#brevity-penalty

Reference: "a small cat sat on the warm mat" (8 words)

Candidate: "the cat sat on the mat" (6 words)

Compute BLEU with unigrams and bigrams only, uniform weights $w_1 = w_2 = \tfrac12$: $\mathrm{BLEU} = \mathrm{BP} \cdot \exp\big(\tfrac12 \ln p_1 + \tfrac12 \ln p_2\big)$, where $p_n$ are the clipped (modified) n-gram precisions and $\mathrm{BP} = e^{1 - r/c}$ if the candidate length $c$ is at most the reference length $r$ (else 1).