calib·HumanEval/31
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 is_prime to fn_e35c267aea so the judges can't pattern-match a memorized HumanEval solution.
def fn_e35c267aea(n):
"""Return true if a given number is prime, and false otherwise.
>>> fn_e35c267aea(6)
False
>>> fn_e35c267aea(101)
True
>>> fn_e35c267aea(11)
True
>>> fn_e35c267aea(13441)
True
>>> fn_e35c267aea(61)
True
>>> fn_e35c267aea(4)
False
>>> fn_e35c267aea(1)
False
"""
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_e35c267aea(n):
"""Return true if a given number is prime, and false otherwise.
>>> fn_e35c267aea(6)
False
>>> fn_e35c267aea(101)
True
>>> fn_e35c267aea(11)
True
>>> fn_e35c267aea(13441)
True
>>> fn_e35c267aea(61)
True
>>> fn_e35c267aea(4)
False
>>> fn_e35c267aea(1)
False
"""
if n < 2:
return False
for k in range(2, n - 1):
if n % k == 0:
return False
return True
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.
Three statistical methods computed on top of the raw scores above. Each one tells you something different about how much to trust the headline number.
How to read these: self-consistency = does the judge agree with itself when resampled? Narrower CI means more consistent. Semantic entropy = do the judge's rationales cluster into one meaning, or several? Higher entropy means the judge is internally conflicted about why. Decomposition = how much of the total variance comes from within-judge sampling noise (aleatoric, hard to fix) vs between-judge disagreement (epistemic, fixable by calling more judges).
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.
The solution is logically correct for all provided test cases and handles edge cases like n=1 (returns False) and n=2 (loop range(2,1) is empty, returns True correctly). The only issue is efficiency: it iterates up to n-2 instead of sqrt(n), making it O(n) rather than O(sqrt(n)). For the given test case n=13441 (which is prime), it would still return True but would be slow for large inputs. No correctness bugs are present — `range(2, n-1)` correctly excludes n itself, and n=2 works because range(2,1) is empty. Minor style/efficiency concern but functionally correct.
The candidate solution correctly identifies non-prime numbers less than 2 and checks divisibility for numbers greater than 1. However, the loop iterates from 2 to n-2, which is inefficient and incorrect for larger numbers. The loop should iterate up to the square root of n to improve efficiency and correctness. This solution will fail for larger numbers due to time complexity issues, and it incorrectly identifies 4 as prime because it checks divisibility only up to n-2, missing the divisor 2 for n=4. Thus, it passes some tests but fails on efficiency and correctness for larger inputs.