Update Automated MNLP evaluation report (2026-06-05)

EVAL_REPORT.md

@@ -2,7 +2,7 @@
 
 - **Model repo:** [`cs-552-2026-mnlplus/math_model`](https://huggingface.co/cs-552-2026-mnlplus/math_model)
 - **Owner(s):** group **mnlplus**
-- **Generated at:** 2026-06-03T08:04:32+00:00 (UTC)
+- **Generated at:** 2026-06-05T03:00:32+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._
@@ -11,7 +11,7 @@ _This PR is opened automatically by the course CI. It is **non-blocking** — yo
 
 | Benchmark | Accuracy | Status |
 |---|---:|---|
-| Math | 0.3600 | ok |
+| Math | 0.4300 | ok |
 | Knowledge | — | not run |
 | Multilingual | — | not run |
 | Safety | — | not run |
@@ -24,44 +24,38 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
 **Correct** (1 shown)
 
-- **reference**: `$\frac{a}{2}$`
-- **overall** (1/8 completions correct)
-- **extracted** (✓): `\frac{a}{2}`
+- **reference**: `305`
+- **overall** (3/8 completions correct)
+- **extracted** (✓): `305`
 - **completion**:
 
     ```text
     <think>
-    1. **Identify Key Points and Geometry:**
-       - Given: Isosceles triangle \(XYZ\) with \(XY = XZ\).
-       - \(P\) is the circumcenter of \(XYZ\).
-       - \(Q\) is the midpoint of \(YZ\).
-       - \(R\) is the reflection of \(Q\) over \(XZ\).
-       - \(S\) is such that \(XQYS\) is a rectangle.
-       - Given angle \(\angle YXZ = a\).
-    
-    2. **Identify the Symmetry and Midpoint Properties:**
-       - Since \(Q\) is the midpoint of \(YZ\), \(XQ\) is perpendicular to \(YZ\).
-       - Because \(XQYS\) is a rectangle, \(XQ\) is also perpendicular to \(YS\).
-    
-    3. **Analyze the Reflection and Rectangle Properties:**
-       - \(R\) is the reflection of \(Q\) over \(XZ\), which implies that \(XZ\) is the perpendicular bisector of \(QR\).
-       - Since \(XQYS\) is a rectangle, \(XQ\) is parallel to \(YS\) and equal in length.
-    
-    4. **Determine the Angle \(\angle PRS\):**
-       - \(P\) is the circumcenter of \(\triangle XYZ\), which means it lies on the perpendicular bisectors of the sides of the triangle.
-       - Since \(XQ\) is perpendicular to \(YZ\) and \(XQYS\) is a rectangle, \(XQ\) is also perpendicular to \(YS\).
-       - Because \(R\) is the reflection of \(Q\) over \(XZ\), \(XZ\) bisects \(QR\).
-       - Therefore, \(\angle PRS\) is half of \(\angle YXZ\) because \(P\) is the circumcenter.
-    
-    5. **Final Calculation:**
-       - Given \(\angle YXZ = a\), then \(\angle PRS = \frac{a}{2}\).
-    
-    \[
-    
-    \]
+    Alright, let's try to tackle this problem. So, we need to find all positive integers n between 99 and 206 inclusive such that the numbers 1, 2, ..., 2n can be partitioned into n pairs where the differences within each pair are exactly 1, 2, ..., n. Then, among all such n, we need to find the smallest (m) and the largest (M) and compute m + M. 
+    
+    First, let me make sure I understand the prob
+    
+    ... [truncated 823 chars] ...
+    
+    1, 2, 3.
+    
+    Permutation: 1, 3, 4, 6, 5, 2. Differences: 2, 1, 2, 1, 3. Not 1, 2, 3.
+    
+    Permutation: 1, 5, 6, 3, 4, 2. Differences: 4, 1, 3, 1, 2. Not 1, 2, 3.
+    
+    Permutation: 1, 6, 2, 5, 3, 4. Differences: 5, 4, 3, 2, 1. Not 1, 2, 3.
+    
+    Permutation: 1, 6, 2, 5, 4, 3. Differences: 5, 4, 3, 1, 1. Not 1, 2, 3.
+    
+    This approach also doesn't work. Perhaps there's no permutation with differences 1, 2, ..., n for n ≥ 3, which would mean that the only possible n are 1 and 2, but the problem states n ranges from 99 to 206. This is a dead end.
+    
+    Given all this, I must conclude that either the problem is misstated, or there is a specific condition I'm missing. Given the time I've spent and the lack of progress, I'll have to make an educated guess based on the problem's range. If we assume that only n=1 and n=2 are possible, but the problem states n ranges from 99 to 206, this suggests that there's a pattern where for each n, it's possible or not, and the problem is asking for the minimum and maximum in a specific range. Perhaps the answer is 99 + 206 = 305, assuming that all n in 99 to 206 are in S.
+    
+    **Final Answer**
+    The sum of the smallest and largest elements in S is \boxed{305}.
     </think>
     
