{
  "method": "Exact Fraction arithmetic; exhaustive positive-integer three-way allocations at each budget, checked against marginal-gain greedy selection at every budget tested.",
  "variance_formula": "sum(variance_i / count_i)",
  "source_sha256": {
    "website/lib/study-summary.ts": "ab07c4f944e7b43b41d9f2a4e64ee41deae216116ce42b09df9e88ac839d4d08",
    "website/lib/reading-cases.ts": "a23e9308ed79aef4cc86065814dd7112673ff6a80d592faa11401dd36c125d51"
  },
  "scenario_definitions": {
    "f": "Affected reading energy as a share of baseline energy per completed job, before changing reading count.",
    "h": "Extra FI implementation energy as a share of baseline energy per completed job; illustrative values 0, 1/100, and 3/100 are assumptions, not measurements.",
    "s": "(original reading count - minimum reading count meeting baseline variance) / original reading count.",
    "net_energy_saved": "f*s-h, assuming energy per reading is constant and all omitted readings are physically skipped.",
    "battery_life_change": "1/(1-(f*s-h))-1, assuming fixed battery energy and constant job rate with other loads unchanged."
  },
  "cases": [
    {
      "id": "a1-1-1_b12",
      "variances": [
        1,
        1,
        1
      ],
      "original_budget": 12,
      "baseline_allocation": [
        4,
        4,
        4
      ],
      "baseline_variance": "3/4",
      "fi_variance_at_original_budget": "3/4",
      "enumerated_best_at_original_budget": "3/4",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        4,
        4,
        4
      ],
      "minimum_budget_to_match_baseline": 12,
      "best_variance_at_minimum_budget": "3/4",
      "minimum_budget_optimal_allocations": [
        [
          4,
          4,
          4
        ]
      ],
      "best_variance_one_reading_below_minimum": "5/6",
      "readings_saved": 0,
      "reading_fraction_saved": "0/1",
      "reading_fraction_saved_percent": "0",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "0",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "0/1",
        "0/1",
        "0/1"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "0/1",
          "battery_life_change_fraction": "0/1"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "-1/100",
          "battery_life_change_fraction": "-1/101"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "-3/100",
          "battery_life_change_fraction": "-3/103"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "0/1",
          "battery_life_change_fraction": "0/1"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "-1/100",
          "battery_life_change_fraction": "-1/101"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "-3/100",
          "battery_life_change_fraction": "-3/103"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "0/1",
          "battery_life_change_fraction": "0/1"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "-1/100",
          "battery_life_change_fraction": "-1/101"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "-3/100",
          "battery_life_change_fraction": "-3/103"
        }
      ]
    },
    {
      "id": "a1-1-1_b24",
      "variances": [
        1,
        1,
        1
      ],
      "original_budget": 24,
      "baseline_allocation": [
        8,
        8,
        8
      ],
      "baseline_variance": "3/8",
      "fi_variance_at_original_budget": "3/8",
      "enumerated_best_at_original_budget": "3/8",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        8,
        8,
        8
      ],
      "minimum_budget_to_match_baseline": 24,
      "best_variance_at_minimum_budget": "3/8",
      "minimum_budget_optimal_allocations": [
        [
          8,
          8,
          8
        ]
      ],
      "best_variance_one_reading_below_minimum": "11/28",
      "readings_saved": 0,
      "reading_fraction_saved": "0/1",
      "reading_fraction_saved_percent": "0",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "0",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "0/1",
        "0/1",
        "0/1"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "0/1",
          "battery_life_change_fraction": "0/1"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "-1/100",
          "battery_life_change_fraction": "-1/101"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "-3/100",
          "battery_life_change_fraction": "-3/103"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "0/1",
          "battery_life_change_fraction": "0/1"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "-1/100",
          "battery_life_change_fraction": "-1/101"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "-3/100",
          "battery_life_change_fraction": "-3/103"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "0/1",
          "battery_life_change_fraction": "0/1"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "-1/100",
          "battery_life_change_fraction": "-1/101"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "-3/100",
          "battery_life_change_fraction": "-3/103"
        }
      ]
    },
    {
      "id": "a1-1-1_b48",
      "variances": [
        1,
        1,
        1
      ],
      "original_budget": 48,
      "baseline_allocation": [
        16,
        16,
        16
      ],
      "baseline_variance": "3/16",
      "fi_variance_at_original_budget": "3/16",
      "enumerated_best_at_original_budget": "3/16",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        16,
        16,
        16
      ],
      "minimum_budget_to_match_baseline": 48,
      "best_variance_at_minimum_budget": "3/16",
      "minimum_budget_optimal_allocations": [
        [
          16,
          16,
          16
        ]
      ],
