Automated MNLP evaluation report (2026-06-11)

EVAL_REPORT.md

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+# Automated MNLP evaluation report
+
+- **Model repo:** [`cs-552-2026-clankers-builder/math_model`](https://huggingface.co/cs-552-2026-clankers-builder/math_model)
+- **Owner(s):** group **clankers-builder**
+- **Generated at:** 2026-06-11T06:23:10+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._
+
+## Evaluated checkpoint
+
+- **Commit:** [`c55f18f`](https://huggingface.co/cs-552-2026-clankers-builder/math_model/commit/c55f18fe609f4cd49f840fb2b0d2cb75728ac973)
+- **Message:** Upload folder using huggingface_hub
+- **Committed:** 2026-06-09T10:11:23+00:00
+
+## Summary
+
+| Benchmark | Accuracy | Status |
+|---|---:|---|
+| Math | 0.5100 | ok |
+| Knowledge | — | not run |
+| Multilingual | — | not run |
+| Safety | — | not run |
+
+## Sample completions
+
+_Prompts are intentionally omitted to avoid revealing benchmark contents. For multi-completion problems, only one completion is shown per sample._
+
+### Math
+
+**Correct** (1 shown)
+
+- **reference**: `$6\rho$`
+- **overall** (4/8 completions correct)
+- **extracted** (✓): `6\rho`
+- **completion**:
+
+    ```text
+    <think>
+    Okay, so I need to find the least possible value of this expression:
+    
+    \[
+    \left(\frac{xy(s-z)}{s}\right)^{1/2} + \left(\frac{zx(s-y)}{s}\right)^{1/2} + \left(\frac{yz(s-x)}{s}\right)^{1/2}
+    \]
+    
+    where \(x\), \(y\), and \(z\) are the sides of a triangle with semiperimeter \(s\) and inradius \(\rho\). Hmm, let's start by recalling some formulas related to triangles. The semiperimeter \(s = \fra
+    
+    ... [truncated 823 chars] ...
+    
+    }{\rho \sqrt{s}},
+       \]
+       \[
+       \sqrt{\frac{yz(s - x)}{s}} = \frac{\sqrt{yz(s - x)}}{\rho \sqrt{s}}.
+       \]
+    
+    3. **Symmetry and Equilateral Triangle:**
+       The expression is symmetric in \(x, y, z\). To find the minimum value, we consider the case where the triangle is equilateral. In an equilateral triangle, \(x = y = z\), and the semiperimeter \(s\) is:
+       \[
+       s = \frac{3x}{2}.
+       \]
+       The inradius \(\rho\) is:
+       \[
+       \rho = \frac{\sqrt{3}}{6} x.
+       \]
+       Substituting \(x = 2\sqrt{3} \rho\) into the expression, we get:
+       \[
+       \left(\frac{xy(s - z)}{s}\right)^{1/2} + \left(\frac{zx(s - y)}{s}\right)^{1/2} + \left(\frac{yz(s - x)}{s}\right)^{1/2} = 6\rho.
+       \]
+    
+    4. **Verification and Conclusion:**
+       To verify, consider other configurations of the triangle, such as right-angled or isoceles triangles. In these cases, the expression is greater than \(6\rho\). Additionally, as the triangle becomes degenerate, the inradius \(\rho\) approaches 0, but the expression also approaches 0. However, degenerate triangles are not valid, so the minimum value is achieved in the equilateral triangle configuration.
+    
+    Thus, the least possible value of the given expression is:
+    \[
+    \boxed{6\rho}.
+    \]
+    ```
+
+**Incorrect** (1 shown)
+
+- **reference**: `7200`
+- **overall** (0/8 completions correct)
+- **extracted** (✗): `1200`
+- **completion**:
+
+    ```text
+    <think>
+    Okay, let's try to tackle this problem step by step. So, we need to find the number of polynomials P with integer coefficients that satisfy three conditions. The polynomial has degree at most 3, all coefficients are between 0 and 2012 inclusive. Also, for each positive integer x ≤ 100, P(x) + P(-x) is divisible by 2013. Additionally, the residues modulo 2013 of P(0), P(1), ..., P(2012) are
+    
+    ... [truncated 823 chars] ...
+    
+    ( d \) must be between 0 and 2012, the only valid values are \( b = 0 \) and \( d = 0 \). Thus, \( P(x) = ax^3 + cx \).
+    
+    3. **Condition (3)**:
+       - The residues modulo 2013 of \( P(0), P(1), \ldots, P(2012) \) must be distinct. For \( P(x) = ax^3 + cx \), we need to ensure that \( ax^3 + cx \) is a permutation polynomial modulo 3, 11, and 61.
+    
+    ### Analysis of Permutation Polynomials:
+    - **Modulo 3**: \( P(x) = ax^3 + cx \) must be injective. This requires \( a + c \not\equiv 0 \pmod{3} \). The valid pairs \((a, c)\) are those where \( a \equiv 0 \pmod{3} \) and \( c \equiv 1, 2 \pmod{3} \). There are 2 valid pairs.
+    - **Modulo 11**: \( P(x) = ax^3 + cx \) must be injective. This requires \( a \equiv 0 \pmod{11} \) and \( c \not\equiv 0 \pmod{11} \). There are 10 valid pairs.
+    - **Modulo 61**: \( P(x) = ax^3 + cx \) must be injective. This requires \( a \equiv 0 \pmod{61} \) and \( c \not\equiv 0 \pmod{61} \). There are 60 valid pairs.
+    
+    ### Total Number of Polynomials:
+    - The total number of valid pairs \((a, c)\) modulo 2013 is the product of the valid pairs modulo 3, 11, and 61:
+      \[
+      2 \times 10 \times 60 = 1200
+      \]
+    
+    Thus, the number of such polynomials \( P \) is \(\boxed{1200}\).
+    ```