calib·HumanEval/8
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 sum_product to fn_3e38f74dda so the judges can't pattern-match a memorized HumanEval solution.
from typing import List, Tuple
def fn_3e38f74dda(numbers: List[int]) -> Tuple[int, int]:
""" For a given list of integers, return a tuple consisting of a sum and a product of all the integers in a list.
Empty sum should be equal to 0 and empty product should be equal to 1.
>>> fn_3e38f74dda([])
(0, 1)
>>> fn_3e38f74dda([1, 2, 3, 4])
(10, 24)
"""
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.
from typing import List, Tuple
def fn_3e38f74dda(numbers: List[int]) -> Tuple[int, int]:
""" For a given list of integers, return a tuple consisting of a sum and a product of all the integers in a list.
Empty sum should be equal to 0 and empty product should be equal to 1.
>>> fn_3e38f74dda([])
(0, 1)
>>> fn_3e38f74dda([1, 2, 3, 4])
(10, 24)
"""
sum_value = 0
prod_value = 1
for n in numbers:
sum_value += n
prod_value *= n
return sum_value, prod_value
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 correctly initializes sum to 0 and product to 1 (matching empty-list edge case), then iterates through the list accumulating both values. Both provided doctests pass: `[]` → `(0, 1)` and `[1,2,3,4]` → `(10, 24)`. The logic is sound for all edge cases including single-element lists and negative numbers. Code is clean and idiomatic.
The candidate solution correctly implements the function to return a tuple consisting of the sum and product of all integers in the list. It handles the edge case of an empty list by returning (0, 1), as specified in the prompt. The implementation is clear and idiomatic, using a simple loop to accumulate the sum and product. The provided examples in the docstring are correctly handled by the function.