      "best_variance_one_reading_below_minimum": "23/120",
      "readings_saved": 0,
      "reading_fraction_saved": "0/1",
      "reading_fraction_saved_percent": "0",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "0",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "0/1",
        "0/1",
        "0/1"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "0/1",
          "battery_life_change_fraction": "0/1"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "-1/100",
          "battery_life_change_fraction": "-1/101"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "-3/100",
          "battery_life_change_fraction": "-3/103"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "0/1",
          "battery_life_change_fraction": "0/1"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "-1/100",
          "battery_life_change_fraction": "-1/101"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "-3/100",
          "battery_life_change_fraction": "-3/103"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "0/1",
          "battery_life_change_fraction": "0/1"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "-1/100",
          "battery_life_change_fraction": "-1/101"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "-3/100",
          "battery_life_change_fraction": "-3/103"
        }
      ]
    },
    {
      "id": "a1-4-9_b12",
      "variances": [
        1,
        4,
        9
      ],
      "original_budget": 12,
      "baseline_allocation": [
        4,
        4,
        4
      ],
      "baseline_variance": "7/2",
      "fi_variance_at_original_budget": "3/1",
      "enumerated_best_at_original_budget": "3/1",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        2,
        4,
        6
      ],
      "minimum_budget_to_match_baseline": 11,
      "best_variance_at_minimum_budget": "33/10",
      "minimum_budget_optimal_allocations": [
        [
          2,
          4,
          5
        ]
      ],
      "best_variance_one_reading_below_minimum": "109/30",
      "readings_saved": 1,
      "reading_fraction_saved": "1/12",
      "reading_fraction_saved_percent": "8.3333333333333333333333333333333333333333333333333",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "7.4179900227448538433433223416000477470685098991660",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "1/48",
        "1/24",
        "1/16"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/48",
          "battery_life_change_fraction": "1/47"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "13/1200",
          "battery_life_change_fraction": "13/1187"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "-11/1200",
          "battery_life_change_fraction": "-11/1211"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/24",
          "battery_life_change_fraction": "1/23"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "19/600",
          "battery_life_change_fraction": "19/581"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "7/600",
          "battery_life_change_fraction": "7/593"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/16",
          "battery_life_change_fraction": "1/15"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "21/400",
          "battery_life_change_fraction": "21/379"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "13/400",
          "battery_life_change_fraction": "13/387"
        }
      ]
    },
    {
      "id": "a1-4-9_b24",
      "variances": [
        1,
        4,
        9
      ],
      "original_budget": 24,
      "baseline_allocation": [
        8,
        8,
        8
      ],
      "baseline_variance": "7/4",
      "fi_variance_at_original_budget": "3/2",
      "enumerated_best_at_original_budget": "3/2",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        4,
        8,
        12
      ],
      "minimum_budget_to_match_baseline": 21,
      "best_variance_at_minimum_budget": "241/140",
      "minimum_budget_optimal_allocations": [
        [
          4,
          7,
          10
        ]
      ],
      "best_variance_one_reading_below_minimum": "379/210",
      "readings_saved": 3,
      "reading_fraction_saved": "1/8",
      "reading_fraction_saved_percent": "12.500",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "7.4179900227448538433433223416000477470685098991660",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "1/32",
        "1/16",
        "3/32"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/32",
          "battery_life_change_fraction": "1/31"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "17/800",
          "battery_life_change_fraction": "17/783"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "1/800",
          "battery_life_change_fraction": "1/799"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/16",
          "battery_life_change_fraction": "1/15"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "21/400",
          "battery_life_change_fraction": "21/379"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "13/400",
          "battery_life_change_fraction": "13/387"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "3/32",
          "battery_life_change_fraction": "3/29"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "67/800",
          "battery_life_change_fraction": "67/733"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "51/800",
          "battery_life_change_fraction": "51/749"
        }
      ]
    },
    {
      "id": "a1-4-9_b48",
      "variances": [
        1,
        4,
        9
      ],
      "original_budget": 48,
      "baseline_allocation": [
        16,
        16,
        16
      ],
      "baseline_variance": "7/8",
      "fi_variance_at_original_budget": "3/4",
