outputs/budget_bound_check.json

{
 "bound": "k ~= max(1, V/(d+1))",
 "sim": [
  {
   "V": 4,
   "d": 3,
   "bound": 1.0,
   "sim_mean_k": 1.0118577075098814,
   "ratio": 1.0118577075098814,
   "max_ic": 4
  },
  {
   "V": 4,
   "d": 2,
   "bound": 1.3333333333333333,
   "sim_mean_k": 1.3473684210526315,
   "ratio": 1.0105263157894737,
   "max_ic": 4
  },
  {
   "V": 4,
   "d": 1,
   "bound": 2.0,
   "sim_mean_k": 2.015748031496063,
   "ratio": 1.0078740157480315,
   "max_ic": 4
  },
  {
   "V": 4,
   "d": 0,
   "bound": 4.0,
   "sim_mean_k": 4.0,
   "ratio": 1.0,
   "max_ic": 4
  },
  {
   "V": 8,
   "d": 3,
   "bound": 2.0,
   "sim_mean_k": 2.048,
   "ratio": 1.024,
   "max_ic": 8
  },
  {
   "V": 16,
   "d": 3,
   "bound": 4.0,
   "sim_mean_k": 4.19672131147541,
   "ratio": 1.0491803278688525,
   "max_ic": 16
  },
  {
   "V": 24,
   "d": 3,
   "bound": 6.0,
   "sim_mean_k": 6.2439024390243905,
   "ratio": 1.0406504065040652,
   "max_ic": 24
  },
  {
   "V": 6,
   "d": 3,
   "bound": 1.5,
   "sim_mean_k": 1.514792899408284,
   "ratio": 1.009861932938856,
   "max_ic": 6
  },
  {
   "V": 2,
   "d": 3,
   "bound": 1.0,
   "sim_mean_k": 1.003921568627451,
   "ratio": 1.003921568627451,
   "max_ic": 2
  }
 ],
 "required_V": {
  "Trip Plan": {
   "speedup": 3.48,
   "needed_V": 13.92
  },
  "HumanEval": {
   "speedup": 3.04,
   "needed_V": 12.16
  },
  "MBPP": {
   "speedup": 3.78,
   "needed_V": 15.12
  },
  "GSM8K": {
   "speedup": 1.82,
   "needed_V": 7.28
  },
  "MATH": {
   "speedup": 1.58,
   "needed_V": 6.32
  }
 },
 "worst_ratio": 1.0491803278688525
}