Automated MNLP evaluation report (2026-05-26)

EVAL_REPORT.md

@@ -2,7 +2,7 @@
 
 - **Model repo:** [`cs-552-2026-MandMP/math_model`](https://huggingface.co/cs-552-2026-MandMP/math_model)
 - **Owner(s):** group **MandMP**
-- **Generated at:** 2026-05-25T02:20:01+00:00 (UTC)
+- **Generated at:** 2026-05-26T12:29:10+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._
@@ -11,7 +11,7 @@ _This PR is opened automatically by the course CI. It is **non-blocking** — yo
 
 | Benchmark | Accuracy | Status |
 |---|---:|---|
-| Math | 0.1600 | ok |
+| Math | 0.2200 | ok |
 | Knowledge | — | not run |
 | Multilingual | — | not run |
 | Safety | — | not run |
@@ -24,88 +24,60 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
 **Correct** (1 shown)
 
-- **reference**: `4`
+- **reference**: `1600`
 - **overall** (8/8 completions correct)
-- **extracted** (✓): `4`
+- **extracted** (✓): `1600`
 - **completion**:
 
     ```text
-    Okay, so I need to solve the equation 10^x minus 10 equals 9990. Let me write that down first to make sure I have it right: 10^x - 10 = 9990. Alright, so I need to find the value of x that makes this equation true. Let me think about how to approach this.
+    Okay, so I need to figure out what this expression equals: 441 plus 2 times 21 times 19 plus 361. Let me write that down again to make sure I have it right:
     
-    First, I remember that equations involving exponents can sometimes be solved by isolating the exponential term and then taking logarithms. Let
+    $441 + 2 \times 21 \times 19 + 361 = x$
     
-    ... [truncated 822 chars] ...
-    
-    and then try to solve for x, but that would be wrong because the equation is 10^x - 10 = 9990. So if you subtract 10 from both sides, you get 10^x = 9990 - 10 = 9980, which is not 10000. So that would be a mistake. 
-    
-    But I think the correct approach is adding 10 to both sides. 
+    Hmm, let me break this down step by step. First, maybe I should calculate each part separately and then add them up. Let me start with the multiplication part because there's a 2 times 21 times 19 insi
     
-    Another possible mistake could be if someone thought that 10^x - 10 = 9990 implies that 10^x = 9990, but that would be incorrect. Because if you subtract 10 from both sides, you get 10^x = 9990 - 10 = 9980. But in reality, the equation is 10^x - 10 = 9990, so adding 10 gives 10^x = 9990 + 10 = 10000. 
-    
-    So, that's another way to see it. 
+    ... [truncated 822 chars] ...
     
-    Therefore, the key step is to recognize that 10^x - 10 = 9990 implies 10^x = 10000, which is a power of 10, so x is 4. 
+    o recognize this expression without calculating each term separately? Let me think. The original expression is 441 + 2×21×19 + 361. Wait, 441 and 361 are both squares. 21 squared is 441, right? 21×21 is 441. And 19 squared is 361. Oh! Wait, that's a key insight. So the expression is 21² + 2×21×19 + 19². Which is a perfect square. Specifically, it's (a + b)² where a = 21 and b = 19. Let me check that.
     
-    Alternatively, if someone didn't recognize that 10^4 is 10000, they might have to use logarithms, which is what I did. 
+    (a + b)² = a² + 2ab + b². Exactly! So that's exactly the expression given. Therefore, x = (21 + 19)². Let me compute that. 21 + 19 is 40. Then 40 squared is 1600. There we go! So that's a much quicker way. Instead of computing each term separately, recognizing the pattern as a perfect square. That makes sense. So x is 1600.
     
-    So, in conclusion, the solution is x = 4. 
+    But just to be thorough, let me confirm once more. If I expand (21 + 19)^2, it's 21^2 + 2*21*19 + 19^2. Which is exactly the original expression. Therefore, substituting 21 + 19 = 40, so 40 squared is 1600. Yep, that's correct.
     
-    I think that's thorough. I considered different methods, checked my answer by plugging it back in, considered possible mistakes, and confirmed that there's only one solution. So I feel confident that x = 4 is the correct answer.
+    Therefore, the answer is 1600. I think that's solid. I don't see any mistakes in my reasoning. Both methods gave me the same result, so I feel confident about this.
     
