[
  {
    "id": "s01",
    "description": "Task 1: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.975,
      0.39,
      0.504,
      0.592,
      0.464,
      0.191,
      0.103,
      0.434
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.146,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.153,
        -0.594,
        -0.465,
        0.0
      ],
      [
        0.146,
        0.0,
        0.0,
        0.0,
        -0.441,
        0.0,
        0.0,
        0.532
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.725,
        0.81,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.153,
        -0.441,
        0.725,
        0.0,
        0.0,
        0.0,
        0.455
      ],
      [
        0.0,
        -0.594,
        0.0,
        0.81,
        0.0,
        0.0,
        0.0,
        0.789
      ],
      [
        0.0,
        -0.465,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.532,
        0.0,
        0.455,
        0.789,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      3,
      5,
      7
    ],
    "optimal_score": 2.816
  },
  {
    "id": "s02",
    "description": "Task 2: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.216,
      0.101,
      0.48,
      0.721,
      0.308,
      0.786,
      0.147,
      0.051
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.239,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.492,
        0.654
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.872,
        0.0,
        0.014
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.724,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.525,
        -0.374,
        0.0
      ],
      [
        -0.239,
        0.0,
        0.872,
        0.0,
        0.525,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.492,
        0.0,
        0.724,
        -0.374,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.654,
        0.014,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      2,
      4,
      5
    ],
    "optimal_score": 2.971
  },
  {
    "id": "s03",
    "description": "Task 3: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.116,
      0.421,
      0.756,
      0.391,
      0.856,
      0.714,
      0.466,
      0.446
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.25,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.25,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.485,
        -0.539,
        0.0,
        0.363
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.485,
        0.0,
        0.0,
        -0.272,
        0.081
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.539,
        0.0,
        0.0,
        0.0,
        -0.326
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.272,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.363,
        0.081,
        -0.326,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      2,
      4,
      5
    ],
    "optimal_score": 2.326
  },
  {
    "id": "s04",
    "description": "Task 4: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.994,
      0.151,
      0.58,
      0.926,
      0.542,
      0.293,
      0.377,
      0.314
    ],
    "synergy": [
      [
        0.0,
        0.305,
        0.7,
        0.534,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.305,
        0.0,
        0.0,
        -0.1,
        0.0,
        0.0,
        -0.217,
        0.0
      ],
      [
        0.7,
        0.0,
        0.0,
        0.0,
        0.178,
        0.506,
        0.0,
        0.0
      ],
      [
        0.534,
        -0.1,
        0.0,
        0.0,
        0.0,
        0.417,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.178,
        0.0,
        0.0,
        -0.036,
        0.45,
        0.0
      ],
      [
        0.0,
        0.0,
        0.506,
        0.417,
        -0.036,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.217,
        0.0,
        0.0,
        0.45,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      2,
      3
    ],
    "optimal_score": 3.734
  },
  {
    "id": "s05",
    "description": "Task 5: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.628,
      0.055,
      0.211,
      0.406,
      0.613,
      0.276,
      0.095,
      0.882
    ],
    "synergy": [
      [
        0.0,
        0.0,
        -0.334,
        0.0,
        0.39,
        0.0,
        0.0,
        -0.161
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.4,
        0.843,
        -0.407,
        -0.115
      ],
      [
        -0.334,
        0.0,
        0.0,
        0.497,
        -0.194,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.497,
        0.0,
        0.0,
        0.0,
        0.0,
        0.084
      ],
      [
        0.39,
        -0.4,
        -0.194,
        0.0,
        0.0,
        -0.04,
        0.0,
        0.0
      ],
      [
        0.0,
        0.843,
        0.0,
        0.0,
        -0.04,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.407,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.161,
        -0.115,
        0.0,
        0.084,
        0.0,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      4,
      7
    ],
    "optimal_score": 2.352
  },
  {
    "id": "s06",
    "description": "Task 6: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.975,
      0.27,
      0.618,
      0.661,
      0.512,
      0.349,
      0.813,
      0.78
    ],
    "synergy": [
      [
        0.0,
        -0.43,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.43,
        0.0,
        0.0,
        0.0,
        0.0,
        0.739,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.072,
        0.245,
        -0.377,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.122,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.072,
        -0.122,
        0.0,
        0.018,
        0.0,
        0.0
      ],
      [
        0.0,
        0.739,
        0.245,
        0.0,
        0.018,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.377,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      6,
      7
    ],
    "optimal_score": 2.568
  },
  {
    "id": "s07",
    "description": "Task 7: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.442,
      0.413,
      0.176,
      0.627,
      0.981,
      0.099,
      0.703,
      0.477
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.004,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.238,
        0.015,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.347,
        -0.036,
        0.802,
        0.168,
        0.0
      ],
      [
        0.0,
        0.238,
        -0.347,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.166
      ],
      [
        0.004,
        0.015,
        -0.036,
        0.0,
        0.0,
        0.228,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.802,
        0.0,
        0.228,
        0.0,
        0.273,
        0.0
      ],
      [
        0.0,
        0.0,
        0.168,
        0.0,
        0.0,
        0.273,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.166,
        0.0,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      3,
      4,
      6
    ],
    "optimal_score": 2.311
  },
  {
    "id": "s08",
    "description": "Task 8: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.735,
      0.447,
      0.656,
      0.926,
      0.897,
      0.896,
      0.461,
      0.888
    ],
    "synergy": [
      [
        0.0,
        -0.141,
        0.318,
        0.0,
        0.0,
        0.0,
        0.0,
        0.053
      ],
      [
        -0.141,
        0.0,
        0.0,
        0.0,
        0.0,
        0.643,
        0.0,
        0.0
      ],
      [
        0.318,
        0.0,
        0.0,
        -0.232,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.232,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.481
      ],
      [
        0.0,
        0.643,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.045
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.212
      ],
      [
        0.053,
        0.0,
        0.0,
        0.0,
        -0.481,
        -0.045,
        -0.212,
        0.0
      ]
    ],
    "optimal_subset": [
      1,
      3,
      5
    ],
    "optimal_score": 2.912
  },
  {
    "id": "s09",
    "description": "Task 9: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.098,
      0.07,
      0.257,
      0.839,
      0.291,
      0.253,
      0.925,
      0.061
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.42
      ],
      [
        0.0,
        0.0,
        0.0,
        0.72,
        0.0,
        -0.17,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.432,
        0.0
      ],
      [
        0.0,
        0.72,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.457,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.17,
        0.0,
        0.0,
        -0.457,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.432,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.42,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      1,
      3,
      6
    ],
    "optimal_score": 2.554
  },
  {
    "id": "s10",
    "description": "Task 10: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.358,
      0.635,
      0.135,
      0.147,
      0.371,
      0.56,
      0.426,
      0.257
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.153,
        -0.083,
        0.825,
        0.867,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.153,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.121,
        0.0
      ],
      [
        0.0,
        -0.083,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.253,
        0.0
      ],
      [
        0.0,
        0.825,
        0.0,
        0.0,
        0.0,
        0.0,
        0.495,
        0.602
      ],
      [
        0.0,
        0.867,
        0.0,
        0.0,
        0.0,
        0.0,
        0.761,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.121,
        -0.253,
        0.495,
        0.761,
        0.0,
        0.83
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.602,
        0.0,
        0.83,
        0.0
      ]
    ],
    "optimal_subset": [
      1,
      4,
      5
    ],
    "optimal_score": 3.258
  },
  {
    "id": "s11",
    "description": "Task 11: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.673,
      0.27,
      0.353,
      0.501,
      0.519,
      0.507,
      0.68,
      0.235
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.236,
        0.0,
        0.0,
        -0.53
      ],
      [
        0.0,
        0.0,
        -0.503,
        0.0,
        0.0,
        0.866,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.503,
        0.0,
        0.706,
        0.0,
        0.0,
        0.0,
        -0.356
      ],
      [
        0.0,
        0.0,
        0.706,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.236,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.866,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.294
      ],
      [
        -0.53,
        0.0,
        -0.356,
        0.0,
        0.0,
        0.0,
        0.294,
        0.0
      ]
    ],
    "optimal_subset": [
      1,
      5,
      6
    ],
    "optimal_score": 2.323
  },
  {
    "id": "s12",
    "description": "Task 12: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.789,
      0.179,
      0.718,
      0.698,
      0.058,
      0.146,
      0.144,
      0.436
    ],
    "synergy": [
      [
        0.0,
        0.0,
        -0.47,
        0.0,
        0.0,
        0.459,
        0.43,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.208,
        0.0,
        0.617,
        0.0
      ],
      [
        -0.47,
        0.0,
        0.0,
        0.442,
        0.0,
        -0.258,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.442,
        0.0,
        -0.251,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.208,
        0.0,
        -0.251,
        0.0,
        0.0,
        0.0,
        0.536
      ],
      [
        0.459,
        0.0,
        -0.258,
        0.0,
        0.0,
        0.0,
        -0.282,
        0.0
      ],
      [
        0.43,
        0.617,
        0.0,
        0.0,
        0.0,
        -0.282,
        0.0,
        0.767
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.536,
        0.0,
        0.767,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      6,
      7
    ],
    "optimal_score": 2.566
  },
  {
    "id": "s13",
    "description": "Task 13: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.629,
      0.795,
      0.323,
      0.248,
      0.366,
      0.551,
      0.776,
      0.947
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.563,
        0.834,
        0.111
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.872,
        0.051,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.62,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.337,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.872,
        0.62,
        -0.337,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.563,
        0.051,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.834,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.111,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      5,
      6
    ],
    "optimal_score": 3.353
  },
  {
    "id": "s14",
    "description": "Task 14: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.458,
      0.373,
      0.74,
      0.88,
      0.326,
      0.192,
      0.88,
      0.805
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.662,
        0.304,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.169,
        0.073,
        0.0
      ],
      [
        0.662,
        0.0,
        0.0,
        0.0,
        -0.578,
        -0.264,
        0.0,
        -0.428
      ],
      [
        0.304,
        0.0,
        0.0,
        0.0,
        0.037,
        0.0,
        0.055,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.578,
        0.037,
        0.0,
        0.146,
        0.0,
        -0.442
      ],
      [
        0.0,
        0.169,
        -0.264,
        0.0,
        0.146,
        0.0,
        -0.526,
        0.185
      ],
      [
        0.0,
        0.073,
        0.0,
        0.055,
        0.0,
        -0.526,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.428,
        0.0,
        -0.442,
        0.185,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      2,
      3
    ],
    "optimal_score": 3.044
  },
  {
    "id": "s15",
    "description": "Task 15: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.128,
      0.23,
      0.515,
      0.574,
      0.529,
      0.786,
      0.961,
      0.982
    ],
    "synergy": [
      [
        0.0,
        0.004,
        0.0,
        0.718,
        0.206,
        0.528,
        0.0,
        0.093
      ],
      [
        0.004,
        0.0,
        0.0,
        0.0,
        0.637,
        0.0,
        0.839,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.244,
        0.0,
        0.0,
        0.0
      ],
      [
        0.718,
        0.0,
        0.0,
        0.0,
        0.268,
        -0.338,
        0.225,
        0.0
      ],
      [
        0.206,
        0.637,
        0.244,
        0.268,
        0.0,
        0.486,
        0.0,
        0.467
      ],
      [
        0.528,
        0.0,
        0.0,
        -0.338,
        0.486,
        0.0,
        -0.045,
        0.0
      ],
      [
        0.0,
        0.839,
        0.0,
        0.225,
        0.0,
        -0.045,
        0.0,
        0.0
      ],
