Cosine Similarity

Calculate the cosine similarity between two vectors.

Cosine similarity measures the angle between two vectors, regardless of their magnitude:

$\text{cosine\_similarity}(A, B) = \frac{A \cdot B}{\|A\| \times \|B\|}$

Where:

• $A \cdot B = \sum_i A_i \times B_i$ (dot product)
• $\|A\| = \sqrt{\sum_i A_i^2}$ (Euclidean norm)

This is widely used in NLP to measure document or word similarity.

Input format:

• Line 1: Space-separated floats for vector A
• Line 2: Space-separated floats for vector B

Output: Cosine similarity rounded to 4 decimal places.