11,
   "program": [
    "1",
    "2",
    "3",
    "4",
    "16",
    "19",
    "22",
    "35",
    "665",
    "14630",
    "442225",
    "442221",
    "6469693230"
   ],
   "tau": 12
  },
  "31#": {
   "value": "200560490130",
   "shortest_found": 12,
   "no_program_of_length_at_most": 11,
   "program": [
    "1",
    "2",
    "3",
    "5",
    "10",
    "100",
    "1000",
    "1001",
    "10010",
    "2001",
    "10013",
    "20030010",
    "200560490130"
   ],
   "tau": 12
  }
 },
 "runs": {
  "decide11_core.json": {
   "mode": "decide",
   "steps": 11,
   "prefix_depth": 8,
   "threads": 8,
   "seconds": 50.3,
   "nodes_per_depth": [
    1,
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    8,
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    663,
    10609,
    225219,
    6057298
   ],
   "leaves": 6057298,
   "pruned": 0,
   "leaf_target_pairs_filtered_by_size": 40136159
  },
  "decide12.json": {
   "mode": "decide",
   "steps": 12,
   "prefix_depth": 9,
   "threads": 8,
   "seconds": 2998.0,
   "nodes_per_depth": [
    1,
    2,
    8,
    59,
    663,
    10609,
    225219,
    6057298,
    199290037
   ],
   "leaves": 199290037,
   "pruned": 0,
   "leaf_target_pairs_filtered_by_size": 979391334
  }
 }
}