      [
        0.093,
        0.0,
        0.0,
        0.0,
        0.467,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      4,
      5,
      7
    ],
    "optimal_score": 3.25
  },
  {
    "id": "s16",
    "description": "Task 16: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.07,
      0.978,
      0.224,
      0.239,
      0.293,
      0.801,
      0.175,
      0.533
    ],
    "synergy": [
      [
        0.0,
        -0.203,
        0.0,
        0.0,
        0.0,
        0.0,
        0.446,
        -0.091
      ],
      [
        -0.203,
        0.0,
        0.335,
        0.0,
        0.0,
        0.078,
        0.0,
        0.0
      ],
      [
        0.0,
        0.335,
        0.0,
        0.892,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.892,
        0.0,
        0.0,
        0.469,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.289,
        0.0,
        0.836
      ],
      [
        0.0,
        0.078,
        0.0,
        0.469,
        -0.289,
        0.0,
        -0.294,
        0.0
      ],
      [
        0.446,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.294,
        0.0,
        0.876
      ],
      [
        -0.091,
        0.0,
        0.0,
        0.0,
        0.836,
        0.0,
        0.876,
        0.0
      ]
    ],
    "optimal_subset": [
      4,
      6,
      7
    ],
    "optimal_score": 2.713
  },
  {
    "id": "s17",
    "description": "Task 17: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.215,
      0.095,
      0.43,
      0.845,
      0.939,
      0.075,
      0.699,
      0.236
    ],
    "synergy": [
      [
        0.0,
        0.838,
        -0.593,
        0.0,
        0.0,
        0.538,
        0.0,
        -0.037
      ],
      [
        0.838,
        0.0,
        0.04,
        0.445,
        0.0,
        0.0,
        0.0,
        -0.095
      ],
      [
        -0.593,
        0.04,
        0.0,
        0.385,
        0.72,
        0.0,
        0.0,
        0.295
      ],
      [
        0.0,
        0.445,
        0.385,
        0.0,
        0.2,
        0.0,
        0.0,
        0.38
      ],
      [
        0.0,
        0.0,
        0.72,
        0.2,
        0.0,
        0.0,
        0.0,
        -0.019
      ],
      [
        0.538,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.037,
        -0.095,
        0.295,
        0.38,
        -0.019,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      2,
      3,
      4
    ],
    "optimal_score": 3.519
  },
  {
    "id": "s18",
    "description": "Task 18: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.406,
      0.14,
      0.888,
      0.627,
      0.244,
      0.349,
      0.323,
      0.6
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.137,
        0.0,
        0.015,
        0.0,
        -0.435
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.379,
        0.0,
        0.0,
        0.0,
        0.024
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.027,
        0.0,
        -0.16,
        0.0
      ],
      [
        0.137,
        -0.379,
        0.0,
        0.0,
        0.0,
        -0.35,
        0.26,
        0.313
      ],
      [
        0.0,
        0.0,
        -0.027,
        0.0,
        0.0,
        0.006,
        0.0,
        0.744
      ],
      [
        0.015,
        0.0,
        0.0,
        -0.35,
        0.006,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.16,
        0.26,
        0.0,
        0.0,
        0.0,
        0.061
      ],
      [
        -0.435,
        0.024,
        0.0,
        0.313,
        0.744,
        0.0,
        0.061,
        0.0
      ]
    ],
    "optimal_subset": [
      3,
      4,
      7
    ],
    "optimal_score": 2.528
  },
  {
    "id": "s19",
    "description": "Task 19: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.507,
      0.738,
      0.286,
      0.887,
      0.559,
      0.622,
      0.285,
      0.607
    ],
    "synergy": [
      [
        0.0,
        0.0,
        -0.328,
        0.815,
        0.282,
        0.341,
        0.0,
        0.539
      ],
      [
        0.0,
        0.0,
        0.0,
        0.054,
        -0.278,
        0.791,
        0.0,
        0.26
      ],
      [
        -0.328,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.243,
        0.0
      ],
      [
        0.815,
        0.054,
        0.0,
        0.0,
        0.535,
        -0.147,
        0.76,
        0.0
      ],
      [
        0.282,
        -0.278,
        0.0,
        0.535,
        0.0,
        0.0,
        0.559,
        0.0
      ],
      [
        0.341,
        0.791,
        0.0,
        -0.147,
        0.0,
        0.0,
        0.591,
        -0.357
      ],
      [
        0.0,
        0.0,
        0.243,
        0.76,
        0.559,
        0.591,
        0.0,
        0.0
      ],
      [
        0.539,
        0.26,
        0.0,
        0.0,
        0.0,
        -0.357,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      3,
      4
    ],
    "optimal_score": 3.585
  },
  {
    "id": "s20",
    "description": "Task 20: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.436,
      0.816,
      0.472,
      0.715,
      0.646,
      0.315,
      0.077,
      0.559
    ],
    "synergy": [
      [
        0.0,
        -0.439,
        -0.472,
        0.0,
        0.0,
        0.0,
        -0.483,
        0.294
      ],
      [
        -0.439,
        0.0,
        -0.542,
        0.042,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.472,
        -0.542,
        0.0,
        0.0,
        -0.237,
        0.88,
        0.0,
        -0.084
      ],
      [
        0.0,
        0.042,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.341
      ],
      [
        0.0,
        0.0,
        -0.237,
        0.0,
        0.0,
        0.364,
        0.0,
        -0.505
      ],
      [
        0.0,
        0.0,
        0.88,
        0.0,
        0.364,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.483,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.294,
        0.0,
        -0.084,
        0.341,
        -0.505,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      1,
      3,
      7
    ],
    "optimal_score": 2.473
  },
  {
    "id": "s21",
    "description": "Task 21: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.609,
      0.414,
      0.379,
      0.631,
      0.435,
      0.587,
      0.292,
      0.067
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.233,
        0.251,
        0.896,
        -0.332,
        0.0
      ],
      [
        0.0,
        0.0,
        0.835,
        -0.587,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.835,
        0.0,
        0.0,
        0.0,
        -0.412,
        0.0,
        -0.581
      ],
      [
        0.233,
        -0.587,
        0.0,
        0.0,
        -0.45,
        -0.235,
        0.0,
        0.0
      ],
      [
        0.251,
        0.0,
        0.0,
        -0.45,
        0.0,
        0.0,
        0.659,
        -0.337
      ],
      [
        0.896,
        0.0,
        -0.412,
        -0.235,
        0.0,
        0.0,
        0.743,
        -0.503
      ],
      [
        -0.332,
        0.0,
        0.0,
        0.0,
        0.659,
        0.743,
        0.0,
        0.414
      ],
      [
        0.0,
        0.0,
        -0.581,
        0.0,
        -0.337,
        -0.503,
        0.414,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      5,
      6
    ],
    "optimal_score": 2.795
  },
  {
    "id": "s22",
    "description": "Task 22: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.774,
      0.376,
      0.949,
      0.287,
      0.174,
      0.128,
      0.247,
      0.171
    ],
    "synergy": [
      [
        0.0,
        0.265,
        0.476,
        0.0,
        0.377,
        0.0,
        -0.407,
        0.0
      ],
      [
        0.265,
        0.0,
        -0.095,
        0.0,
        0.0,
        0.373,
        0.0,
        0.0
      ],
      [
        0.476,
        -0.095,
        0.0,
        0.0,
        0.059,
        0.544,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.519,
        -0.506,
        0.0,
        0.0
      ],
      [
        0.377,
        0.0,
        0.059,
        0.519,
        0.0,
        0.0,
        0.603,
        0.0
      ],
      [
        0.0,
        0.373,
        0.544,
        -0.506,
        0.0,
        0.0,
        0.36,
        0.169
      ],
      [
        -0.407,
        0.0,
        0.0,
        0.0,
        0.603,
        0.36,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.169,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      2,
      5
    ],
    "optimal_score": 2.871
  },
  {
    "id": "s23",
    "description": "Task 23: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.421,
      0.704,
      0.128,
      0.378,
      0.532,
      0.959,
      0.307,
      0.496
    ],
    "synergy": [
      [
        0.0,
        0.566,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.566,
        0.0,
        0.767,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.767,
        0.0,
        0.0,
        -0.338,
        0.611,
        -0.476,
        0.227
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.338,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.611,
        0.0,
        0.0,
        0.0,
        -0.305,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.476,
        0.0,
        0.0,
        -0.305,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.227,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      1,
      2,
      5
    ],
    "optimal_score": 3.169
  },
  {
    "id": "s24",
    "description": "Task 24: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.506,
      0.615,
      0.688,
      0.687,
      0.588,
      0.352,
      0.911,
      0.628
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.004,
        0.0,
        0.886,
        -0.526,
        0.0,
        -0.074
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.592,
        0.142,
        0.0,
        0.0,
        0.0
      ],
      [
        0.004,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.001,
        0.0
      ],
      [
        0.0,
        -0.592,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.654
      ],
      [
        0.886,
        0.142,
        0.0,
        0.0,
        0.0,
        0.201,
        0.0,
        0.0
      ],
      [
        -0.526,
        0.0,
        0.0,
        0.0,
        0.201,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.001,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.186
      ],
      [
        -0.074,
        0.0,
        0.0,
        0.654,
        0.0,
        0.0,
        -0.186,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      4,
      6
    ],
    "optimal_score": 2.891
  },
  {
    "id": "s25",
    "description": "Task 25: choose the 3 most useful tools from 8 candidates (small pool).",
    "tier": "small",
    "n_tools": 8,
    "k": 3,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      }
    ],
    "weights": [
      0.443,
      0.444,
      0.274,
      0.583,
      0.411,
      0.862,
      0.872,
      0.548
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.21,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.014,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.014,
        0.0,
        -0.211,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.21,
        0.0,
        -0.211,
        0.0,
        0.296,
        0.836,
        0.626,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.296,
        0.0,
        0.0,
        0.189,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.836,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.626,
        0.189,
        0.0,
        0.0,
        -0.424
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.424,
        0.0
      ]
    ],
    "optimal_subset": [
      3,
      5,
      6
    ],
    "optimal_score": 3.779
  },
  {
    "id": "f01",
    "description": "Task 26: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.6,
      0.469,
      0.164,
      0.779,
      0.516,
      0.54,
      0.897,
      0.277,
      0.208,
      0.369,
      0.531,
      0.206,
      0.735,
      0.24,
      0.298,
      0.986
    ],
    "synergy": [
      [
        0.0,
        0.342,
        0.469,
        0.0,
        0.589,
        -0.405,
        -0.378,
        0.0,
        0.0,
        0.5,
        0.0,
        -0.189,
        0.0,
        -0.239,
        0.218,
        0.0
      ],
      [
        0.342,
        0.0,
        -0.03,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.352,
        0.0,
        0.0,
        0.0
      ],
      [
        0.469,
        -0.03,
        0.0,
        -0.012,
        0.0,
        0.0,
        -0.517,
        0.0,
        0.753,
        0.0,
        0.0,
        0.0,
        -0.185,
        0.384,
        0.0,
        -0.112
      ],
      [
        0.0,
        0.0,
        -0.012,
        0.0,
        0.0,
        0.116,
        0.026,
        0.0,
        0.0,
        0.0,
        -0.149,
        0.0,
        0.0,
        -0.349,
        0.0,
        0.0
      ],
      [
        0.589,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.179,
        -0.078,
        0.0,
        0.0,
        0.0,
        0.686,
        0.646,
        0.0,
        0.0
      ],
      [
        -0.405,
        0.0,
        0.0,
        0.116,
        0.0,
        0.0,
        0.0,
        0.0,
        0.892,
        0.0,
        0.625,
        0.0,
        0.0,
        0.0,
        0.204,
        0.0
      ],
      [
        -0.378,
        0.0,
        -0.517,
        0.026,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.167,
        0.0,
        0.0,
        -0.41,
        0.0,
        0.138,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.179,
        0.0,
        0.0,
        0.0,
        0.0,
        0.299,
        0.0,
        -0.293,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.753,
        0.0,
        -0.078,
        0.892,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.471,
        0.0,
        0.0,
        0.272,
        0.0,
        0.309
      ],
      [
        0.5,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.167,
        0.299,
        0.0,
        0.0,
        0.0,
        0.881,
        0.0,
        0.603,
        0.0,
        0.193
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.149,
        0.0,
        0.625,
        0.0,
        0.0,
        -0.471,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.189,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.293,
        0.0,
        0.881,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.352,
        -0.185,
        0.0,
        0.686,
        0.0,
        -0.41,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.538,
        0.0,
        0.596
      ],
      [
        -0.239,
        0.0,
        0.384,
        -0.349,
        0.646,
        0.0,
        0.0,
        0.0,
        0.272,
        0.603,
        0.0,
        0.0,
        0.538,
        0.0,
        0.0,
        0.0
      ],
      [
        0.218,
        0.0,
        0.0,
        0.0,
        0.0,
        0.204,
        0.138,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.112,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.309,
        0.193,
        0.0,
        0.0,
        0.596,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      4,
