> ## Documentation Index
> Fetch the complete documentation index at: https://docs.swarms.world/llms.txt
> Use this file to discover all available pages before exploring further.

# Fermi estimate with sampling and votes

> Estimate the kinetic energy of every car on US roads at rush hour, with independently sampled steps compared by vote.

A Fermi estimate has no single correct path, only more and less defensible assumptions. Rating one assumption on an absolute scale is hard; comparing three and picking the most defensible is easier. So this search samples each candidate step with its own call and scores the candidates by vote.

| | |
| - | - |
| **Class** | [`TreeOfThoughts`](/agents/tree-of-thoughts) |
| **Search** | `"bfs"`, beam of 2 |
| **Generation** | `"sample"` |
| **Evaluation** | `"vote"`, 3 votes per comparison |
| **Expected answer** | about 10¹³ J |

## Prerequisites

```bash theme={null}
pip install git+https://github.com/kyegomez/swarms.git
export OPENAI_API_KEY="sk-..."
```

`TreeOfThoughts` is not in `swarms` 15.0.3 on PyPI, so install from GitHub until the next release.

## The code

```python fermi_estimation.py theme={null}
from swarms import TreeOfThoughts

agent = TreeOfThoughts(
    name="Fermi-Estimator",
    model_name="gpt-5.4",
    search_algorithm="bfs",
    generation_strategy="sample",
    evaluation_strategy="vote",
    num_thoughts=3,
    breadth=2,
    max_depth=4,
    n_evaluate_samples=3,
    thought_description=(
        "One estimation step: a single quantity with a stated, justified "
        "assumption (for example the number of cars moving, a typical "
        "mass, a typical speed), or a combination of earlier quantities."
    ),
    evaluation_criteria=(
        "Prefer realistic, explicitly justified assumptions, correct "
        "arithmetic and units, and steady progress toward one number in "
        "joules."
    ),
)

answer = agent.run(
    "Estimate, to an order of magnitude, the total kinetic energy in "
    "joules of all cars moving on United States roads during a weekday "
    "rush hour. State your assumptions."
)
print(f"Answer: {answer}\n")

result = agent.last_result
for number, step in enumerate(result.steps, 1):
    print(f"{number}. {step}")
print(
    f"\nsolved={result.solved} nodes_expanded={result.nodes_expanded} "
    f"llm_calls={result.llm_calls} tokens={result.usage['total_tokens']}"
)
```

```bash theme={null}
python fermi_estimation.py
```

It prints the estimate with its assumptions, the steps on the best path, and what the search cost.

## What the settings do

* `generation_strategy="sample"` makes three independent calls for one step each, instead of one call for three. Independent calls give more varied assumptions.
* `evaluation_strategy="vote"` shows the evaluator every candidate on the level and asks which is most defensible. A candidate's score is its votes divided by the leader's votes.
* `n_evaluate_samples=3` casts three votes per comparison. With one vote, only the winner would clear the default `value_threshold` of 0.5. With three, a runner-up with at least half the leader's votes stays in the beam.
* `evaluation_criteria` tells the voter what defensible means here: justified assumptions, correct units, and progress toward one number in joules.

## Check the answer

One defensible chain of assumptions:

* About 5 × 10⁷ cars are moving at rush hour.
* A typical car has a mass of about 1,500 kg.
* A typical speed, mixing highway and city traffic, is about 15 m/s.

Each car carries ½ × 1,500 × 15² ≈ 1.7 × 10⁵ J, and 5 × 10⁷ cars carry about 8 × 10¹² J. A reasonable answer lands near **10¹³ J**. Different defensible assumptions move the estimate within the same order of magnitude.

## Cost

This configuration expands at most 7 nodes and makes at most 34 model calls: 21 generation calls (3 per expanded node), 12 votes (3 per level over 4 levels) and 1 answer call. See [Cost](/agents/tree-of-thoughts#cost) for the formula.

## Next

<CardGroup cols={2}>
  <Card title="Knights and knaves" icon="chess-knight" href="/examples/tree-of-thoughts/knights-and-knaves">
    DFS case analysis with backtracking.
  </Card>

  <Card title="TreeOfThoughts reference" icon="book" href="/agents/tree-of-thoughts">
    Every parameter, strategy, and result field.
  </Card>
</CardGroup>