Automated MNLP evaluation report (2026-06-11)

EVAL_REPORT.md

@@ -2,7 +2,7 @@
 
 - **Model repo:** [`cs-552-2026-emainelpe/math_model`](https://huggingface.co/cs-552-2026-emainelpe/math_model)
 - **Owner(s):** group **emainelpe**
-- **Generated at:** 2026-06-06T17:20:53+00:00 (UTC)
+- **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._
@@ -17,7 +17,7 @@ _This PR is opened automatically by the course CI. It is **non-blocking** — yo
 
 | Benchmark | Accuracy | Status |
 |---|---:|---|
-| Math | 0.3400 | ok |
+| Math | 0.3300 | ok |
 | Knowledge | — | not run |
 | Multilingual | — | not run |
 | Safety | — | not run |
@@ -30,94 +30,62 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
 **Correct** (1 shown)
 
-- **reference**: `90`
-- **overall** (1/8 completions correct)
-- **extracted** (✓): `90`
+- **reference**: `\frac{7}{4}`
+- **overall** (5/8 completions correct)
+- **extracted** (✓): `\frac{7}{4}`
 - **completion**:
 
     ```text
     <think>
-    ## Step 1:  To solve this problem, we first need to understand the given information and the relationships between the various points and lines involved.
-    ## Step 2:  We are given a triangle $XYZ$ with $\angle X = 120^\circ$. The incenter is denoted as $J$, and $N$ is the midpoint of $YZ$.
-    ## Step 3:  We draw a line through $N$ parallel to $XJ$, intersecting the circle with diameter $YZ$ at $U$ and $V$, with $U$ chosen so that $X$ and $U$ are on the same side of line $YZ$.
-    ## Step 4:  Through $U$, we draw the line perpendicular to $VJ$, intersecting $XY$ at $R$ and $XZ$ at $S$.
-    ## Step 5:  We need to determine the measure of $\angle RJS$ in degrees.
-    ## Step 6:  To approach this problem, we can start by analyzing the properties of the incenter and the relationships between the various points and lines involved.
-    ## Step 7:  We can also use the properties of parallel lines and perpendicular lines to establish relationships between the various angles and segments involved.
-    ## Step 8:  By carefully analyzing the given information and applying the properties of triangles and circles, we can determine the measure of $\angle RJS$.
-    ## Step 9:  We can use the fact that the incenter is the intersection of the angle bisectors of the triangle, and the properties of parallel and perpendicular lines to establish the necessary relationships.
-    ## Step 10:  By following these steps, we can determine the measure of $\angle RJS$ and provide the final answer.
+    The direction vector of the line is $\begin{pmatrix} -7 \\ b \end{pmatrix}$. We can find the slope of the line using the direction vector.
     
-    The final answer is: $\boxed{90}
+    The slope of the line is given by the formula:
+    \[ \text{slope} = \frac{\text{change in } y}{\text{change in } x} \]
+    
+    Using the direction vector, we have:
+    \[ \text{slope} = \frac{b}{-7} \]
+    
+    The slope of the line is also equal to the slope of the red line. We can find the slope of the red line by using the coordinates of the points on the line.
+    
+    The points on the line are $(-5, 4)$ and $(-1, 3)$. The slope of the line is:
+    \[ \text{slope} = \frac{3 - 4}{-1 - (-5)} = \frac{-1}{4} \]
+    
+    Since the slope of the line is the same, we can set up the equation:
+    \[ \frac{b}{-7} = \frac{-1}{4} \]
+    
+    Solving for $b$, we get:
+    \[ b = \frac{-7}{4} \cdot -1 = \boxed{\frac{7}{4}} \]
     </think>
     
-    \boxed{90}
+    \boxed{\frac{7}{4}}
     ```
 
 **Incorrect** (1 shown)
 
 - **reference**: `756`
 - **overall** (0/8 completions correct)
-- **extracted** (✗): `970`
+- **extracted** (✗): `1584`
 - **completion**:
 