      9,
      12,
      13,
      15
    ],
    "optimal_score": 6.108
  },
  {
    "id": "f02",
    "description": "Task 27: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.971,
      0.422,
      0.191,
      0.604,
      0.608,
      0.271,
      0.753,
      0.878,
      0.438,
      0.274,
      0.242,
      0.471,
      0.63,
      0.157,
      0.44,
      0.411
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.157,
        0.0,
        -0.097,
        0.0,
        0.543,
        0.0,
        0.865,
        0.162,
        0.025,
        0.825,
        0.0,
        -0.26,
        0.652
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.123,
        0.0,
        0.0,
        0.287,
        0.0,
        0.266,
        -0.261,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.452,
        0.0,
        0.0,
        0.0,
        0.0,
        0.142,
        -0.119,
        0.23,
        0.674,
        0.0,
        0.474,
        0.0,
        0.051
      ],
      [
        0.157,
        0.0,
        0.452,
        0.0,
        0.0,
        0.0,
        0.0,
        0.873,
        0.205,
        0.0,
        0.0,
        0.0,
        0.218,
        -0.016,
        0.0,
        0.576
      ],
      [
        0.0,
        0.123,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.075,
        0.0,
        0.0,
        0.224,
        0.0,
        0.725,
        -0.081,
        -0.211,
        0.006
      ],
      [
        -0.097,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.637,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.461,
        0.047,
        -0.323,
        -0.012
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.637,
        0.0,
        -0.448,
        0.108,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.543,
        0.287,
        0.0,
        0.873,
        -0.075,
        0.0,
        -0.448,
        0.0,
        0.0,
        0.0,
        0.475,
        0.815,
        0.0,
        0.0,
        -0.383,
        0.0
      ],
      [
        0.0,
        0.0,
        0.142,
        0.205,
        0.0,
        0.0,
        0.108,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.174,
        0.0,
        0.414,
        0.0
      ],
      [
        0.865,
        0.266,
        -0.119,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.269,
        0.0,
        -0.517,
        0.485,
        -0.49
      ],
      [
        0.162,
        -0.261,
        0.23,
        0.0,
        0.224,
        0.0,
        0.0,
        0.475,
        0.0,
        0.0,
        0.0,
        -0.33,
        0.798,
        0.0,
        0.0,
        0.0
      ],
      [
        0.025,
        0.0,
        0.674,
        0.0,
        0.0,
        0.0,
        0.0,
        0.815,
        0.0,
        -0.269,
        -0.33,
        0.0,
        0.0,
        0.586,
        0.888,
        0.0
      ],
      [
        0.825,
        0.0,
        0.0,
        0.218,
        0.725,
        0.461,
        0.0,
        0.0,
        -0.174,
        0.0,
        0.798,
        0.0,
        0.0,
        0.644,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.474,
        -0.016,
        -0.081,
        0.047,
        0.0,
        0.0,
        0.0,
        -0.517,
        0.0,
        0.586,
        0.644,
        0.0,
        -0.503,
        -0.034
      ],
      [
        -0.26,
        0.0,
        0.0,
        0.0,
        -0.211,
        -0.323,
        0.0,
        -0.383,
        0.414,
        0.485,
        0.0,
        0.888,
        0.0,
        -0.503,
        0.0,
        0.0
      ],
      [
        0.652,
        0.0,
        0.051,
        0.576,
        0.006,
        -0.012,
        0.0,
        0.0,
        0.0,
        -0.49,
        0.0,
        0.0,
        0.0,
        -0.034,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      3,
      7,
      10,
      12
    ],
    "optimal_score": 7.376
  },
  {
    "id": "f03",
    "description": "Task 28: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.462,
      0.221,
      0.361,
      0.746,
      0.397,
      0.17,
      0.936,
      0.229,
      0.307,
      0.738,
      0.878,
      0.324,
      0.79,
      0.368,
      0.474,
      0.229
    ],
    "synergy": [
      [
        0.0,
        0.0,
        -0.548,
        -0.202,
        0.577,
        0.0,
        0.0,
        0.0,
        -0.329,
        0.0,
        0.14,
        -0.583,
        0.0,
        0.0,
        0.0,
        -0.511
      ],
      [
        0.0,
        0.0,
        0.0,
        0.139,
        0.0,
        0.0,
        -0.392,
        0.457,
        0.572,
        0.0,
        0.141,
        0.0,
        0.0,
        0.0,
        -0.427,
        0.158
      ],
      [
        -0.548,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.186,
        -0.257,
        0.0,
        0.0,
        0.0,
        0.0,
        0.859,
        -0.281,
        0.865,
        0.0,
        -0.383
      ],
      [
        -0.202,
        0.139,
        0.0,
        0.0,
        0.762,
        -0.246,
        0.0,
        -0.271,
        0.847,
        0.0,
        0.0,
        0.785,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.577,
        0.0,
        0.0,
        0.762,
        0.0,
        0.0,
        -0.41,
        0.0,
        0.0,
        -0.052,
        0.0,
        0.0,
        0.561,
        0.119,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.186,
        -0.246,
        0.0,
        0.0,
        0.045,
        0.0,
        -0.493,
        0.179,
        0.0,
        0.533,
        0.0,
        0.63,
        0.0,
        -0.228
      ],
      [
        0.0,
        -0.392,
        -0.257,
        0.0,
        -0.41,
        0.045,
        0.0,
        0.0,
        -0.148,
        0.0,
        0.0,
        0.0,
        0.0,
        0.767,
        0.0,
        0.0
      ],
      [
        0.0,
        0.457,
        0.0,
        -0.271,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.156,
        -0.168,
        0.399,
        -0.101,
        -0.198,
        0.0,
        0.306
      ],
      [
        -0.329,
        0.572,
        0.0,
        0.847,
        0.0,
        -0.493,
        -0.148,
        0.0,
        0.0,
        0.0,
        0.695,
        0.0,
        -0.534,
        -0.212,
        0.101,
        0.26
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.052,
        0.179,
        0.0,
        0.156,
        0.0,
        0.0,
        0.649,
        0.284,
        -0.289,
        0.0,
        -0.223,
        0.0
      ],
      [
        0.14,
        0.141,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.168,
        0.695,
        0.649,
        0.0,
        -0.079,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.583,
        0.0,
        0.859,
        0.785,
        0.0,
        0.533,
        0.0,
        0.399,
        0.0,
        0.284,
        -0.079,
        0.0,
        0.525,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.281,
        0.0,
        0.561,
        0.0,
        0.0,
        -0.101,
        -0.534,
        -0.289,
        0.0,
        0.525,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.865,
        0.0,
        0.119,
        0.63,
        0.767,
        -0.198,
        -0.212,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.676,
        0.0
      ],
      [
        0.0,
        -0.427,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.101,
        -0.223,
        0.0,
        0.0,
        0.0,
        0.676,
        0.0,
        -0.074
      ],
      [
        -0.511,
        0.158,
        -0.383,
        0.0,
        0.0,
        -0.228,
        0.0,
        0.306,
        0.26,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.074,
        0.0
      ]
    ],
    "optimal_subset": [
      3,
      8,
      9,
      10,
      11
    ],
    "optimal_score": 6.174
  },
  {
    "id": "f04",
    "description": "Task 29: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.376,
      0.116,
      0.892,
      0.715,
      0.786,
      0.269,
      0.286,
      0.932,
      0.482,
      0.701,
      0.857,
      0.385,
      0.893,
      0.649,
      0.848,
      0.468
    ],
    "synergy": [
      [
        0.0,
        0.723,
        -0.106,
        0.51,
        0.0,
        0.0,
        0.689,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.122,
        0.614,
        0.619,
        0.286,
        -0.459
      ],
      [
        0.723,
        0.0,
        0.0,
        0.0,
        -0.12,
        -0.228,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.039,
        -0.14,
        0.0,
        -0.449
      ],
      [
        -0.106,
        0.0,
        0.0,
        0.0,
        0.0,
        0.066,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.424,
        0.0,
        0.827,
        0.0,
        0.0
      ],
      [
        0.51,
        0.0,
        0.0,
        0.0,
        0.083,
        0.0,
        -0.285,
        0.132,
        0.0,
        -0.254,
        -0.497,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.196
      ],
      [
        0.0,
        -0.12,
        0.0,
        0.083,
        0.0,
        0.0,
        0.0,
        -0.568,
        0.0,
        -0.059,
        0.0,
        0.0,
        0.0,
        0.0,
        0.465,
        0.0
      ],
      [
        0.0,
        -0.228,
        0.066,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.462,
        0.742,
        0.276,
        -0.206
      ],
      [
        0.689,
        0.0,
        0.0,
        -0.285,
        0.0,
        0.0,
        0.0,
        -0.188,
        0.0,
        -0.53,
        0.0,
        0.461,
        0.0,
        -0.593,
        -0.427,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.132,
        -0.568,
        0.0,
        -0.188,
        0.0,
        0.875,
        0.164,
        -0.259,
        0.198,
        0.255,
        0.0,
        0.835,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.875,
        0.0,
        -0.009,
        0.0,
        0.0,
        0.0,
        -0.078,
        0.0,
        0.053
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.254,
        -0.059,
        0.0,
        -0.53,
        0.164,
        -0.009,
        0.0,
        0.0,
        0.643,
        0.682,
        0.0,
        0.572,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.497,
        0.0,
        0.0,
        0.0,
        -0.259,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.268,
        0.0
      ],
      [
        -0.122,
        0.0,
        0.424,
        0.0,
        0.0,
        0.0,
        0.461,
        0.198,
        0.0,
        0.643,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.614,
        0.039,
        0.0,
        0.0,
        0.0,
        -0.462,
        0.0,
        0.255,
        0.0,
        0.682,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.109,
        0.248
      ],
      [
        0.619,
        -0.14,
        0.827,
        0.0,
        0.0,
        0.742,
        -0.593,
        0.0,
        -0.078,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.741
      ],
      [
        0.286,
        0.0,
        0.0,
        0.0,
        0.465,
        0.276,
        -0.427,
        0.835,
        0.0,
        0.572,
        0.268,
        0.0,
        -0.109,
        0.0,
        0.0,
        -0.073
      ],
      [
        -0.459,
        -0.449,
        0.0,
        -0.196,
        0.0,
        -0.206,
        0.0,
        0.0,
        0.053,
        0.0,
        0.0,
        0.0,
        0.248,
        0.741,
        -0.073,
        0.0
      ]
    ],
    "optimal_subset": [
      7,
      8,
      9,
      12,
      14
    ],
    "optimal_score": 7.121
  },
  {
    "id": "f05",
    "description": "Task 30: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.341,
      0.143,
      0.174,
      0.258,
      0.724,
      0.765,
      0.326,
      0.134,
      0.506,
      0.767,
      0.41,
      0.591,
      0.312,
      0.93,
      0.264,
      0.449
    ],
    "synergy": [
      [
        0.0,
        -0.541,
        0.488,
        0.0,
        0.689,
        0.07,
        0.0,
        0.0,
        0.339,
        0.0,
        -0.123,
        -0.551,
        0.783,
        0.0,
        -0.031,
        0.0
      ],
      [
        -0.541,
        0.0,
        0.707,
        0.0,
        0.0,
        -0.555,
        0.0,
        0.0,
        0.0,
        -0.413,
        0.054,
        0.0,
        0.0,
        0.257,
        0.0,
        0.38
      ],
      [
        0.488,
        0.707,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.742,
        0.0,
        0.0,
        0.743,
        -0.312,
        0.0,
        0.0,
        -0.332,
        -0.035
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.439,
        0.0,
        -0.546,
        0.0,
        0.0,
        0.0,
        0.128,
        0.0,
        0.0
      ],
      [
        0.689,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.258,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.388,
        0.34,
        0.463,
        0.0
      ],
      [
        0.07,
        -0.555,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.098,
        0.0,
        0.527,
        0.0,
        0.0,
        -0.489,
        0.067,
        -0.157,
        0.155
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.258,
        0.0,
        0.0,
        0.0,
        0.018,
        0.0,
        -0.036,
        0.0,
        0.0,
        -0.293,
        0.0,
        0.321
      ],
      [
        0.0,
        0.0,
        0.742,
        -0.439,
        0.0,
        0.098,
        0.0,
        0.0,
        0.0,
        0.195,
        0.383,
        0.0,
        0.0,
        0.0,
        -0.254,
        -0.303
      ],
      [
        0.339,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.018,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.014,
        0.0
      ],
      [
        0.0,
        -0.413,
        0.0,
        -0.546,
        0.0,
        0.527,
        0.0,
        0.195,
        0.0,
        0.0,
        0.0,
        0.593,
        0.0,
        -0.185,
        0.0,
        0.0
      ],
      [
        -0.123,
        0.054,
        0.743,
        0.0,
        0.0,
        0.0,
        -0.036,
        0.383,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.587,
        0.0
      ],
      [
        -0.551,
        0.0,
        -0.312,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.593,
        0.0,
        0.0,
        0.0,
        0.721,
        0.0,
        0.0
      ],
      [
        0.783,
        0.0,
        0.0,
        0.0,
        -0.388,
        -0.489,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.257,
        0.0,
        0.128,
        0.34,
        0.067,
        -0.293,
        0.0,
        0.0,
        -0.185,
        0.0,
        0.721,
        0.0,
        0.0,
        0.0,
        0.658
      ],
      [
        -0.031,
        0.0,
        -0.332,
        0.0,
        0.463,
        -0.157,
        0.0,
        -0.254,
        -0.014,
        0.0,
        -0.587,
        0.0,
        0.0,
        0.0,
        0.0,
        0.881
      ],
      [
        0.0,
        0.38,
        -0.035,
        0.0,
        0.0,
        0.155,
        0.321,
        -0.303,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.658,
        0.881,
        0.0
      ]
    ],
    "optimal_subset": [
      5,
      9,
      11,
      13,
