Automated MNLP evaluation report (2026-06-01)

EVAL_REPORT.md

@@ -2,7 +2,7 @@
 
 - **Model repo:** [`cs-552-2026-the-transformers/math_model`](https://huggingface.co/cs-552-2026-the-transformers/math_model)
 - **Owner(s):** group **the-transformers**
-- **Generated at:** 2026-05-29T06:54:15+00:00 (UTC)
+- **Generated at:** 2026-06-01T06:13:57+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._
@@ -24,57 +24,37 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
 **Correct** (1 shown)
 
-- **reference**: `\frac{639}{40}`
-- **overall** (5/8 completions correct)
-- **extracted** (✓): `\frac{639}{40}`
+- **reference**: `$\frac{a}{2}$`
+- **overall** (1/8 completions correct)
+- **extracted** (✓): `\frac{a}{2}`
 - **completion**:
 
     ```text
     <think>
-    To solve this problem, we need to find the distance between two buildings on the map given the actual distance and the scale of the map.
+    1. **Identify Key Points and Relationships:**
+       - Given that $XYZ$ is an isosceles triangle with $XY = XZ$, the circumcenter $P$ lies on the perpendicular bisector of $YZ$.
+       - $Q$ is the midpoint of $YZ$, and $R$ is the reflection of $Q$ across $XZ$.
+       - $S$ is chosen such that $XQYS$ forms a rectangle.
     
-    First, let's understand the scale of the map. According to the problem, a length of 3 inches on the map represents 10 miles in the real world. This means that for every 3 inches on the map, the actual distance is 10 miles.
+    2. **Determine the Angles:**
+       - Since $XQYS$ is a rectangle, $\angle XQY = 90^\circ$.
+       - Because $Q$ is the midpoint of $YZ$, $QY = QZ$.
+       - Since $XQYS$ is a rectangle, $\angle XQS = 90^\circ$.
+       - Given $\angle YXZ = a$, we have $\angle QXZ = \frac{a}{2}$ because $Q$ is the midpoint of $YZ$.
     
-    We can set up a proportion to find the distance on the map that corresponds to 53.25 miles in the real world. Let's denote the distance on the map as \(x\) inches.
+    3. **Calculate $\angle QXR$:**
+       - Since $R$ is the reflection of $Q$ across $XZ$, $\angle QXR = \angle QXZ = \frac{a}{2}$.
+       - Therefore, $\angle QXR = \frac{a}{2}$.
     
-    The proportion can be written as:
-    \[
-    \frac{3 \text{ inches}}{10 \text{ miles}} = \frac{x \text{ inches}}{53.25 \text{ miles}}
-    \]
-    
-    To solve for \(x\), we can cross-multiply:
-    \[
-    3 \times 53.25 = 10 \times x
-    \]
-    
-    Calculating the left side:
-    \[
-    3 \times 53.25 = 159.75
-    \]
-    
-    So, we have:
-    \[
-    159.75 = 10x
-    \]
-    
-    To find \(x\), we divide both sides by 10:
-    \[
-    x = \frac{159.75}{10} = 15.975
-    \]
-    
-    Now, we need to express 15.975 as a fraction. We can write 15.975 as:
-    \[
-    15.975 = \frac{15975}{1000}
-    \]
+    4. **Determine $\angle PRS$:**
+       - Since $P$ is the circumcenter of $\triangle XYZ$, $\angle PRS = \angle QXR$.
+       - Therefore, $\angle PRS = \frac{a}{2}$.
     
-    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 25:
+    ### Conclusion:
     \[
-    \frac{15975 \div 25}{1000 \div 25} = \frac{639}{40}
-    \]
+    </think>
     
-    Therefore, the distance between the two buildings on the map, written as a fraction, is:
-    \[
-    \boxed{\frac{639}{40}}
+    \boxed{\frac{a}{2}}
     \]
     ```
 
@@ -87,32 +67,45 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
     ```text
     <think>
-    To solve this problem, we need to use the properties of spheres and the distances between their centers. Let's denote the centers of the three balloons as points $X$, $Y$, and $Z$, and their radii as $r_1 = 11$, $r_2 = 13$, and $r_3 = 19$, respectively.
+    To solve this problem, we need to find the squared distance between the centers of the three spherical balloons, given that the centers of the balloons lie on one side of a plane that cuts the balloons into three congruent circular cross-sections. We are given that the radii of the balloons are \(11\), \(13\), and \(19\), and the squared distance between the centers of the first and second
+    
+    ... [truncated 821 chars] ...
+    
+    226. **Calculate the squared distance between the centers of the first and third balloons:**
+        Using the Pythagorean theorem again, we have:
+        \[
+        AC^2 = 11^2 + 19^2 = 121 + 361 = 482
+        \]
+    
+    227. **Calculate the squared distance between the centers of the first and third balloons:**
+        Using the Pythagorean theorem again, we have:
+        \[
+        AC^2 = 11^2 + 19^2 = 121 + 361 = 482
+        \]
+    
+    228. **Calculate the squared distance between the centers of the first and third balloons:**
+        Using the Pythagorean theorem again, we have:
+        \[
+        AC^2 = 11^2 + 19^2 = 121 + 361 = 482
+        \]
+    
+    229. **Calculate the squared distance between the centers of the first and third balloons:**
+        Using the Pythagorean theorem again, we have:
+        \[
+        AC^2 = 11^2 + 19^2 = 121 + 361 = 482
+        \]
     
-    Since the balloons are externally tangent to each other, the distance between any two centers is the sum of their radii. Therefore, we ha
+    230. **Calculate the squared distance between the centers of the first and third balloons:**
+        Using the Pythagorean theorem again, we have:
+        \[
+        AC^2 = 11^2 + 19^2 = 121 + 361 = 482
+        \]
     
-    ... [truncated 822 chars] ...
+    231. **Calculate the squared distance between the centers of the first and third balloons:**
+        Using the Pythagorean theorem again, we have:
+        \[
+        AC^2 = 11^2 + 19^2 = 121 + 361 = 482
+        \]
     
-    XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 24 \cdot \frac{10912}{480}. \]
-    \[ XZ^2 = 1600 - 2 \cdot 2
+    232.
     ```