Test whether a new agent version really regressed

You changed your agent's prompt and reran the same eval tasks. Each task gets a score from 0 to 10, and the new version's total came out lower. Before you roll back, you want to know how often a drop this big turns up by chance when the change did nothing.

Write regression_p_value(before, after) that returns that chance.

Input and output:

• before, after: the old and the new version's scores, as two lists of the same length, up to 300 whole numbers from 0 to 10. Index i in both lists is the same task.
• Return a float. The tests accept any value within 0.000001 of the exact one.

Rules:

• A task's difference is its after score minus its before score. The observed total is the sum of the differences.
• If the change did nothing, each difference was as likely to come out with the opposite sign. So take every way of keeping or flipping the sign of each difference: 2 to the power n ways for n tasks, all equally likely. A difference of 0 stays 0 either way, and both ways still count.
• Return the share of those ways whose total is at most the observed total. With no tasks, return 1.0.