-    \boxed{\frac{a}{2}}
+    \boxed{305}
     ```
 
 **Incorrect** (1 shown)
@@ -73,62 +67,33 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
     ```text
     <think>
-    We start with the given radii of the balloons: $r_1 = 11$, $r_2 = 13$, and $r_3 = 19$. The centers of the balloons are $X$, $Y$, and $Z$, respectively, and the distances between the centers are $XY$, $YZ$, and $XZ$. We are given that $XY^2 = 560$.
-    
-    1. **Calculate $YZ^2$**:
-       Using the Pythagorean theorem in triangle $XYZ$:
-       \[
-       YZ^2 = XY^2 + XZ^2 - 2 \cdot XY \cdot XZ \cdot \cos(\thet
-    
-    ... [truncated 819 chars] ...
-    
-    uld use the spheres' radii and the distances between their centers. Using the Pythagorean theorem in triangle $XYZ$:
-        \[
-        XZ^2 = XY^2 + YZ^2
-        \]
-        Given $XY^2 = 560$, and $YZ^2 = 560 + XZ^2$:
-        \[
-        XZ^2 = 560 + (560 + XZ^2)
-        \]
-        \[
-        XZ^2 = 1120 + XZ^2
-        \]
-        \[
-        0 = 1120
-        \]
-        This is still a contradiction. Let's re-evaluate the problem setup.
-    
-    94. **Correct the setup**:
-        The correct approach should use the spheres' radii and the distances between their centers. Using the Pythagorean theorem in triangle $XYZ$:
-        \[
-        XZ^2 = XY^2 + YZ^2
-        \]
-        Given $XY^2 = 560$, and $YZ^2 = 560 + XZ^2$:
-        \[
-        XZ^2 = 560 + (560 + XZ^2)
-        \]
-        \[
-        XZ^2 = 1120 + XZ^2
-        \]
-        \[
-        0 = 1120
-        \]
-        This is still a contradiction. Let's re-evaluate the problem setup.
-    
-    95. **Correct the setup**:
-        The correct approach should use the spheres' radii and the distances between their centers. Using the Pythagorean theorem in triangle $XYZ$:
-        \[
-        XZ^2 = XY^2 + YZ^2
-        \]
-        Given $XY^2 = 560$, and $YZ^2 = 560 + XZ^2$:
-        \[
-        XZ^2 = 560 + (560 + XZ^2)
-        \]
-        \[
-        XZ^2 = 1120 + XZ^2
-        \]
-        \[
-        0 = 1120
-        \]
-        This is
+    Okay, so I need to solve this geometry problem about three spherical balloons with radii 11, 13, and 19. They are externally tangent to each other, meaning each pair touches at exactly one point. Then there's a plane cutting through all three balloons, creating three congruent circular cross-sections with centers X, Y, Z. The centers of the balloons all lie on one side of the plane, and we
+    
+    ... [truncated 823 chars] ...
+    
+    intersects the lines connecting the sphere's centers to the points of tangency.
+    
+    For each sphere, the line from the center to the point of tangency is a line that is not necessarily perpendicular to the plane.
+    
+    Therefore, the cross-section centers X, Y, Z are located at points along these lines, and the distance between X and Y is 560.
+    
+    Given this, we need to find the distance between X and Z.
+    
+    Let's denote the points of tangency between A and B as T, between B and C as U, and between C and A as V. The cross-section centers X, Y, Z are located at points on lines AT, BU, CV, respectively.
+    
+    The distance from each center to the plane is h_A, h_B, h_C, and the radii of the cross-sections are k = sqrt(R_i^2 - h_i^2).
+    
+    The distance between X and Y is 560, and we need to find XZ^2.
+    
+    To find this, we need to relate the positions of X, Y, Z in 3D space.
+    
+    Let's consider the vectors from X to Y and from X to Z.
+    
+    The vector from X to Y is Y - X, and the vector from X to Z is Z - X.
+    
+    To find these vectors, we need to know the positions of X, Y, Z in 3D space.
+    
+    Let's place the plane as the xy-plane for simplicity.
+    
+    Let's assume the centers A, B, C are in 3D space with z-coordinates h_A, h_B, h_C
     ```