Automated MNLP evaluation report (2026-06-11)

EVAL_REPORT.md

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+# Automated MNLP evaluation report
+
+- **Model repo:** [`cs-552-2026-llmfao/math_model`](https://huggingface.co/cs-552-2026-llmfao/math_model)
+- **Owner(s):** group **llmfao**
+- **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:** [`f327cba`](https://huggingface.co/cs-552-2026-llmfao/math_model/commit/f327cba6ed4915a4aac202c1326e80d6e7d370d5)
+- **Message:** Upload new math model checkpoint
+- **Committed:** 2026-06-03T18:31:59+00:00
+
+## Summary
+
+| Benchmark | Accuracy | Status |
+|---|---:|---|
+| Math | 0.4000 | 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**: `501`
+- **overall** (2/8 completions correct)
+- **extracted** (✓): `501`
+- **completion**:
+
+    ```text
+    <think>
+    Okay, so I need to figure out how many integers k between -500 and 500 inclusive make the equation log(kx) = 2 log(x + 2) have exactly one real solution. Hmm, let's start by recalling some logarithm properties. 
+    
+    First, the equation given is log(kx) = 2 log(x + 2). I know that 2 log(x + 2) can be rewritten using logarithm rules as log((x + 2)^2). So the equation becomes log(kx) = log((x +
+    
+    ... [truncated 822 chars] ...
+    
+    2) \implies kx = (x + 2)^2
+    \]
+    
+    This quadratic equation is \(x^2 + (4 - k)x + 4 = 0\). For this equation to have exactly one real solution, the discriminant must be zero. The discriminant \(D\) is given by:
+    
+    \[
+    D = (4 - k)^2 - 16
+    \]
+    
+    Setting \(D = 0\), we solve:
+    
+    \[
+    (4 - k)^2 - 16 = 0 \implies (4 - k)^2 = 16 \implies 4 - k = \pm 4 \implies k = 0 \text{ or } k = 8
+    \]
+    
+    However, \(k = 0\) is invalid because \(\log(0x)\) is undefined. Thus, \(k = 8\) is valid. 
+    
+    Next, we check for \(k < 0\) values. For \(k < 0\), the quadratic equation \(x^2 + (4 - k)x + 4 = 0\) has two real roots. Since \(k < 0\), \(x\) must be in \((-2, 0)\). Evaluating the quadratic function at \(x = -2\) and \(x = 0\) confirms the function changes sign, ensuring exactly one root in \((-2, 0)\).
+    
+    For \(k > 8\), the quadratic equation has two positive roots, leading to two solutions, which are both valid. Thus, these values of \(k\) are excluded.
+    
+    Therefore, the valid integers \(k\) are all negative integers from \(-500\) to \(-1\) inclusive, plus \(k = 8\). The count of negative integers from \(-500\) to \(-1\) is 500, and adding \(k = 8\) gives:
+    
+    \[
+    500 + 1 = 501
+    \]
+    
+    The number of integers \(k\) is \(\boxed{501}\).
+    ```
+
+**Incorrect** (1 shown)
+
+- **reference**: `756`
+- **overall** (0/8 completions correct)
+- **extracted** (✗): `240`
+- **completion**:
+
+    ```text
+    <think>
+    Okay, so I need to solve this problem about three spherical balloons with radii 11, 13, and 19. Each pair of balloons is externally tangent, which means the distance between their centers is equal to the sum of their radii. Then there's a plane that cuts each balloon, creating three congruent circular cross-sections. The centers of these cross-sections are points X, Y, and Z, which are all
+    
+    ... [truncated 823 chars] ...
+    
+    ^2 - k^2} = \sqrt{19^2 - m^2}\).
+    
+    3. **Set up equations for the radii:**
+       - \(11^2 - h^2 = 13^2 - k^2\) implies \(k^2 - h^2 = 48\).
+       - \(13^2 - k^2 = 19^2 - m^2\) implies \(m^2 - k^2 = 192\).
+    
+    4. **Solve for \(m^2\) in terms of \(h^2\):**
+       - From \(k^2 - h^2 = 48\), we get \(k^2 = h^2 + 48\).
+       - Substitute \(k^2\) into \(m^2 - k^2 = 192\): \(m^2 = h^2 + 48 + 192 = h^2 + 240\).
+    
+    5. **Calculate the distance between the centers of the balloons:**
+       - The distance between \(A\) and \(B\) is 24, which is the hypotenuse of a right triangle with legs \(h - k\) and 560. This gives:
+         \[
+         (h - k)^2 + 560^2 = 24^2
+         \]
+       - This equation is impossible because \((h - k)^2\) must be non-negative, leading to a contradiction. However, considering the problem's constraints, we proceed with the equations derived from the radii.
+    
+    6. **Determine \(XZ^2\) using the distances:**
+       - Using the distances \(h\), \(k\), and \(m\) and the congruent cross-sections, we find \(XZ^2\) by solving the system of equations:
+         \[
+         (h - m)^2 + D^2 = 32^2
+         \]
+       - Substituting \(m^2 = h^2 + 240\) and solving for \(D^2\), we find \(D^2 = 240\).
+    
+    Thus, the final answer is \(\boxed{240}\).
+    ```