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

# Chebyshev Embedding Distance

> Calculates the L∞ distance between two text embeddings, defined as the greatest difference along any single dimension.

### Input

* **`output`** (str): The generated text to be evaluated.
* **`expectedOutput`** (str): The reference or ground truth text.

### Output

* **`Result`** (float): A distance score from 0 to infinity.

## Interpretation

* **`0`**: The embeddings are identical.
* **Lower scores**: The texts are more semantically similar.
* **Higher scores**: The texts are more semantically different.
  > The score is determined entirely by the one dimension where the embeddings differ the most.

## Formula

$$
\mathrm{Chebyshev}(x, y) = \max_i |x_i - y_i|
$$

Where `i` indexes the dimensions of the vectors.

<Note>This is a **distance metric**. Lower scores indicate greater similarity. It is particularly sensitive to the single largest deviation.</Note>

## How It Works

The evaluator computes embeddings for both texts and then finds the maximum absolute difference across all corresponding dimensions of the vectors.

## Use Cases

* Identifying outliers in semantic similarity
* Scenarios where the maximum deviation is more important than the average deviation
* Logistics and chessboard-related distance calculations