      15
    ],
    "optimal_score": 6.038
  },
  {
    "id": "f06",
    "description": "Task 31: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.476,
      0.651,
      0.184,
      0.31,
      0.308,
      0.457,
      0.258,
      0.715,
      0.575,
      0.422,
      0.886,
      0.808,
      0.577,
      0.722,
      0.305,
      0.651
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.404,
        0.667,
        0.0,
        0.0,
        0.0,
        0.0,
        0.639,
        0.2,
        0.0,
        0.0,
        -0.001,
        0.749,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.34,
        0.0,
        -0.133,
        0.0,
        -0.254,
        0.0,
        0.0,
        0.497,
        0.0,
        0.0,
        0.33,
        0.666,
        -0.073,
        0.0
      ],
      [
        0.404,
        -0.34,
        0.0,
        0.0,
        -0.033,
        0.0,
        0.0,
        0.0,
        0.588,
        0.821,
        0.0,
        0.0,
        0.0,
        0.13,
        0.0,
        0.306
      ],
      [
        0.667,
        0.0,
        0.0,
        0.0,
        0.796,
        0.0,
        0.0,
        0.203,
        0.526,
        0.319,
        0.44,
        0.0,
        -0.205,
        -0.215,
        -0.471,
        0.0
      ],
      [
        0.0,
        -0.133,
        -0.033,
        0.796,
        0.0,
        0.531,
        0.0,
        0.0,
        0.0,
        0.0,
        0.368,
        0.282,
        0.0,
        0.416,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.531,
        0.0,
        -0.108,
        -0.582,
        0.0,
        -0.255,
        0.0,
        0.01,
        0.0,
        0.667,
        0.0,
        0.019
      ],
      [
        0.0,
        -0.254,
        0.0,
        0.0,
        0.0,
        -0.108,
        0.0,
        0.0,
        0.544,
        0.287,
        0.81,
        0.595,
        -0.548,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.203,
        0.0,
        -0.582,
        0.0,
        0.0,
        0.167,
        0.604,
        0.0,
        0.0,
        0.0,
        -0.357,
        0.468,
        0.0
      ],
      [
        0.639,
        0.0,
        0.588,
        0.526,
        0.0,
        0.0,
        0.544,
        0.167,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.513,
        0.0
      ],
      [
        0.2,
        0.497,
        0.821,
        0.319,
        0.0,
        -0.255,
        0.287,
        0.604,
        0.0,
        0.0,
        0.895,
        0.021,
        -0.575,
        0.0,
        0.612,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.44,
        0.368,
        0.0,
        0.81,
        0.0,
        0.0,
        0.895,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.282,
        0.01,
        0.595,
        0.0,
        0.0,
        0.021,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.27,
        0.0
      ],
      [
        -0.001,
        0.33,
        0.0,
        -0.205,
        0.0,
        0.0,
        -0.548,
        0.0,
        0.0,
        -0.575,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.749,
        0.666,
        0.13,
        -0.215,
        0.416,
        0.667,
        0.0,
        -0.357,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.073,
        0.0,
        -0.471,
        0.0,
        0.0,
        0.0,
        0.468,
        0.513,
        0.612,
        0.0,
        -0.27,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.306,
        0.0,
        0.0,
        0.019,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      3,
      8,
      9,
      10
    ],
    "optimal_score": 6.355
  },
  {
    "id": "f07",
    "description": "Task 32: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.352,
      0.15,
      0.487,
      0.782,
      0.419,
      0.487,
      0.453,
      0.851,
      0.99,
      0.126,
      0.234,
      0.963,
      0.888,
      0.108,
      0.237,
      0.523
    ],
    "synergy": [
      [
        0.0,
        0.322,
        0.0,
        -0.199,
        0.184,
        0.0,
        0.0,
        0.848,
        0.0,
        0.871,
        0.0,
        -0.207,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.322,
        0.0,
        0.0,
        0.0,
        0.875,
        0.214,
        0.0,
        -0.334,
        0.0,
        -0.179,
        0.287,
        0.839,
        0.0,
        0.604,
        0.713,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.701,
        0.546,
        -0.449,
        0.345,
        -0.016,
        0.431,
        0.0,
        0.0,
        0.0,
        0.241,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.199,
        0.0,
        0.701,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.531,
        0.0,
        0.0,
        0.0,
        0.223,
        0.0,
        0.0,
        -0.28
      ],
      [
        0.184,
        0.875,
        0.546,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.179,
        0.373,
        0.0,
        -0.3,
        0.0,
        -0.359,
        0.0,
        0.539
      ],
      [
        0.0,
        0.214,
        -0.449,
        0.0,
        0.0,
        0.0,
        0.235,
        0.304,
        -0.33,
        -0.083,
        0.181,
        0.0,
        -0.219,
        0.0,
        0.0,
        -0.332
      ],
      [
        0.0,
        0.0,
        0.345,
        0.0,
        0.0,
        0.235,
        0.0,
        0.0,
        0.491,
        0.0,
        0.0,
        0.0,
        -0.409,
        0.0,
        -0.151,
        0.0
      ],
      [
        0.848,
        -0.334,
        -0.016,
        0.0,
        0.0,
        0.304,
        0.0,
        0.0,
        0.0,
        0.0,
        0.058,
        0.0,
        0.058,
        0.546,
        0.0,
        -0.585
      ],
      [
        0.0,
        0.0,
        0.431,
        0.531,
        -0.179,
        -0.33,
        0.491,
        0.0,
        0.0,
        0.888,
        0.154,
        0.212,
        0.0,
        -0.158,
        0.425,
        0.0
      ],
      [
        0.871,
        -0.179,
        0.0,
        0.0,
        0.373,
        -0.083,
        0.0,
        0.0,
        0.888,
        0.0,
        0.0,
        -0.126,
        0.0,
        0.0,
        0.298,
        0.0
      ],
      [
        0.0,
        0.287,
        0.0,
        0.0,
        0.0,
        0.181,
        0.0,
        0.058,
        0.154,
        0.0,
        0.0,
        0.0,
        0.646,
        -0.21,
        0.0,
        0.0
      ],
      [
        -0.207,
        0.839,
        0.0,
        0.0,
        -0.3,
        0.0,
        0.0,
        0.0,
        0.212,
        -0.126,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.241,
        0.223,
        0.0,
        -0.219,
        -0.409,
        0.058,
        0.0,
        0.0,
        0.646,
        0.0,
        0.0,
        0.0,
        -0.246,
        0.0
      ],
      [
        0.0,
        0.604,
        0.0,
        0.0,
        -0.359,
        0.0,
        0.0,
        0.546,
        -0.158,
        0.0,
        -0.21,
        0.0,
        0.0,
        0.0,
        -0.415,
        -0.013
      ],
      [
        0.0,
        0.713,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.151,
        0.0,
        0.425,
        0.298,
        0.0,
        0.0,
        -0.246,
        -0.415,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.28,
        0.539,
        -0.332,
        0.0,
        -0.585,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.013,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      2,
      3,
      8,
      11,
      12
    ],
    "optimal_score": 6.449
  },
  {
    "id": "f08",
    "description": "Task 33: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.636,
      0.638,
      0.926,
      0.339,
      0.531,
      0.207,
      0.824,
      0.776,
      0.527,
      0.094,
      0.144,
      0.802,
      0.99,
      0.279,
      0.815,
      0.56
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.868,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.233,
        0.762,
        0.0,
        -0.157,
        0.0,
        0.0,
        0.879,
        0.0,
        0.227
      ],
      [
        0.0,
        0.0,
        0.587,
        0.0,
        0.0,
        0.0,
        0.674,
        0.0,
        0.0,
        0.0,
        0.699,
        -0.58,
        0.0,
        0.355,
        0.67,
        0.026
      ],
      [
        0.868,
        0.587,
        0.0,
        0.0,
        0.0,
        0.0,
        0.678,
        -0.273,
        0.0,
        -0.078,
        0.024,
        0.322,
        0.0,
        -0.577,
        0.0,
        0.575
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.417,
        0.0,
        0.352,
        0.0,
        0.0,
        0.425
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.311,
        0.184,
        0.042,
        -0.403,
        0.0,
        0.0,
        0.0,
        0.535,
        -0.244,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.311,
        0.0,
        0.0,
        -0.393,
        0.0,
        0.0,
        -0.43,
        0.0,
        0.685,
        0.566,
        0.244,
        0.0
      ],
      [
        0.0,
        0.674,
        0.678,
        0.0,
        0.184,
        0.0,
        0.0,
        0.0,
        -0.424,
        0.741,
        -0.225,
        -0.267,
        -0.571,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.233,
        0.0,
        -0.273,
        0.0,
        0.042,
        -0.393,
        0.0,
        0.0,
        0.0,
        0.483,
        0.0,
        0.893,
        0.0,
        0.559,
        -0.46,
        0.0
      ],
      [
        0.762,
        0.0,
        0.0,
        0.0,
        -0.403,
        0.0,
        -0.424,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.078,
        0.0,
        0.0,
        0.0,
        0.741,
        0.483,
        0.0,
        0.0,
        0.622,
        0.0,
        0.636,
        -0.349,
        0.0,
        0.0
      ],
      [
        -0.157,
        0.699,
        0.024,
        0.417,
        0.0,
        -0.43,
        -0.225,
        0.0,
        0.0,
        0.622,
        0.0,
        -0.361,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.58,
        0.322,
        0.0,
        0.0,
        0.0,
        -0.267,
        0.893,
        0.0,
        0.0,
        -0.361,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.352,
        0.535,
        0.685,
        -0.571,
        0.0,
        0.0,
        0.636,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.176
      ],
      [
        0.879,
        0.355,
        -0.577,
        0.0,
        -0.244,
        0.566,
        0.0,
        0.559,
        0.0,
        -0.349,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.214,
        0.37
      ],
      [
        0.0,
        0.67,
        0.0,
        0.0,
        0.0,
        0.244,
        0.0,
        -0.46,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.214,
        0.0,
        -0.009
      ],
      [
        0.227,
        0.026,
        0.575,
        0.425,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.176,
        0.37,
        -0.009,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      1,
      2,
      6,
      14
    ],
    "optimal_score": 7.316
  },
  {
    "id": "f09",
    "description": "Task 34: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.955,
      0.171,
      0.282,
      0.227,
      0.699,
      0.936,
      0.789,
      0.897,
      0.585,
      0.618,
      0.477,
      0.369,
      0.662,
      0.541,
      0.675,
      0.291
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.883,
        0.0,
        0.0,
        -0.145,
        0.0,
        0.37,
        0.259,
        0.0,
        0.0,
        0.0,
        -0.526,
        0.0,
        -0.419
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.889,
        0.0,
        0.085,
        0.0,
        0.657,
        0.0,
        0.721,
        0.0,
        -0.473
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.189,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.668,
        0.0,
        0.0,
        0.599
      ],
      [
        0.883,
        0.0,
        0.0,
        0.0,
        0.0,
        0.105,
        0.865,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.615,
        0.0,
        -0.36,
        -0.546
      ],
      [
        0.0,
        0.0,
        -0.189,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.394,
        0.0,
        0.271,
        0.0,
        0.0,
        0.623,
        0.675
      ],
      [
        0.0,
        0.0,
        0.0,
        0.105,
        0.0,
        0.0,
        0.84,
        0.0,
        0.0,
        0.0,
        0.0,
        0.073,
        0.0,
        0.728,
        0.043,
        -0.327
      ],
      [
        -0.145,
        0.0,
        0.0,
        0.865,
        0.0,
        0.84,
        0.0,
        0.0,
        0.0,
        0.112,
        0.0,
        0.402,
        0.0,
        0.0,
        -0.273,
        -0.245
      ],
      [
        0.0,
        0.889,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.027,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.37,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.212,
        -0.321,
        0.0,
        0.0,
        -0.19,
        0.352,
        0.0
      ],
      [
        0.259,
        0.085,
        0.0,
        0.0,
        -0.394,
        0.0,
        0.112,
        0.0,
        -0.212,
        0.0,
        0.0,
        -0.243,
        0.0,
        0.106,
        0.062,
        0.813
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.321,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.209,
        0.0
      ],
      [
        0.0,
        0.657,
        0.0,
        0.0,
        0.271,
        0.073,
        0.402,
        -0.027,
        0.0,
        -0.243,
        0.0,
        0.0,
        0.42,
        0.0,
        0.0,
        0.211
      ],
      [
        0.0,
        0.0,
        0.668,
        0.615,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.42,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.526,
        0.721,
        0.0,
        0.0,
        0.0,
        0.728,
        0.0,
        0.0,
        -0.19,
        0.106,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.36,
        0.623,
        0.043,
        -0.273,
        0.0,
        0.352,
        0.062,
        0.209,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.205
      ],
      [
        -0.419,
        -0.473,
        0.599,
        -0.546,
        0.675,
        -0.327,
        -0.245,
        0.0,
        0.0,
        0.813,
        0.0,
        0.211,
        0.0,
        0.0,
        -0.205,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      3,
      5,
      6,
      12
    ],
    "optimal_score": 6.732
  },
  {
    "id": "f10",
    "description": "Task 35: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.522,
      0.517,
      0.773,
      0.259,
      0.216,
      0.211,
      0.241,
      0.219,
      0.857,
      0.124,
      0.566,
      0.513,
      0.394,
      0.19,
      0.653,
      0.739
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.782,
        0.0,
        0.0,
        0.267,
        -0.143,
        0.0,
        0.773,
        -0.463,
        -0.516,
        0.381,
        0.0,
        0.433,
        -0.315,
        0.65
      ],
      [
        0.0,
