Update Automated MNLP evaluation report (2026-05-16)

EVAL_REPORT.md

@@ -2,7 +2,7 @@
 
 - **Model repo:** [`cs-552-2026-flab/math_model`](https://huggingface.co/cs-552-2026-flab/math_model)
 - **Owner(s):** group **flab**
-- **Generated at:** 2026-05-13T23:30:17+00:00 (UTC)
+- **Generated at:** 2026-05-16T04:57:46+00:00 (UTC)
 - **Pipeline:** [mnlp-project-ci](https://github.com/eric11eca/mnlp-project-ci)
 
 _This PR is opened automatically by the course CI. It is **non-blocking** — you do not need to merge it. The next nightly run will refresh this file._
@@ -11,17 +11,71 @@ _This PR is opened automatically by the course CI. It is **non-blocking** — yo
 
 | Benchmark | Accuracy | Status |
 |---|---:|---|
-| Math | — | error (generation_config) |
+| Math | 0.3200 | ok |
 | Knowledge | — | not run |
 | Multilingual | — | not run |
 | Safety | — | not run |
 
-## Errors
+## Sample completions
 
-### math — `generation_config`
+_Prompts are intentionally omitted to avoid revealing benchmark contents. For multi-completion problems, only one completion is shown per sample._
 
-```
-generation_config.json not found: 404 Client Error. (Request ID: Root=1-6a04f381-79f2d0676120463b77421940;79d82689-bb4c-4128-bd24-43d2f71d00c4)
+### Math
 
-Entry Not Found for url: https://huggingface.co/cs-552-2026-flab/math_model/resolve/main/generation_config.json.
-```
+**Correct** (1 shown)
+
+- **reference**: `0`
+- **overall** (3/8 completions correct)
+- **extracted** (✓): `0`
+- **completion**:
+
+    ```text
+    </think>
+    
+    The polynomial \(p(x)\) is a rational function with distinct linear factors in the denominator. By polynomial division, \(p(x)\) can be written as a polynomial plus a proper rational function. The rational part simplifies to \(1\), so \(p(x) = q(x) + 1\) for some polynomial \(q\). Since \(p(x)\) is a polynomial of degree \(\le 2\) (the degree of the numerator is at most \(2\)), the degree of \(p\) is at most \(2\). Moreover, \(p(x)\) vanishes at \(x=a,b,c\) (because each term has a factor \((x-a)\), \((x-b)\), \((x-c)\)). A non‑constant polynomial that vanishes at three distinct points must be the zero polynomial. Hence \(p(x) \equiv 1\), a constant polynomial. Therefore the degree is \(0\).
+    
+    \[
+    \boxed{0}
+    \]
+    ```
+
+**Incorrect** (1 shown)
+
+- **reference**: `$(n-2)2^n +1$`
+- **overall** (0/8 completions correct)
+- **extracted** (✗): `2^n - 1`
+- **completion**:
+
+    ```text
+    </think>
+    
+    We are given a positive integer \(n \ge 2\) and the set  
+    \[
+    C_n = \{2^n - 2^i : i \in \mathbb{Z}, 0 \le i < n\}.
+    \]  
+    We need the greatest positive integer that cannot be written as a sum of elements of \(C_n\) (with repetition allowed).
+    
+    Let \(N = 2^n - 1\).  
+    For any \(i \in [0,n]\), \(2^i \in C_n\). Moreover,  
+    \[
+    2^i + 2^j = 2^{\min(i,j)}\bigl(1+2^{|i-j|}\bigr).
+    \]  
+    Thus each eleme
+    
+    ... [truncated 686 chars] ...
+    
+    m\) divides \(k\), we can write \(k = 2^m \cdot t\) with \(t\) odd.  
+    The binary digits of \(t\) are the binary digits of \(k\) shifted left by \(m\) places.  
+    Thus \(t = k \oplus (k \gg m)\).  
+    Because \(t\) is odd, the rightmost bit of \(t\) must be \(1\).  
+    This means that the binary representation of \(k\) has a \(1\) in the \(m\)-th position.  
+    In other words, \(m\) must be the position of the least significant \(1\) in \(k\).
+    
+    Therefore, for a given \(k\), the number of elements of \(C_n\) whose sum equals \(k\) is non‑zero if and only if \(k\) has exactly one \(1\) in its binary expansion, and that \(1\) lies in some position \(m\) (i.e., \(m\) is the position of the least significant \(1\)).  
+    In this case, the representation is unique: the element is \(2^m\) and the remaining part \(k - 2^m\) is exactly \(t = 1+2^m\).
+    
+    Consequently, the numbers that cannot be expressed are those that have **more than one** \(1\) in their binary representation (since with two or more \(1\)’s we cannot obtain an odd number).  
+    The largest such number is \(N = 2^n - 1\) itself (which has exactly one \(1\)).
+    
+    Hence the greatest positive integer that is not representable is \(\boxed{2^n - 1}\).
+    ```