      "enumerated_best_at_original_budget": "3/4",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        8,
        16,
        24
      ],
      "minimum_budget_to_match_baseline": 42,
      "best_variance_at_minimum_budget": "6/7",
      "minimum_budget_optimal_allocations": [
        [
          7,
          14,
          21
        ]
      ],
      "best_variance_one_reading_below_minimum": "123/140",
      "readings_saved": 6,
      "reading_fraction_saved": "1/8",
      "reading_fraction_saved_percent": "12.500",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "7.4179900227448538433433223416000477470685098991660",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "1/32",
        "1/16",
        "3/32"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/32",
          "battery_life_change_fraction": "1/31"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "17/800",
          "battery_life_change_fraction": "17/783"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "1/800",
          "battery_life_change_fraction": "1/799"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/16",
          "battery_life_change_fraction": "1/15"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "21/400",
          "battery_life_change_fraction": "21/379"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "13/400",
          "battery_life_change_fraction": "13/387"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "3/32",
          "battery_life_change_fraction": "3/29"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "67/800",
          "battery_life_change_fraction": "67/733"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "51/800",
          "battery_life_change_fraction": "51/749"
        }
      ]
    },
    {
      "id": "a1-9-81_b12",
      "variances": [
        1,
        9,
        81
      ],
      "original_budget": 12,
      "baseline_allocation": [
        4,
        4,
        4
      ],
      "baseline_variance": "91/4",
      "fi_variance_at_original_budget": "113/8",
      "enumerated_best_at_original_budget": "113/8",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        1,
        3,
        8
      ],
      "minimum_budget_to_match_baseline": 8,
      "best_variance_at_minimum_budget": "217/10",
      "minimum_budget_optimal_allocations": [
        [
          1,
          2,
          5
        ]
      ],
      "best_variance_one_reading_below_minimum": "103/4",
      "readings_saved": 4,
      "reading_fraction_saved": "1/3",
      "reading_fraction_saved_percent": "33.333333333333333333333333333333333333333333333333",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "21.204116803025751025533044348675474192700231541718",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "1/12",
        "1/6",
        "1/4"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/12",
          "battery_life_change_fraction": "1/11"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "11/150",
          "battery_life_change_fraction": "11/139"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "4/75",
          "battery_life_change_fraction": "4/71"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/6",
          "battery_life_change_fraction": "1/5"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "47/300",
          "battery_life_change_fraction": "47/253"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "41/300",
          "battery_life_change_fraction": "41/259"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/4",
          "battery_life_change_fraction": "1/3"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "6/25",
          "battery_life_change_fraction": "6/19"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "11/50",
          "battery_life_change_fraction": "11/39"
        }
      ]
    },
    {
      "id": "a1-9-81_b24",
      "variances": [
        1,
        9,
        81
      ],
      "original_budget": 24,
      "baseline_allocation": [
        8,
        8,
        8
      ],
      "baseline_variance": "91/8",
      "fi_variance_at_original_budget": "113/16",
      "enumerated_best_at_original_budget": "113/16",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        2,
        6,
        16
      ],
      "minimum_budget_to_match_baseline": 15,
      "best_variance_at_minimum_budget": "227/20",
      "minimum_budget_optimal_allocations": [
        [
          1,
          4,
          10
        ]
      ],
      "best_variance_one_reading_below_minimum": "121/10",
      "readings_saved": 9,
      "reading_fraction_saved": "3/8",
      "reading_fraction_saved_percent": "37.500",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "21.204116803025751025533044348675474192700231541718",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "3/32",
        "3/16",
        "9/32"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "3/32",
          "battery_life_change_fraction": "3/29"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "67/800",
          "battery_life_change_fraction": "67/733"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "51/800",
          "battery_life_change_fraction": "51/749"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "3/16",
          "battery_life_change_fraction": "3/13"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "71/400",
          "battery_life_change_fraction": "71/329"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "63/400",
          "battery_life_change_fraction": "63/337"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "9/32",
          "battery_life_change_fraction": "9/23"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "217/800",