        0.0,
        0.49,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.836,
        -0.414,
        0.0,
        0.0,
        0.0,
        0.038,
        0.0,
        0.713
      ],
      [
        0.782,
        0.49,
        0.0,
        0.0,
        0.0,
        0.242,
        0.113,
        -0.35,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.189,
        -0.004,
        -0.217,
        0.0,
        0.0,
        0.232,
        0.066,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.451,
        0.0,
        0.0,
        0.0,
        -0.019,
        0.721,
        0.0,
        -0.582,
        0.0,
        0.0,
        0.0
      ],
      [
        0.267,
        0.0,
        0.242,
        0.0,
        -0.451,
        0.0,
        0.0,
        0.399,
        -0.482,
        -0.483,
        0.0,
        0.803,
        0.277,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.143,
        0.0,
        0.113,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.086,
        0.526,
        0.283,
        0.0,
        0.0,
        0.023,
        -0.327,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.35,
        -0.189,
        0.0,
        0.399,
        -0.086,
        0.0,
        -0.579,
        -0.432,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.351,
        0.0
      ],
      [
        0.773,
        0.836,
        0.0,
        -0.004,
        0.0,
        -0.482,
        0.526,
        -0.579,
        0.0,
        0.427,
        0.0,
        0.0,
        0.0,
        0.129,
        0.0,
        -0.481
      ],
      [
        -0.463,
        -0.414,
        0.0,
        -0.217,
        -0.019,
        -0.483,
        0.283,
        -0.432,
        0.427,
        0.0,
        -0.5,
        -0.164,
        0.885,
        0.0,
        0.303,
        0.0
      ],
      [
        -0.516,
        0.0,
        0.0,
        0.0,
        0.721,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.5,
        0.0,
        0.59,
        0.344,
        0.0,
        0.0,
        -0.199
      ],
      [
        0.381,
        0.0,
        0.0,
        0.0,
        0.0,
        0.803,
        0.0,
        0.0,
        0.0,
        -0.164,
        0.59,
        0.0,
        0.0,
        0.0,
        0.38,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.232,
        -0.582,
        0.277,
        0.023,
        0.0,
        0.0,
        0.885,
        0.344,
        0.0,
        0.0,
        0.0,
        0.0,
        0.141
      ],
      [
        0.433,
        0.038,
        0.0,
        0.066,
        0.0,
        0.0,
        -0.327,
        0.0,
        0.129,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.315,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.351,
        0.0,
        0.303,
        0.0,
        0.38,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.65,
        0.713,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.481,
        0.0,
        -0.199,
        0.0,
        0.141,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      1,
      2,
      8,
      15
    ],
    "optimal_score": 7.171
  },
  {
    "id": "f11",
    "description": "Task 36: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.932,
      0.698,
      0.258,
      0.264,
      0.392,
      0.106,
      0.155,
      0.879,
      0.885,
      0.327,
      0.115,
      0.51,
      0.157,
      0.357,
      0.176,
      0.325
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        -0.393,
        -0.274,
        0.688,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.068,
        0.0,
        0.0,
        -0.515,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.729,
        -0.44,
        0.169,
        -0.112,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.297,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.822,
        0.0,
        -0.57,
        0.0,
        0.0,
        0.0,
        -0.03,
        0.0,
        0.0,
        0.439,
        0.0,
        -0.266,
        0.0
      ],
      [
        -0.393,
        0.0,
        0.822,
        0.0,
        0.812,
        0.469,
        -0.037,
        0.0,
        0.761,
        0.828,
        0.0,
        -0.131,
        0.0,
        -0.3,
        0.248,
        0.0
      ],
      [
        -0.274,
        0.0,
        0.0,
        0.812,
        0.0,
        0.0,
        -0.125,
        0.0,
        0.0,
        0.0,
        0.0,
        0.4,
        0.598,
        -0.357,
        0.102,
        0.396
      ],
      [
        0.688,
        0.729,
        -0.57,
        0.469,
        0.0,
        0.0,
        0.0,
        0.0,
        0.653,
        -0.363,
        0.14,
        -0.59,
        0.0,
        0.397,
        -0.418,
        -0.441
      ],
      [
        0.0,
        -0.44,
        0.0,
        -0.037,
        -0.125,
        0.0,
        0.0,
        0.0,
        -0.552,
        0.0,
        0.0,
        0.74,
        0.0,
        0.19,
        0.693,
        -0.378
      ],
      [
        0.0,
        0.169,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.473,
        0.0,
        0.0,
        0.558,
        0.0,
        0.298,
        0.0
      ],
      [
        0.0,
        -0.112,
        0.0,
        0.761,
        0.0,
        0.653,
        -0.552,
        0.0,
        0.0,
        -0.454,
        -0.326,
        -0.582,
        0.0,
        0.0,
        -0.443,
        0.399
      ],
      [
        0.0,
        0.0,
        -0.03,
        0.828,
        0.0,
        -0.363,
        0.0,
        -0.473,
        -0.454,
        0.0,
        0.0,
        0.0,
        0.49,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.14,
        0.0,
        0.0,
        -0.326,
        0.0,
        0.0,
        0.0,
        0.763,
        -0.047,
        0.0,
        0.0
      ],
      [
        -0.068,
        0.0,
        0.0,
        -0.131,
        0.4,
        -0.59,
        0.74,
        0.0,
        -0.582,
        0.0,
        0.0,
        0.0,
        0.0,
        0.187,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.439,
        0.0,
        0.598,
        0.0,
        0.0,
        0.558,
        0.0,
        0.49,
        0.763,
        0.0,
        0.0,
        -0.101,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.3,
        -0.357,
        0.397,
        0.19,
        0.0,
        0.0,
        0.0,
        -0.047,
        0.187,
        -0.101,
        0.0,
        -0.144,
        0.0
      ],
      [
        -0.515,
        -0.297,
        -0.266,
        0.248,
        0.102,
        -0.418,
        0.693,
        0.298,
        -0.443,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.144,
        0.0,
        -0.265
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.396,
        -0.441,
        -0.378,
        0.0,
        0.399,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.265,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      1,
      3,
      5,
      8
    ],
    "optimal_score": 5.68
  },
  {
    "id": "f12",
    "description": "Task 37: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.881,
      0.468,
      0.334,
      0.6,
      0.071,
      0.565,
      0.926,
      0.495,
      0.739,
      0.712,
      0.705,
      0.186,
      0.566,
      0.25,
      0.701,
      0.118
    ],
    "synergy": [
      [
        0.0,
        0.83,
        0.843,
        0.0,
        -0.543,
        0.0,
        -0.303,
        -0.503,
        0.0,
        0.103,
        0.0,
        0.549,
        0.0,
        0.202,
        0.0,
        0.0
      ],
      [
        0.83,
        0.0,
        0.0,
        -0.582,
        0.644,
        0.0,
        0.0,
        -0.409,
        -0.39,
        0.0,
        -0.202,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.843,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.884,
        -0.487,
        0.0,
        0.844
      ],
      [
        0.0,
        -0.582,
        0.0,
        0.0,
        0.819,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.092,
        0.0,
        0.299,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.543,
        0.644,
        0.0,
        0.819,
        0.0,
        0.096,
        0.0,
        0.0,
        0.0,
        -0.219,
        0.0,
        0.0,
        0.0,
        0.718,
        0.293,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.096,
        0.0,
        -0.243,
        0.0,
        0.0,
        0.0,
        0.0,
        0.7,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.303,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.243,
        0.0,
        -0.342,
        0.126,
        0.125,
        0.0,
        0.0,
        0.0,
        -0.038,
        0.0,
        0.808
      ],
      [
        -0.503,
        -0.409,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.342,
        0.0,
        0.067,
        0.0,
        0.637,
        0.0,
        0.0,
        0.002,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.39,
        0.0,
        0.0,
        0.0,
        0.0,
        0.126,
        0.067,
        0.0,
        0.283,
        0.0,
        0.841,
        0.0,
        0.367,
        0.0,
        0.693
      ],
      [
        0.103,
        0.0,
        0.0,
        0.0,
        -0.219,
        0.0,
        0.125,
        0.0,
        0.283,
        0.0,
        0.0,
        -0.485,
        0.239,
        0.0,
        -0.499,
        0.0
      ],
      [
        0.0,
        -0.202,
        0.0,
        0.092,
        0.0,
        0.0,
        0.0,
        0.637,
        0.0,
        0.0,
        0.0,
        0.659,
        0.0,
        0.0,
        0.0,
        0.727
      ],
      [
        0.549,
        0.0,
        0.0,
        0.0,
        0.0,
        0.7,
        0.0,
        0.0,
        0.841,
        -0.485,
        0.659,
        0.0,
        0.0,
        0.041,
        -0.316,
        -0.39
      ],
      [
        0.0,
        0.0,
        0.884,
        0.299,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.239,
        0.0,
        0.0,
        0.0,
        0.163,
        0.0,
        0.0
      ],
      [
        0.202,
        0.0,
        -0.487,
        0.0,
        0.718,
        0.0,
        -0.038,
        0.002,
        0.367,
        0.0,
        0.0,
        0.041,
        0.163,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.293,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.499,
        0.0,
        -0.316,
        0.0,
        0.0,
        0.0,
        0.282
      ],
      [
        0.0,
        0.0,
        0.844,
        0.0,
        0.0,
        0.0,
        0.808,
        0.0,
        0.693,
        0.0,
        0.727,
        -0.39,
        0.0,
        0.0,
        0.282,
        0.0
      ]
    ],
    "optimal_subset": [
      6,
      8,
      10,
      11,
      15
    ],
    "optimal_score": 6.138
  },
  {
    "id": "f13",
    "description": "Task 38: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.934,
      0.732,
      0.681,
      0.872,
      0.401,
      0.184,
      0.422,
      0.989,
      0.652,
      0.936,
      0.487,
      0.863,
      0.454,
      0.283,
      0.198,
      0.516
    ],
    "synergy": [
      [
        0.0,
        -0.369,
        0.0,
        0.125,
        0.667,
        0.615,
        0.0,
        0.0,
        0.348,
        0.271,
        0.218,
        0.0,
        0.764,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.369,
        0.0,
        0.0,
        0.0,
        0.549,
        0.0,
        0.0,
        0.0,
        0.0,
        0.641,
        0.121,
        -0.27,
        0.015,
        -0.477,
        0.325,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.587,
        0.751,
        0.762,
        0.0,
        -0.4,
        0.0,
        -0.292,
        -0.135,
        0.499,
        0.0,
        0.0,
        0.554,
        0.0
      ],
      [
        0.125,
        0.0,
        -0.587,
        0.0,
        0.838,
        0.0,
        0.861,
        0.312,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.222,
        -0.357,
        0.0
      ],
      [
        0.667,
        0.549,
        0.751,
        0.838,
        0.0,
        0.431,
        -0.155,
        0.0,
        0.368,
        -0.384,
        -0.026,
        0.644,
        0.0,
        0.0,
        0.0,
        0.824
      ],
      [
        0.615,
        0.0,
        0.762,
        0.0,
        0.431,
        0.0,
        0.0,
        0.274,
        0.0,
        -0.554,
        0.676,
        0.0,
        -0.234,
        0.321,
        0.0,
        0.735
      ],
      [
        0.0,
        0.0,
        0.0,
        0.861,
        -0.155,
        0.0,
        0.0,
        -0.487,
        0.0,
        0.0,
        0.0,
        -0.13,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.4,
        0.312,
        0.0,
        0.274,
        -0.487,
        0.0,
        0.807,
        0.0,
        0.109,
        0.658,
        0.0,
        0.0,
        0.0,
        -0.078
      ],
      [
        0.348,
        0.0,
        0.0,
        0.0,
        0.368,
        0.0,
        0.0,
        0.807,
        0.0,
        0.0,
        0.0,
        0.0,
        0.063,
        0.0,
        0.0,
        0.751
      ],
      [
        0.271,
        0.641,
        -0.292,
        0.0,
        -0.384,
        -0.554,
        0.0,
        0.0,
        0.0,
        0.0,
        0.853,
        0.0,
        0.0,
        -0.022,
        0.788,
        0.0
      ],
      [
        0.218,
        0.121,
        -0.135,
        0.0,
        -0.026,
        0.676,
        0.0,
        0.109,
        0.0,
        0.853,
        0.0,
        -0.384,
        0.783,
        0.0,
        0.825,
        -0.026
      ],
      [
        0.0,
        -0.27,
        0.499,
        0.0,
        0.644,
        0.0,
        -0.13,
        0.658,
        0.0,
        0.0,
        -0.384,
        0.0,
        0.0,
        0.0,
        0.072,
        0.0
      ],
      [
        0.764,
        0.015,
        0.0,
        0.0,
        0.0,
        -0.234,
        0.0,
        0.0,
        0.063,
        0.0,
        0.783,
        0.0,
        0.0,
        0.0,
        0.0,
        0.088
      ],
      [
        0.0,
        -0.477,
        0.0,
        -0.222,
        0.0,
        0.321,
        0.0,
        0.0,
        0.0,
        -0.022,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.325,
        0.554,
        -0.357,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.788,
        0.825,
        0.072,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.824,
        0.735,
        0.0,
        -0.078,
        0.751,
        0.0,
        -0.026,
        0.0,
        0.088,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      9,
      10,
      12,
      14
    ],
    "optimal_score": 7.511
  },
  {
    "id": "f14",
    "description": "Task 39: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.854,
      0.299,
      0.075,
      0.464,
      0.851,
      0.121,
      0.654,
      0.934,
      0.208,
      0.286,
      0.967,
      0.338,
      0.111,
      0.106,
      0.879,
      0.313
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.13,
        0.879,
        0.213,
        0.0,
        0.0,
        0.086,
        -0.332,
        0.0,
        0.0,
        0.614,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.004,
        0.509,
        0.222,
        -0.066,
        -0.47,
        -0.386,
