> ## 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.

# Manhattan Embedding Distance

> Calculates the L1 distance between two text embeddings, representing the sum of absolute differences across all dimensions.

### 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.
* **Higher scores**: The texts are more semantically different.
  > Generally less sensitive to outliers than Euclidean distance.

## Formula

$$
\mathrm{Manhattan}(x, y) = \sum_i |x_i - y_i|
$$

Where `i` indexes the dimensions of the vectors.

<Note>This is a **distance metric**. Lower scores indicate greater similarity.</Note>

## How It Works

The evaluator computes embeddings for both texts and then sums the absolute differences for each corresponding dimension.

## Use Cases

* Scenarios where movement is constrained to a grid (e.g., city blocks)
* Feature engineering in machine learning, as it can be more robust to outliers
* High-dimensional spaces where it can be more effective than Euclidean distance