calib·HumanEval/41
This is one (task, candidate response) pair flowing through the full PANOPTES pipeline. Each section below is a stage of the analysis: the task itself, the candidate solution being evaluated, every judge's score + rationale, the sampling-pass dispersion that captures within-judge noise, and the uncertainty-quantification metrics computed on top.
The function signature + docstring presented to both the model under test and to every judge. The entry-point name was obfuscated from car_race_collision to fn_b3e360ed26 so the judges can't pattern-match a memorized HumanEval solution.
def fn_b3e360ed26(n: int):
"""
Imagine a road that's a perfectly straight infinitely long line.
n cars are driving left to right; simultaneously, a different set of n cars
are driving right to left. The two sets of cars start out being very far from
each other. All cars move in the same speed. Two cars are said to collide
when a car that's moving left to right hits a car that's moving right to left.
However, the cars are infinitely sturdy and strong; as a result, they continue moving
in their trajectory as if they did not collide.
This function outputs the number of such collisions.
"""
The full solution every judge is grading. For these runs the candidate is the reference solution prepended with the task signature so it parses as a complete program.
def fn_b3e360ed26(n: int):
"""
Imagine a road that's a perfectly straight infinitely long line.
n cars are driving left to right; simultaneously, a different set of n cars
are driving right to left. The two sets of cars start out being very far from
each other. All cars move in the same speed. Two cars are said to collide
when a car that's moving left to right hits a car that's moving right to left.
However, the cars are infinitely sturdy and strong; as a result, they continue moving
in their trajectory as if they did not collide.
This function outputs the number of such collisions.
"""
return n**2
One call per judge at temperature=0. This is the "best single guess" each judge has. Disagreement here is structural. The judges literally see this candidate differently.
n draws per judge at temperature=1. Dots are individual draws; vertical bar is the mean; shaded band is ±1σ. Wide band = the judge is uncertain even with itself; narrow band = it's consistent.
The natural-language explanation each judge gave alongside its score. These are produced via tool-use structured output, so the score and the rationale are guaranteed to come from the same forward pass.
Each of the n left-to-right cars will eventually collide with each of the n right-to-left cars exactly once (since all cars move at the same speed on an infinite line and pass through each other). This gives n × n = n² total collisions. The solution `return n**2` is correct, concise, and handles edge cases (n=0 → 0, n=1 → 1, etc.) properly.
The candidate solution correctly implements the logic for counting the number of collisions. Given that there are n cars moving left to right and n cars moving right to left, each car from one direction will collide with each car from the opposite direction. Therefore, the total number of collisions is n * n, which is correctly implemented as n**2 in the solution. The solution is clear, idiomatic, and handles the task as described without any edge cases or boundary issues.