        0.483,
        -0.066,
        0.0,
        0.0,
        0.313,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.312,
        0.0,
        0.0,
        -0.093,
        0.237,
        0.0,
        0.0,
        0.513,
        -0.519,
        -0.522,
        -0.321,
        0.852,
        0.0
      ],
      [
        0.0,
        0.004,
        -0.312,
        0.0,
        0.0,
        0.154,
        -0.556,
        0.0,
        0.0,
        -0.466,
        0.592,
        0.0,
        0.737,
        0.173,
        0.0,
        -0.002
      ],
      [
        0.0,
        0.509,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.593,
        0.0,
        0.0,
        -0.477,
        0.0,
        0.291,
        0.0,
        0.0
      ],
      [
        0.13,
        0.222,
        0.0,
        0.154,
        0.0,
        0.0,
        0.537,
        -0.059,
        0.549,
        0.0,
        0.0,
        0.0,
        0.723,
        0.313,
        0.0,
        0.0
      ],
      [
        0.879,
        -0.066,
        -0.093,
        -0.556,
        0.0,
        0.537,
        0.0,
        0.0,
        -0.1,
        0.312,
        0.59,
        0.115,
        -0.218,
        -0.379,
        0.0,
        0.0
      ],
      [
        0.213,
        -0.47,
        0.237,
        0.0,
        0.0,
        -0.059,
        0.0,
        0.0,
        -0.112,
        0.0,
        0.0,
        0.0,
        0.0,
        0.782,
        0.822,
        0.0
      ],
      [
        0.0,
        -0.386,
        0.0,
        0.0,
        -0.593,
        0.549,
        -0.1,
        -0.112,
        0.0,
        0.438,
        0.0,
        0.0,
        0.0,
        0.238,
        0.0,
        0.0
      ],
      [
        0.0,
        0.483,
        0.0,
        -0.466,
        0.0,
        0.0,
        0.312,
        0.0,
        0.438,
        0.0,
        0.0,
        0.509,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.086,
        -0.066,
        0.513,
        0.592,
        0.0,
        0.0,
        0.59,
        0.0,
        0.0,
        0.0,
        0.0,
        0.885,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.332,
        0.0,
        -0.519,
        0.0,
        -0.477,
        0.0,
        0.115,
        0.0,
        0.0,
        0.509,
        0.885,
        0.0,
        0.0,
        0.0,
        -0.313,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.522,
        0.737,
        0.0,
        0.723,
        -0.218,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.291,
        0.294,
        0.0
      ],
      [
        0.0,
        0.313,
        -0.321,
        0.173,
        0.291,
        0.313,
        -0.379,
        0.782,
        0.238,
        0.0,
        0.0,
        0.0,
        0.291,
        0.0,
        0.0,
        0.296
      ],
      [
        0.614,
        0.0,
        0.852,
        0.0,
        0.0,
        0.0,
        0.0,
        0.822,
        0.0,
        0.0,
        0.0,
        -0.313,
        0.294,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.002,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.296,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      6,
      7,
      10,
      14
    ],
    "optimal_score": 7.492
  },
  {
    "id": "f15",
    "description": "Task 40: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.212,
      0.365,
      0.42,
      0.618,
      0.131,
      0.353,
      0.911,
      0.711,
      0.058,
      0.567,
      0.726,
      0.969,
      0.355,
      0.797,
      0.063,
      0.912
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.182,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.644,
        0.0,
        0.0,
        0.0,
        0.582,
        0.124,
        0.191,
        -0.416
      ],
      [
        0.0,
        0.0,
        0.0,
        0.543,
        0.0,
        0.0,
        0.158,
        0.0,
        -0.185,
        -0.584,
        -0.558,
        0.159,
        0.196,
        0.0,
        0.868,
        0.0
      ],
      [
        0.182,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.107,
        0.743,
        0.0,
        -0.13,
        -0.274,
        0.0,
        0.808,
        -0.23,
        0.07,
        0.332
      ],
      [
        0.0,
        0.543,
        0.0,
        0.0,
        0.0,
        0.698,
        0.0,
        0.0,
        0.433,
        0.0,
        0.0,
        0.145,
        0.0,
        0.284,
        -0.513,
        -0.486
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.459,
        0.0,
        0.0,
        0.683,
        0.784,
        0.129,
        0.0,
        0.459,
        0.598,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.698,
        0.0,
        0.0,
        0.461,
        0.0,
        -0.416,
        -0.497,
        0.129,
        0.0,
        0.0,
        -0.047,
        0.0,
        0.0
      ],
      [
        0.0,
        0.158,
        0.107,
        0.0,
        -0.459,
        0.461,
        0.0,
        -0.065,
        0.264,
        -0.172,
        0.0,
        0.0,
        0.0,
        0.465,
        -0.015,
        0.0
      ],
      [
        0.0,
        0.0,
        0.743,
        0.0,
        0.0,
        0.0,
        -0.065,
        0.0,
        -0.205,
        0.0,
        0.396,
        -0.397,
        0.357,
        0.0,
        0.0,
        0.0
      ],
      [
        0.644,
        -0.185,
        0.0,
        0.433,
        0.0,
        -0.416,
        0.264,
        -0.205,
        0.0,
        0.0,
        0.858,
        0.0,
        0.0,
        0.058,
        0.272,
        0.0
      ],
      [
        0.0,
        -0.584,
        -0.13,
        0.0,
        0.683,
        -0.497,
        -0.172,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.379,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.558,
        -0.274,
        0.0,
        0.784,
        0.129,
        0.0,
        0.396,
        0.858,
        0.0,
        0.0,
        0.0,
        -0.346,
        0.259,
        0.0,
        -0.252
      ],
      [
        0.0,
        0.159,
        0.0,
        0.145,
        0.129,
        0.0,
        0.0,
        -0.397,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.239,
        0.0,
        0.0,
        0.0
      ],
      [
        0.582,
        0.196,
        0.808,
        0.0,
        0.0,
        0.0,
        0.0,
        0.357,
        0.0,
        0.379,
        -0.346,
        -0.239,
        0.0,
        0.0,
        0.0,
        0.102
      ],
      [
        0.124,
        0.0,
        -0.23,
        0.284,
        0.459,
        -0.047,
        0.465,
        0.0,
        0.058,
        0.0,
        0.259,
        0.0,
        0.0,
        0.0,
        0.833,
        0.0
      ],
      [
        0.191,
        0.868,
        0.07,
        -0.513,
        0.598,
        0.0,
        -0.015,
        0.0,
        0.272,
        0.0,
        0.0,
        0.0,
        0.0,
        0.833,
        0.0,
        0.0
      ],
      [
        -0.416,
        0.0,
        0.332,
        -0.486,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.252,
        0.0,
        0.102,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      4,
      9,
      10,
      13,
      14
    ],
    "optimal_score": 5.9
  },
  {
    "id": "f16",
    "description": "Task 41: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.485,
      0.246,
      0.512,
      0.18,
      0.293,
      0.236,
      0.26,
      0.606,
      0.598,
      0.252,
      0.94,
      0.846,
      0.396,
      0.985,
      0.343,
      0.464
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        -0.415,
        0.0,
        0.494,
        0.657,
        0.283,
        0.0,
        -0.327,
        0.398,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.235,
        0.668,
        0.0,
        -0.213,
        0.0,
        0.0,
        0.0,
        -0.409,
        0.0,
        0.0,
        -0.379,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.235,
        0.0,
        0.0,
        -0.117,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.527,
        0.0,
        0.0,
        0.0,
        0.36,
        0.0,
        0.0
      ],
      [
        -0.415,
        0.668,
        0.0,
        0.0,
        -0.287,
        0.0,
        0.0,
        0.0,
        0.0,
        0.294,
        0.0,
        0.034,
        -0.356,
        0.0,
        0.62,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.117,
        -0.287,
        0.0,
        0.0,
        0.0,
        -0.174,
        0.0,
        0.0,
        0.0,
        0.856,
        0.872,
        0.0,
        0.0,
        0.395
      ],
      [
        0.494,
        -0.213,
        0.0,
        0.0,
        0.0,
        0.0,
        0.082,
        0.0,
        0.228,
        0.0,
        0.0,
        -0.594,
        0.0,
        0.0,
        0.0,
        -0.347
      ],
      [
        0.657,
        0.0,
        0.0,
        0.0,
        0.0,
        0.082,
        0.0,
        0.0,
        -0.061,
        0.0,
        0.316,
        -0.186,
        0.176,
        0.294,
        0.376,
        -0.117
      ],
      [
        0.283,
        0.0,
        0.0,
        0.0,
        -0.174,
        0.0,
        0.0,
        0.0,
        0.614,
        0.0,
        -0.144,
        0.0,
        -0.374,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.228,
        -0.061,
        0.614,
        0.0,
        0.0,
        -0.533,
        0.206,
        0.785,
        0.032,
        0.0,
        0.0
      ],
      [
        -0.327,
        -0.409,
        -0.527,
        0.294,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.466,
        -0.188,
        0.009,
        0.0,
        0.59,
        0.54
      ],
      [
        0.398,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.316,
        -0.144,
        -0.533,
        -0.466,
        0.0,
        0.0,
        0.0,
        0.099,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.034,
        0.856,
        -0.594,
        -0.186,
        0.0,
        0.206,
        -0.188,
        0.0,
        0.0,
        -0.013,
        0.0,
        0.0,
        0.397
      ],
      [
        0.0,
        -0.379,
        0.0,
        -0.356,
        0.872,
        0.0,
        0.176,
        -0.374,
        0.785,
        0.009,
        0.0,
        -0.013,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.36,
        0.0,
        0.0,
        0.0,
        0.294,
        0.0,
        0.032,
        0.0,
        0.099,
        0.0,
        0.0,
        0.0,
        -0.107,
        0.733
      ],
      [
        0.0,
        0.0,
        0.0,
        0.62,
        0.0,
        0.0,
        0.376,
        0.0,
        0.0,
        0.59,
        0.0,
        0.0,
        0.0,
        -0.107,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.395,
        -0.347,
        -0.117,
        0.0,
        0.0,
        0.54,
        0.0,
        0.397,
        0.0,
        0.733,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      4,
      11,
      12,
      13,
      15
    ],
    "optimal_score": 6.224
  },
  {
    "id": "f17",
    "description": "Task 42: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.992,
      0.487,
      0.746,
      0.629,
      0.385,
      0.41,
      0.88,
      0.516,
      0.968,
      0.792,
      0.417,
      0.273,
      0.494,
      0.181,
      0.663,
      0.181
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.528,
        -0.254,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.653,
        0.0,
        -0.561
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.452,
        0.425,
        -0.057,
        0.0,
        -0.345,
        0.0,
        0.0,
        0.0,
        -0.485,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.373,
        0.0,
        0.0,
        0.0,
        -0.17,
        0.0,
        -0.522,
        0.0,
        0.473,
        0.0,
        -0.347,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.008,
        0.204,
        0.014,
        0.0,
        0.0,
        0.0,
        -0.237,
        0.384,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.452,
        -0.373,
        0.0,
        0.0,
        0.0,
        0.741,
        0.0,
        0.0,
        0.055,
        -0.491,
        0.0,
        -0.581,
        0.228,
        -0.126,
        0.0
      ],
      [
        0.528,
        0.425,
        0.0,
        0.008,
        0.0,
        0.0,
        0.0,
        0.465,
        -0.249,
        0.651,
        -0.296,
        0.0,
        0.638,
        -0.017,
        0.0,
        -0.522
      ],
      [
        -0.254,
        -0.057,
        0.0,
        0.204,
        0.741,
        0.0,
        0.0,
        -0.548,
        0.0,
        0.0,
        -0.281,
        0.0,
        0.0,
        0.039,
        0.0,
        0.03
      ],
      [
        0.0,
        0.0,
        0.0,
        0.014,
        0.0,
        0.465,
        -0.548,
        0.0,
        0.0,
        0.0,
        0.835,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.345,
        -0.17,
        0.0,
        0.0,
        -0.249,
        0.0,
        0.0,
        0.0,
        0.0,
        0.535,
        0.108,
        0.0,
        0.24,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.055,
        0.651,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.013,
        -0.04,
        -0.555,
        0.077,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.522,
        0.0,
        -0.491,
        -0.296,
        -0.281,
        0.835,
        0.535,
        0.0,
        0.0,
        0.284,
        0.0,
        0.0,
        0.612,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.237,
        0.0,
        0.0,
        0.0,
        0.0,
        0.108,
        0.013,
        0.284,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.485,
        0.473,
        0.384,
        -0.581,
        0.638,
        0.0,
        0.0,
        0.0,
        -0.04,
        0.0,
        0.0,
        0.0,
        0.0,
        0.332,
        0.472
      ],
      [
        0.653,
        0.0,
        0.0,
        0.0,
        0.228,
        -0.017,
        0.039,
        0.0,
        0.24,
        -0.555,
        0.0,
        0.0,
        0.0,
        0.0,
        0.692,
        0.4
      ],
      [
        0.0,
        0.0,
        -0.347,
        0.0,
        -0.126,
        0.0,
        0.0,
        0.0,
        0.0,
        0.077,
        0.612,
        0.0,
        0.332,
        0.692,
        0.0,
        0.0
      ],
      [
        -0.561,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.522,
        0.03,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.472,
        0.4,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      8,
      10,
      13,
      14
    ],
    "optimal_score": 5.953
  },
  {
    "id": "f18",
    "description": "Task 43: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.659,
      0.925,
      0.333,
      0.182,
      0.932,
      0.392,
      0.565,
      0.298,
      0.367,
      0.458,
      0.159,
      0.879,
      0.549,
      0.056,
      0.208,
      0.941
    ],
    "synergy": [
      [
        0.0,
        -0.242,
        0.0,
        0.0,
        0.0,
        0.122,
        0.198,
        0.0,
        0.377,
        0.56,
        0.38,
        0.807,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.242,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.281,