     ```text
     <think>
-    Let the centers of the balloons be $A$, $B$, and $C$, with radii $r_A = 11$, $r_B = 13$, and $r_C = 19$, respectively.
-    
-    Since the centers of the balloons all lie on one side of the plane, we can assume that the plane is parallel to the $xy$-plane.
-    
-    The distance between the centers of the balloons is equal to the sum of their radii:
-    \[ AB = r_A + r_B = 11 + 13 = 24 \]
-    \[ BC = r_B + r_C = 13
-    
-    ... [truncated 453 chars] ...
-    
-    )^2 : 2 - XY^2 - YZ^2 - XZ^2 \]
-    
-    Substituting the given values, we get:
-    \[ XZ^2 = (24)^2 + (32)^2 + (30)^2 : 2 - 560 - YZ^2 - XZ^2 \]
-    
-    Simplifying, we get:
-    \[ XZ^2 = 576 + 1024 + 900 : 2 - 560 - YZ^2 - XZ^2 \]
-    
-    \[ XZ^2 = 2500 - 560 - YZ^2 - XZ^2 \]
-    
-    \[ 2XZ^2 = 1940 - YZ^2 \]
-    
-    \[ XZ^2 = 970 - YZ^2 : 2 \]
-    
-    We can also use the fact that $XY^2 + YZ^2 + XZ^2 = (XY + YZ)^2 + (YZ + XZ)^2 + (XZ + XY)^2 : 2$ to find $YZ^2$:
-    \[ YZ^2 = (XY + YZ)^2 + (YZ + XZ)^2 + (XZ + XY)^2 : 2 - XY^2 - XZ^2 - YZ^2 \]
-    
-    Substituting the given values, we get:
-    \[ YZ^2 = (24)^2 + (32)^2 + (30)^2 : 2 - 560 - XZ^2 - YZ^2 \]
-    
-    Simplifying, we get:
-    \[ YZ^2 = 576 + 1024 + 900 : 2 - 560 - XZ^2 - YZ^2 \]
-    
-    \[ YZ^2 = 2500 - 560 - XZ^2 - YZ^2 \]
-    
-    \[ 2YZ^2 = 1940 - XZ^2 \]
-    
-    \[ YZ^2 = 970 - XZ^2 : 2 \]
-    
-    Substituting this expression for $YZ^2$ into the expression for $XZ^2$, we get:
-    \[ XZ^2 = 970 - (970 - XZ^2 : 2) : 2 \]
-    
-    \[ XZ^2 = 970 - 485 + XZ^2 : 4 \]
-    
-    \[ 4XZ^2 = 485 + 4XZ^2 \]
+    Let's denote the radii of the balloons as $r_1 = 11$, $r_2 = 13$, and $r_3 = 19$. The centers of the balloons are $X$, $Y$, and $Z$, and the distances between the centers are $XY$, $YZ$, and $XZ$.
     
-    \[ 4XZ^2 - 4XZ^2 = 485 \]
+    Since the balloons are externally tangent, the distance between the centers of any two balloons is equal to the sum of their radii. Therefore, we have:
+    \[ XY = r_1 + r_2 = 11 + 13 = 24 \]
+    \[ YZ = r_2 + r_3 = 13 + 19 = 32 \]
+    \[ XZ = r_1 + r_3 = 11 + 19 = 30 \]
     
-    \[ 0 = 485 \]
+    However, we are given that $XY^2 = 560$. We can use this information to find $XZ^2$.
     
-    This is a contradiction, so there must be an error in the problem statement.
+    Notice that $XY^2 + YZ^2 = (XZ + YZ)^2 - 2XZYZ$. Substituting the known values, we get:
+    \[ 560 + 32^2 = (XZ + 32)^2 - 2XZ(32) \]
+    \[ 560 + 1024 = XZ^2 + 64XZ + 1024 - 64XZ \]
+    \[ XZ^2 = 1584 \]
     
-    However, if we ignore the contradiction and continue with the solution, we get:
-    \[ XZ^2 = \boxed{970} \]
+    So, the answer is:
+    \[ \boxed{1584} \]
     </think>
     
-    \boxed{970}
+    \boxed{1584}
     ```