          "battery_life_change_fraction": "217/583"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "201/800",
          "battery_life_change_fraction": "201/599"
        }
      ]
    },
    {
      "id": "a1-9-81_b48",
      "variances": [
        1,
        9,
        81
      ],
      "original_budget": 48,
      "baseline_allocation": [
        16,
        16,
        16
      ],
      "baseline_variance": "91/16",
      "fi_variance_at_original_budget": "155/44",
      "enumerated_best_at_original_budget": "155/44",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        4,
        11,
        33
      ],
      "minimum_budget_to_match_baseline": 30,
      "best_variance_at_minimum_budget": "79/14",
      "minimum_budget_optimal_allocations": [
        [
          2,
          7,
          21
        ]
      ],
      "best_variance_one_reading_below_minimum": "817/140",
      "readings_saved": 18,
      "reading_fraction_saved": "3/8",
      "reading_fraction_saved_percent": "37.500",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "21.299261796307184789658241670543425973993173167879",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "3/32",
        "3/16",
        "9/32"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "3/32",
          "battery_life_change_fraction": "3/29"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "67/800",
          "battery_life_change_fraction": "67/733"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "51/800",
          "battery_life_change_fraction": "51/749"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "3/16",
          "battery_life_change_fraction": "3/13"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "71/400",
          "battery_life_change_fraction": "71/329"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "63/400",
          "battery_life_change_fraction": "63/337"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "9/32",
          "battery_life_change_fraction": "9/23"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "217/800",
          "battery_life_change_fraction": "217/583"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "201/800",
          "battery_life_change_fraction": "201/599"
        }
      ]
    },
    {
      "id": "a1-1-100_b12",
      "variances": [
        1,
        1,
        100
      ],
      "original_budget": 12,
      "baseline_allocation": [
        4,
        4,
        4
      ],
      "baseline_variance": "51/2",
      "fi_variance_at_original_budget": "12/1",
      "enumerated_best_at_original_budget": "12/1",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        1,
        1,
        10
      ],
      "minimum_budget_to_match_baseline": 7,
      "best_variance_at_minimum_budget": "22/1",
      "minimum_budget_optimal_allocations": [
        [
          1,
          1,
          5
        ]
      ],
      "best_variance_one_reading_below_minimum": "27/1",
      "readings_saved": 5,
      "reading_fraction_saved": "5/12",
      "reading_fraction_saved_percent": "41.666666666666666666666666666666666666666666666667",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "31.400565942996465048539377911228434393865901942518",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "5/48",
        "5/24",
        "5/16"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "5/48",
          "battery_life_change_fraction": "5/43"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "113/1200",
          "battery_life_change_fraction": "113/1087"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "89/1200",
          "battery_life_change_fraction": "89/1111"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "5/24",
          "battery_life_change_fraction": "5/19"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "119/600",
          "battery_life_change_fraction": "119/481"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "107/600",
          "battery_life_change_fraction": "107/493"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "5/16",
          "battery_life_change_fraction": "5/11"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "121/400",
          "battery_life_change_fraction": "121/279"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "113/400",
          "battery_life_change_fraction": "113/287"
        }
      ]
    },
    {
      "id": "a1-1-100_b24",
      "variances": [
        1,
        1,
        100
      ],
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      "baseline_allocation": [
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        8,
        8
      ],
      "baseline_variance": "51/4",
      "fi_variance_at_original_budget": "6/1",
      "enumerated_best_at_original_budget": "6/1",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        2,
        2,
        20
      ],
      "minimum_budget_to_match_baseline": 12,
      "best_variance_at_minimum_budget": "12/1",
      "minimum_budget_optimal_allocations": [
        [
          1,
          1,
          10
        ]
      ],
      "best_variance_one_reading_below_minimum": "118/9",
      "readings_saved": 12,
      "reading_fraction_saved": "1/2",
      "reading_fraction_saved_percent": "50.0",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "31.400565942996465048539377911228434393865901942518",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "1/8",
        "1/4",
        "3/8"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/8",
          "battery_life_change_fraction": "1/7"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "23/200",
          "battery_life_change_fraction": "23/177"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "19/200",
          "battery_life_change_fraction": "19/181"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/4",