        0.68,
        0.009,
        0.0,
        0.831,
        0.0,
        0.0,
        0.0,
        0.887,
        -0.264,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.579,
        0.0,
        0.0,
        -0.35,
        0.0,
        0.883,
        0.0,
        0.0,
        0.261
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.152,
        0.0,
        0.0,
        0.225,
        0.9,
        0.0,
        -0.381,
        -0.59,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.561,
        0.0,
        0.059,
        0.0,
        0.0,
        0.0,
        0.747,
        0.0,
        -0.466
      ],
      [
        0.122,
        -0.281,
        0.0,
        0.0,
        0.0,
        0.0,
        0.009,
        0.0,
        0.0,
        0.0,
        0.496,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.501
      ],
      [
        0.198,
        0.68,
        0.0,
        -0.152,
        0.0,
        0.009,
        0.0,
        0.36,
        0.0,
        0.222,
        0.35,
        0.0,
        -0.308,
        0.0,
        -0.546,
        0.0
      ],
      [
        0.0,
        0.009,
        0.579,
        0.0,
        0.561,
        0.0,
        0.36,
        0.0,
        0.0,
        0.377,
        0.0,
        0.293,
        0.0,
        0.429,
        0.0,
        -0.138
      ],
      [
        0.377,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.039,
        0.859,
        0.717,
        0.829,
        0.344
      ],
      [
        0.56,
        0.831,
        0.0,
        0.225,
        0.059,
        0.0,
        0.222,
        0.377,
        0.0,
        0.0,
        -0.067,
        0.0,
        0.0,
        0.0,
        -0.259,
        0.0
      ],
      [
        0.38,
        0.0,
        -0.35,
        0.9,
        0.0,
        0.496,
        0.35,
        0.0,
        0.0,
        -0.067,
        0.0,
        0.0,
        0.0,
        0.818,
        0.0,
        0.242
      ],
      [
        0.807,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.293,
        -0.039,
        0.0,
        0.0,
        0.0,
        0.038,
        0.683,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.883,
        -0.381,
        0.0,
        0.0,
        -0.308,
        0.0,
        0.859,
        0.0,
        0.0,
        0.038,
        0.0,
        -0.102,
        0.0,
        0.0
      ],
      [
        0.0,
        0.887,
        0.0,
        -0.59,
        0.747,
        0.0,
        0.0,
        0.429,
        0.717,
        0.0,
        0.818,
        0.683,
        -0.102,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.264,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.546,
        0.0,
        0.829,
        -0.259,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.261,
        0.0,
        -0.466,
        -0.501,
        0.0,
        -0.138,
        0.344,
        0.0,
        0.242,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      1,
      4,
      7,
      11,
      13
    ],
    "optimal_score": 6.699
  },
  {
    "id": "f19",
    "description": "Task 44: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.574,
      0.315,
      0.22,
      0.655,
      0.848,
      0.268,
      0.348,
      0.521,
      0.62,
      0.176,
      0.144,
      0.253,
      0.987,
      0.339,
      0.064,
      0.895
    ],
    "synergy": [
      [
        0.0,
        -0.49,
        0.0,
        0.356,
        0.0,
        0.318,
        -0.465,
        0.0,
        0.77,
        0.0,
        0.876,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.49,
        0.0,
        0.0,
        0.038,
        0.0,
        0.459,
        0.0,
        0.0,
        -0.563,
        0.0,
        0.027,
        0.0,
        0.0,
        0.857,
        0.172,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.079,
        0.0,
        0.511,
        0.0,
        0.0,
        0.0,
        0.0,
        0.101,
        0.0
      ],
      [
        0.356,
        0.038,
        0.0,
        0.0,
        0.857,
        0.847,
        0.0,
        0.0,
        -0.325,
        0.0,
        0.0,
        -0.317,
        -0.112,
        0.0,
        0.0,
        0.179
      ],
      [
        0.0,
        0.0,
        0.0,
        0.857,
        0.0,
        -0.515,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.285,
        0.0,
        0.612,
        0.0,
        0.0
      ],
      [
        0.318,
        0.459,
        0.0,
        0.847,
        -0.515,
        0.0,
        -0.193,
        0.821,
        0.0,
        0.239,
        0.0,
        0.084,
        0.446,
        0.796,
        0.0,
        0.0
      ],
      [
        -0.465,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.193,
        0.0,
        0.821,
        -0.218,
        -0.494,
        -0.49,
        0.0,
        0.0,
        -0.437,
        -0.223,
        0.0
      ],
      [
        0.0,
        0.0,
        0.079,
        0.0,
        0.0,
        0.821,
        0.821,
        0.0,
        0.0,
        0.0,
        -0.288,
        0.0,
        0.0,
        0.0,
        -0.318,
        0.06
      ],
      [
        0.77,
        -0.563,
        0.0,
        -0.325,
        0.0,
        0.0,
        -0.218,
        0.0,
        0.0,
        0.0,
        0.0,
        0.676,
        0.0,
        0.0,
        -0.4,
        0.315
      ],
      [
        0.0,
        0.0,
        0.511,
        0.0,
        0.0,
        0.239,
        -0.494,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.341,
        0.0,
        0.485,
        0.0,
        0.0
      ],
      [
        0.876,
        0.027,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.49,
        -0.288,
        0.0,
        0.0,
        0.0,
        0.44,
        0.698,
        -0.106,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.317,
        -0.285,
        0.084,
        0.0,
        0.0,
        0.676,
        -0.341,
        0.44,
        0.0,
        -0.382,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.112,
        0.0,
        0.446,
        0.0,
        0.0,
        0.0,
        0.0,
        0.698,
        -0.382,
        0.0,
        -0.059,
        0.0,
        0.0
      ],
      [
        0.0,
        0.857,
        0.0,
        0.0,
        0.612,
        0.796,
        -0.437,
        0.0,
        0.0,
        0.485,
        -0.106,
        0.0,
        -0.059,
        0.0,
        0.846,
        0.0
      ],
      [
        0.0,
        0.172,
        0.101,
        0.0,
        0.0,
        0.0,
        -0.223,
        -0.318,
        -0.4,
        0.0,
        0.0,
        0.0,
        0.0,
        0.846,
        0.0,
        0.539
      ],
      [
        0.0,
        0.0,
        0.0,
        0.179,
        0.0,
        0.0,
        0.0,
        0.06,
        0.315,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.539,
        0.0
      ]
    ],
    "optimal_subset": [
      1,
      3,
      4,
      5,
      13
    ],
    "optimal_score": 6.376
  },
  {
    "id": "f20",
    "description": "Task 45: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.546,
      0.623,
      0.825,
      0.25,
      0.44,
      0.398,
      0.278,
      0.212,
      0.428,
      0.668,
      0.323,
      0.77,
      0.394,
      0.587,
      0.206,
      0.153
    ],
    "synergy": [
      [
        0.0,
        -0.419,
        0.0,
        0.0,
        0.0,
        -0.598,
        -0.039,
        0.244,
        0.504,
        0.0,
        0.266,
        0.0,
        0.14,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.419,
        0.0,
        0.013,
        0.0,
        0.0,
        0.842,
        0.0,
        -0.224,
        0.0,
        0.068,
        0.0,
        0.0,
        0.0,
        0.0,
        0.117,
        0.0
      ],
      [
        0.0,
        0.013,
        0.0,
        -0.374,
        0.0,
        0.0,
        0.211,
        0.0,
        0.0,
        0.837,
        0.0,
        0.0,
        -0.59,
        0.418,
        0.091,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.374,
        0.0,
        0.645,
        0.0,
        0.0,
        0.0,
        0.0,
        0.421,
        0.0,
        0.0,
        -0.011,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.645,
        0.0,
        0.0,
        -0.387,
        0.368,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.598,
        0.842,
        0.0,
        0.0,
        0.0,
        0.0,
        0.069,
        0.572,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.2,
        0.0,
        0.144,
        0.327
      ],
      [
        -0.039,
        0.0,
        0.211,
        0.0,
        -0.387,
        0.069,
        0.0,
        0.076,
        0.398,
        -0.029,
        0.0,
        0.0,
        0.0,
        0.0,
        0.154,
        0.0
      ],
      [
        0.244,
        -0.224,
        0.0,
        0.0,
        0.368,
        0.572,
        0.076,
        0.0,
        0.218,
        0.0,
        -0.175,
        0.0,
        0.0,
        0.0,
        -0.231,
        0.0
      ],
      [
        0.504,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.398,
        0.218,
        0.0,
        0.0,
        0.0,
        -0.297,
        0.0,
        0.375,
        0.314,
        -0.247
      ],
      [
        0.0,
        0.068,
        0.837,
        0.421,
        0.0,
        0.0,
        -0.029,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.261,
        -0.384,
        -0.451
      ],
      [
        0.266,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.175,
        0.0,
        0.0,
        0.0,
        0.432,
        -0.358,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.297,
        0.0,
        0.432,
        0.0,
        0.0,
        0.0,
        0.0,
        0.641
      ],
      [
        0.14,
        0.0,
        -0.59,
        -0.011,
        0.0,
        -0.2,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.358,
        0.0,
        0.0,
        0.0,
        0.0,
        0.107
      ],
      [
        0.0,
        0.0,
        0.418,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.375,
        0.261,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.117,
        0.091,
        0.0,
        0.0,
        0.144,
        0.154,
        -0.231,
        0.314,
        -0.384,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.449
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.327,
        0.0,
        0.0,
        -0.247,
        -0.451,
        0.0,
        0.641,
        0.107,
        0.0,
        0.449,
        0.0
      ]
    ],
    "optimal_subset": [
      1,
      2,
      5,
      9,
      13
    ],
    "optimal_score": 5.54
  },
  {
    "id": "f21",
    "description": "Task 46: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.403,
      0.856,
      0.778,
      0.44,
      0.948,
      0.337,
      0.219,
      0.848,
      0.193,
      0.868,
      0.088,
      0.122,
      0.915,
      0.06,
      0.379,
      0.652
    ],
    "synergy": [
      [
        0.0,
        0.0,
        -0.498,
        0.0,
        0.815,
        0.0,
        0.0,
        0.0,
        0.0,
        0.073,
        -0.21,
        -0.232,
        0.0,
        0.0,
        0.569,
        0.581
      ],
      [
        0.0,
        0.0,
        0.0,
        0.223,
        0.515,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.663,
        0.0,
        0.0,
        0.0,
        0.085
      ],
      [
        -0.498,
        0.0,
        0.0,
        -0.034,
        -0.276,
        0.0,
        0.0,
        -0.217,
        -0.019,
        0.0,
        -0.05,
        0.7,
        0.83,
        0.0,
        0.436,
        0.0
      ],
      [
        0.0,
        0.223,
        -0.034,
        0.0,
        -0.535,
        0.0,
        0.785,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.482,
        0.0,
        0.0,
        -0.1,
        0.0
      ],
      [
        0.815,
        0.515,
        -0.276,
        -0.535,
        0.0,
        0.0,
        0.0,
        0.421,
        0.507,
        0.0,
        0.0,
        0.0,
        0.0,
        0.547,
        0.0,
        0.589
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.051,
        0.0,
        0.297,
        0.0,
        0.081,
        -0.054,
        0.0,
        0.48,
        0.344,
        0.383
      ],
      [
        0.0,
        0.0,
        0.0,
        0.785,
        0.0,
        0.051,
        0.0,
        0.0,
        0.0,
        -0.174,
        0.245,
        0.0,
        0.899,
        0.041,
        -0.392,
        -0.367
      ],
      [
        0.0,
        0.0,
        -0.217,
        0.0,
        0.421,
        0.0,
        0.0,
        0.0,
        0.0,
        0.684,
        0.0,
        0.223,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        -0.019,
        0.0,
        0.507,
        0.297,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.02,
        0.0,
        0.699,
        0.0,
        0.0,
        0.0
      ],
      [
        0.073,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.174,
        0.684,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.309,
        0.0,
        0.0,
        -0.221
      ],
      [
        -0.21,
        0.0,
        -0.05,
        0.0,
        0.0,
        0.081,
        0.245,
        0.0,
        -0.02,
        0.0,
        0.0,
        0.0,
        -0.51,
        0.0,
        0.0,
        0.388
      ],
      [
        -0.232,
        0.663,
        0.7,
        -0.482,
        0.0,
        -0.054,
        0.0,
        0.223,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.093,
        0.691,
        -0.555,
        0.0
      ],
      [
        0.0,
        0.0,
        0.83,
        0.0,
        0.0,
        0.0,
        0.899,
        0.0,
        0.699,
        -0.309,
        -0.51,
        -0.093,
        0.0,
        0.639,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.547,
        0.48,
        0.041,
        0.0,
        0.0,
        0.0,
        0.0,
        0.691,
        0.639,
        0.0,
        -0.45,
        0.0
      ],
      [
        0.569,
        0.0,
        0.436,
        -0.1,
        0.0,
        0.344,
        -0.392,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.555,
        0.0,
        -0.45,
        0.0,
        -0.3
      ],
      [
        0.581,
        0.085,
        0.0,
        0.0,
        0.589,
        0.383,
        -0.367,
        0.0,
        0.0,
        -0.221,
        0.388,
        0.0,
        0.0,
        0.0,
        -0.3,
        0.0
      ]
    ],
    "optimal_subset": [
      0,
      1,
      4,
      7,
      15
    ],
    "optimal_score": 6.713
  },
  {
    "id": "f22",
    "description": "Task 47: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.136,
      0.529,
      0.736,
      0.696,
      0.451,
      0.119,
      0.517,
      0.34,
      0.729,
      0.237,
      0.757,
      0.093,
      0.16,
      0.335,
      0.057,
      0.79
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.589,
        0.557,
        0.052,
        0.0,
        -0.12,
        0.0,
        0.0,
        -0.46,
        0.705,
        0.801,
        0.795
      ],
      [
        0.0,
        0.0,
        0.601,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.165,
        -0.014,
        0.676,
        0.579,
        -0.353,
        0.0,
        0.0,
        -0.344
      ],
      [
        0.0,
        0.601,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.323,
        0.0,
        -0.079,
        -0.454
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.253,
        0.0,
        0.0,
        -0.188,
        0.278,
        -0.562,
        0.228,
        0.0,
        0.0,
        0.0,
        0.0,
        0.149
      ],
      [
        0.0,
        0.0,
        0.0,
        0.253,
        0.0,
        0.0,
        -0.491,
        0.369,
        -0.143,
        0.0,
        -0.597,
        -0.085,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.589,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.38,
        0.0,
        0.0,
        0.0,
        0.146
      ],
      [
        0.557,
        0.0,
        0.0,
        0.0,
        -0.491,
        0.0,
        0.0,
        -0.36,
        0.0,
        0.415,
        0.371,
        0.0,
        0.0,
        0.0,
        -0.503,
        0.0
      ],
      [
        0.052,
        0.0,
        0.0,
        -0.188,
        0.369,
        0.0,
        -0.36,
        0.0,
        0.0,
        0.625,
        -0.387,
        0.0,
        -0.211,
        0.0,
        0.399,
        0.0
      ],
      [
        0.0,
        -0.165,
        0.0,
        0.278,
        -0.143,
        0.0,
        0.0,
        0.0,
        0.0,
        0.834,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.193
      ],
      [
        -0.12,
        -0.014,
        0.0,
        -0.562,
        0.0,
        0.0,
        0.415,
        0.625,
        0.834,
        0.0,
        0.749,
        -0.108,
        -0.143,
        0.0,
        -0.049,
        0.463
      ],
      [
        0.0,
        0.676,
        0.0,
        0.228,
        -0.597,
        0.0,
        0.371,
        -0.387,
        0.0,
        0.749,
        0.0,
        0.0,
        -0.207,
        0.895,
        0.0,
        -0.161
      ],
      [
        0.0,
        0.579,
        0.0,
        0.0,
        -0.085,
        -0.38,
        0.0,
        0.0,
        0.0,
        -0.108,
        0.0,
        0.0,
        0.0,
        0.561,
        0.0,
        0.802
      ],
      [
        -0.46,
        -0.353,
        -0.323,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.211,
        0.0,
        -0.143,
        -0.207,
        0.0,
        0.0,
        0.0,
        0.565,
        0.441
      ],
      [
        0.705,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.895,
        0.561,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.801,
        0.0,
        -0.079,
        0.0,
        0.0,
        0.0,
        -0.503,
        0.399,
        0.0,
        -0.049,
        0.0,
        0.0,
        0.565,
        0.0,
        0.0,
        0.644
      ],
      [
        0.795,
        -0.344,
        -0.454,
        0.149,
        0.0,
        0.146,
        0.0,
        0.0,
        -0.193,
        0.463,
        -0.161,
        0.802,
        0.441,
        0.0,
        0.644,
        0.0
      ]
    ],
    "optimal_subset": [
      6,
      8,
      9,
      10,
      13
    ],
    "optimal_score": 5.839
  },
  {
    "id": "f23",
    "description": "Task 48: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.097,
      0.922,
      0.932,
      0.741,
      0.264,
      0.613,
      0.878,
      0.25,
      0.072,
      0.852,
      0.294,
      0.851,
      0.955,
      0.814,
      0.487,
      0.231
    ],
    "synergy": [
      [
        0.0,
        0.0,
        0.425,
        0.0,
        0.0,
        0.737,
        0.0,
        0.0,
        0.0,
        0.158,
        0.755,
        0.0,
        0.0,
        0.489,
        -0.317,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.325,
        0.0,
        0.015,
        -0.513,
        0.491,
        0.0,
        0.0,
        0.0,
        0.892,
        0.0,
        0.0,
        0.0,
        0.157
      ],
      [
        0.425,
        0.0,
        0.0,
        0.158,
        0.0,
        0.361,
        0.0,
        -0.574,
        0.0,
        0.277,
        0.0,
        0.0,
        0.736,
        -0.511,
        0.0,
        0.0
      ],
      [
        0.0,
        0.325,
        0.158,
        0.0,
        0.0,
        0.0,
        -0.394,
        -0.343,
        -0.291,
        0.0,
        -0.078,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.599,
        0.0,
        0.0,
        0.0,
        -0.432,
        0.0,
        0.0,
        -0.024
      ],
      [
        0.737,
        0.015,
        0.361,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.339,
        0.0,
        -0.274,
        0.0,
        -0.488,
        0.075,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.513,
        0.0,
        -0.394,
        0.0,
        0.0,
        0.0,
        0.817,
        -0.186,
        -0.04,
        -0.009,
        0.0,
        0.0,
        -0.395,
        0.823,
        0.0
      ],
      [
        0.0,
        0.491,
        -0.574,
        -0.343,
        0.0,
        0.0,
        0.817,
        0.0,
        0.789,
        0.0,
        -0.161,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.526
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.291,
        -0.599,
        -0.339,
        -0.186,
        0.789,
        0.0,
        0.0,
        0.205,
        0.197,
        0.657,
        0.743,
        0.0,
        0.635
      ],
      [
        0.158,
        0.0,
        0.277,
        0.0,
        0.0,
        0.0,
        -0.04,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.235,
        -0.383,
        -0.524,
        0.0
      ],
      [
        0.755,
        0.0,
        0.0,
        -0.078,
        0.0,
        -0.274,
        -0.009,
        -0.161,
        0.205,
        0.0,
        0.0,
        0.0,
        0.0,
        0.49,
        0.129,
        -0.207
      ],
      [
        0.0,
        0.892,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.197,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.736,
        0.0,
        -0.432,
        -0.488,
        0.0,
        0.0,
        0.657,
        0.235,
        0.0,
        0.0,
        0.0,
        0.745,
        0.737,
        0.0
      ],
      [
        0.489,
        0.0,
        -0.511,
        0.0,
        0.0,
        0.075,
        -0.395,
        0.0,
        0.743,
        -0.383,
        0.49,
        0.0,
        0.745,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.317,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.823,
        0.0,
        0.0,
        -0.524,
        0.129,
        0.0,
        0.737,
        0.0,
        0.0,
        -0.45
      ],
      [
        0.0,
        0.157,
        0.0,
        0.0,
        -0.024,
        0.0,
        0.0,
        -0.526,
        0.635,
        0.0,
        -0.207,
        0.0,
        0.0,
        0.0,
        -0.45,
        0.0
      ]
    ],
    "optimal_subset": [
      1,
      8,
      11,
      12,
      13
    ],
    "optimal_score": 6.848
  },
  {
    "id": "f24",
    "description": "Task 49: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.394,
      0.484,
      0.981,
      0.486,
      0.875,
      0.225,
      0.522,
      0.871,
      0.684,
      0.238,
      0.269,
      0.332,
      0.869,
      0.176,
      0.203,
      0.602
    ],
    "synergy": [
      [
        0.0,
        0.0,
        -0.39,
        -0.592,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.281,
        0.0,
        0.0,
        0.412,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.015,
        0.647,
        0.0,
        0.624,
        0.0,
        0.796,
        0.0,
        0.667,
        -0.461,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.39,
        0.0,
        0.0,
        0.0,
        0.222,
        0.503,
        0.0,
        0.0,
        0.0,
        0.647,
        -0.309,
        0.557,
        0.0,
        0.0,
        0.507,
        -0.104
      ],
      [
        -0.592,
        0.015,
        0.0,
        0.0,
        -0.427,
        0.389,
        -0.35,
        -0.436,
        0.064,
        0.0,
        0.195,
        0.0,
        0.195,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.647,
        0.222,
        -0.427,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.726,
        -0.528,
        -0.571,
        0.27
      ],
      [
        0.0,
        0.0,
        0.503,
        0.389,
        0.0,
        0.0,
        0.375,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.45,
        0.0,
        0.128,
        0.0
      ],
      [
        0.0,
        0.624,
        0.0,
        -0.35,
        0.0,
        0.375,
        0.0,
        0.0,
        0.377,
        0.0,
        0.274,
        0.0,
        0.612,
        0.0,
        0.0,
        0.277
      ],
      [
        0.0,
        0.0,
        0.0,
        -0.436,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.138,
        -0.441,
        0.0,
        0.0,
        0.743,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.796,
        0.0,
        0.064,
        0.0,
        0.0,
        0.377,
        -0.138,
        0.0,
        0.0,
        0.353,
        0.0,
        -0.045,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.647,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.441,
        0.0,
        0.0,
        0.0,
        0.0,
        0.369,
        0.0,
        0.546,
        0.0
      ],
      [
        0.0,
        0.667,
        -0.309,
        0.195,
        0.0,
        0.0,
        0.274,
        0.0,
        0.353,
        0.0,
        0.0,
        -0.044,
        0.0,
        0.488,
        0.0,
        -0.33
      ],
      [
        0.281,
        -0.461,
        0.557,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.044,
        0.0,
        0.0,
        0.0,
        0.0,
        0.236
      ],
      [
        0.0,
        0.0,
        0.0,
        0.195,
        0.726,
        0.45,
        0.612,
        0.743,
        -0.045,
        0.369,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.0,
        0.0,
        -0.528,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.488,
        0.0,
        0.0,
        0.0,
        -0.179,
        0.39
      ],
      [
        0.412,
        0.0,
        0.507,
        0.0,
        -0.571,
        0.128,
        0.0,
        0.0,
        0.0,
        0.546,
        0.0,
        0.0,
        0.0,
        -0.179,
        0.0,
        0.895
      ],
      [
        0.0,
        0.0,
        -0.104,
        0.0,
        0.27,
        0.0,
        0.277,
        0.0,
        0.0,
        0.0,
        -0.33,
        0.236,
        0.0,
        0.39,
        0.895,
        0.0
      ]
    ],
    "optimal_subset": [
      1,
      4,
      6,
      8,
      12
    ],
    "optimal_score": 7.171
  },
  {
    "id": "f25",
    "description": "Task 50: choose the 5 most useful tools from 16 candidates (full pool).",
    "tier": "full",
    "n_tools": 16,
    "k": 5,
    "tools": [
      {
        "index": 0,
        "name": "tool_00"
      },
      {
        "index": 1,
        "name": "tool_01"
      },
      {
        "index": 2,
        "name": "tool_02"
      },
      {
        "index": 3,
        "name": "tool_03"
      },
      {
        "index": 4,
        "name": "tool_04"
      },
      {
        "index": 5,
        "name": "tool_05"
      },
      {
        "index": 6,
        "name": "tool_06"
      },
      {
        "index": 7,
        "name": "tool_07"
      },
      {
        "index": 8,
        "name": "tool_08"
      },
      {
        "index": 9,
        "name": "tool_09"
      },
      {
        "index": 10,
        "name": "tool_10"
      },
      {
        "index": 11,
        "name": "tool_11"
      },
      {
        "index": 12,
        "name": "tool_12"
      },
      {
        "index": 13,
        "name": "tool_13"
      },
      {
        "index": 14,
        "name": "tool_14"
      },
      {
        "index": 15,
        "name": "tool_15"
      }
    ],
    "weights": [
      0.703,
      0.731,
      0.364,
      0.489,
      0.555,
      0.795,
      0.817,
      0.267,
      0.137,
      0.507,
      0.4,
      0.228,
      0.76,
      0.676,
      0.993,
      0.534
    ],
    "synergy": [
      [
        0.0,
        -0.498,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.107,
        0.553,
        -0.529,
        0.0,
        0.0,
        -0.098,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        -0.498,
        0.0,
        0.0,
        0.0,
        0.0,
        0.553,
        0.0,
        0.0,
        0.0,
        0.704,
        0.0,
        0.0,
        0.0,
        -0.458,
        0.377,
        0.134
      ],
      [
        0.0,
        0.0,
        0.0,
        0.663,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.31,
        0.0,
        -0.307,
        -0.591,
        -0.106,
        0.0
      ],
      [
        0.0,
        0.0,
        0.663,
        0.0,
        0.674,
        0.0,
        -0.532,
        0.0,
        0.517,
        -0.265,
        -0.171,
        0.613,
        0.0,
        0.0,
        -0.263,
        -0.4
      ],
      [
        0.0,
        0.0,
        0.0,
        0.674,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.491,
        0.0
      ],
      [
        0.0,
        0.553,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.891,
        0.0,
        0.0,
        0.575,
        0.0,
        0.0,
        0.0,
        0.441,
        -0.065
      ],
      [
        -0.107,
        0.0,
        0.0,
        -0.532,
        0.0,
        0.0,
        0.0,
        0.0,
        0.275,
        0.0,
        0.0,
        0.238,
        0.0,
        -0.443,
        0.0,
        0.36
      ],
      [
        0.553,
        0.0,
        0.0,
        0.0,
        0.0,
        0.891,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.651
      ],
      [
        -0.529,
        0.0,
        0.0,
        0.517,
        0.0,
        0.0,
        0.275,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.654,
        0.885
      ],
      [
        0.0,
        0.704,
        0.0,
        -0.265,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.493,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        0.0,
        0.31,
        -0.171,
        0.0,
        0.575,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.243
      ],
      [
        -0.098,
        0.0,
        0.0,
        0.613,
        0.0,
        0.0,
        0.238,
        0.0,
        0.0,
        -0.493,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.298,
        0.104
      ],
      [
        0.0,
        0.0,
        -0.307,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0
      ],
      [
        0.0,
        -0.458,
        -0.591,
        0.0,
        0.0,
        0.0,
        -0.443,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.534,
        0.0
      ],
      [
        0.0,
        0.377,
        -0.106,
        -0.263,
        0.491,
        0.441,
        0.0,
        0.0,
        0.654,
        0.0,
        0.0,
        -0.298,
        0.0,
        -0.534,
        0.0,
        0.0
      ],
      [
        0.0,
        0.134,
        0.0,
        -0.4,
        0.0,
        -0.065,
        0.36,
        0.651,
        0.885,
        0.0,
        -0.243,
        0.104,
        0.0,
        0.0,
        0.0,
        0.0
      ]
    ],
    "optimal_subset": [
      1,
      5,
      7,
      14,
      15
    ],
    "optimal_score": 6.302
  }
]