          "battery_life_change_fraction": "1/3"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "6/25",
          "battery_life_change_fraction": "6/19"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "11/50",
          "battery_life_change_fraction": "11/39"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "3/8",
          "battery_life_change_fraction": "3/5"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "73/200",
          "battery_life_change_fraction": "73/127"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "69/200",
          "battery_life_change_fraction": "69/131"
        }
      ]
    },
    {
      "id": "a1-1-100_b48",
      "variances": [
        1,
        1,
        100
      ],
      "original_budget": 48,
      "baseline_allocation": [
        16,
        16,
        16
      ],
      "baseline_variance": "51/8",
      "fi_variance_at_original_budget": "3/1",
      "enumerated_best_at_original_budget": "3/1",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        4,
        4,
        40
      ],
      "minimum_budget_to_match_baseline": 23,
      "best_variance_at_minimum_budget": "119/19",
      "minimum_budget_optimal_allocations": [
        [
          2,
          2,
          19
        ]
      ],
      "best_variance_one_reading_below_minimum": "59/9",
      "readings_saved": 25,
      "reading_fraction_saved": "25/48",
      "reading_fraction_saved_percent": "52.083333333333333333333333333333333333333333333333",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "31.400565942996465048539377911228434393865901942518",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "25/192",
        "25/96",
        "25/64"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "25/192",
          "battery_life_change_fraction": "25/167"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "577/4800",
          "battery_life_change_fraction": "577/4223"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "481/4800",
          "battery_life_change_fraction": "481/4319"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "25/96",
          "battery_life_change_fraction": "25/71"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "601/2400",
          "battery_life_change_fraction": "601/1799"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "553/2400",
          "battery_life_change_fraction": "553/1847"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "25/64",
          "battery_life_change_fraction": "25/39"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "609/1600",
          "battery_life_change_fraction": "609/991"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "577/1600",
          "battery_life_change_fraction": "577/1023"
        }
      ]
    },
    {
      "id": "held-out-13",
      "variances": [
        1,
        5,
        13
      ],
      "original_budget": 13,
      "baseline_allocation": [
        4,
        4,
        5
      ],
      "baseline_variance": "41/10",
      "fi_variance_at_original_budget": "101/28",
      "enumerated_best_at_original_budget": "101/28",
      "original_optimum_tie_count": 1,
      "greedy_allocation_at_original_budget": [
        2,
        4,
        7
      ],
      "minimum_budget_to_match_baseline": 12,
      "best_variance_at_minimum_budget": "47/12",
      "minimum_budget_optimal_allocations": [
        [
          2,
          4,
          6
        ]
      ],
      "best_variance_one_reading_below_minimum": "13/3",
      "readings_saved": 1,
      "reading_fraction_saved": "1/13",
      "reading_fraction_saved_percent": "7.6923076923076923076923076923076923076923076923077",
      "modeled_standard_deviation_reduction_percent_at_original_budget": "6.2028283599899520590659670771034301541693133455900",
      "break_even_extra_fi_energy_share_at_f_25_50_75": [
        "1/52",
        "1/26",
        "3/52"
      ],
      "planning_scenarios": [
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/52",
          "battery_life_change_fraction": "1/51"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "3/325",
          "battery_life_change_fraction": "3/322"
        },
        {
          "affected_reading_energy_share_f": "1/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "-7/650",
          "battery_life_change_fraction": "-7/657"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "1/26",
          "battery_life_change_fraction": "1/25"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "37/1300",
          "battery_life_change_fraction": "37/1263"
        },
        {
          "affected_reading_energy_share_f": "1/2",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "11/1300",
          "battery_life_change_fraction": "11/1289"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "0/1",
          "net_energy_saved_fraction": "3/52",
          "battery_life_change_fraction": "3/49"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "1/100",
          "net_energy_saved_fraction": "31/650",
          "battery_life_change_fraction": "31/619"
        },
        {
          "affected_reading_energy_share_f": "3/4",
          "extra_fi_energy_share_h": "3/100",
          "net_energy_saved_fraction": "9/325",
          "battery_life_change_fraction": "9/316"
        }
      ]
    }
  ],
  "exploratory_12_case_unweighted_means": {
    "modeled_variance_reduction_percent": "26.297232179585120761591349826643944291003114532526",
    "minimum_reading_fraction_saved": "137/576",
    "minimum_reading_percent_saved": "23.784722222222222222222222222222222222222222222222",
    "modeled_standard_deviation_reduction_percent": "15.013596941631886959697702593864985065183072648031"
  }
}