     **Final Answer**
-    The solution is \boxed{4}.
+    The value of $x$ is \boxed{1600}.
     </think>
     
-    \boxed{4}
+    \boxed{1600}
     ```
 
 **Incorrect** (1 shown)
 
-- **reference**: `\frac{270}7\text{ degrees}`
+- **reference**: `$\frac{1}{3}$`
 - **overall** (0/8 completions correct)
 - **extracted** (✗): `<no answer>`
 - **completion**:
 
     ```text
-    Okay, so I need to find the measure of angle BAC in this figure where a square and a regular heptagon share the side AD. Let me try to visualize the Asymptote code they provided. 
-    
-    First, the Asymptote code draws a regular heptagon and a square sharing the side AD. The points A, B, C, D are labeled, with A and D being vertices of the square and heptagon. The square is drawn from A to C to D to F a
-    
-    ... [truncated 823 chars] ...
-    
-    point A is at 90° + 3*(360/7°) = 90° + 1080/7° = (630 + 1080)/7° = 1710/7° ≈ 244.2857°, as before. 
+    Okay, so I need to solve this geometry problem about a tetrahedron and some points related to it. Let me try to parse the problem step by step.
     
-    Point F is at 90° + 4*(360/7°) = 90° + 1440/7° = (630 + 1440)/7° = 2070/7° ≈ 295.7143°, as before. 
+    First, we have a tetrahedron $ T_1T_2T_3T_4 $ in 3D space. There's a point $ C $ such that its distance to all four vertices is equal. So, $ CT_1 = CT_2 = CT_3 = CT_4 $. That means $ C $ is equidistant from all four vertices of the tetrahedron. 
     
-    So, the angle between point A and point F is 2070/7° - 1710/7° = 360/7°, which is the central angle between two adjacent vertices. 
+    Then, th
     
-    Now, let me compute coordinates of A and F. 
-    
-    Let me denote θ = 360/7°, so that point A is at angle 90° + 3θ, and point F is at angle 90° + 4θ. 
-    
-    So, coordinates of point A: (cos(90° + 3θ), sin(90° + 3θ)) 
-    
-    Similarly, coordinates of point F: (cos(90° + 4θ), sin(90° + 4θ)) 
-    
-    But cos(90° + x) = -sin(x), and sin(90° + x) = cos(x). 
-    
-    Therefore, coordinates of A: (-sin(3θ), cos(3θ)) 
-    
-    Coordinates of F: (-sin(4θ), cos(4θ)) 
-    
-    Similarly, coordinates of point C is A + dir(90)*(F - A). 
-    
-    dir(90) is (0,1), so adding that vector to point A. 
+    ... [truncated 823 chars] ...
     
-    So, point C is A + (F - A) * i, where i is the unit vector in the y-direction. 
+    ,-1,1), C(-1,1,-1), D(1,-1,-1). Let me find the equation of the plane through these three points.
     
-    So, coordinates of C: 
+    First, compute two vectors in the plane: vector BC = (0,2,-2) as before, and vector BD = (2,0,-2). Then, the normal vector is (-4, -4, -4) as before. Therefore, the equation of the plane is -4(x +1) -4(y +1) -4(z -1) = 0? Wait, no. Wait, the plane passes through point B(-1,-1,1). So the equation is -4(x - (-1)) -4(y - (-1)) -4(z - 1) = 0? Wait, no. Wait, the normal vector is (-4, -4, -4), so the plane equation is -4(x - x0) -4(y - y0) -4(z - z0) = 0. Using point B(-1,-1,1):
     
-    x-coordinate: A_x + (F_y - A_y) 
+    -4(x +1) -4(y +1) -4(z -1) = 0 => -4x -4 -4y -4 -4z +4 = 0 => -4x -4y -4z -4 = 0 => divide by -4: x + y + z + 1 = 0. So the plane equation is x + y + z = -1.
     
-    y-coordinate: A_y + (F_y - A_y) 
+    Now, the line $ T_1K $ is the line from A(1,1,1) to K(0,0,0). Parametric equations: x = 1 - t, y = 1 - t, z = 1 - t, where t ranges from 0 to 1. We need to find where this line intersects the plane x + y + z = -1. Substitute x = 1 - t, y = 1 - t, z = 1 - t into the plane equation:
     
-    Wait, because adding (F - A) vector to A. 
+    (1 - t) + (1 - t) + (1 - t) = -1 => 3 - 3t = -1 => 3t = 4 => t = 4/3.
     
-    Wait, the vector from A to F is (F_x - A_x, F_y - A_y). So, adding that vector to A gives (A_x + (F_x - A_x), A
+    Therefore, the intersection point X is at t = 4/3: x = 1 - 4/3 = -1/3, y = -1/3, z = -1/3. So X is (-1/3, -1
     ```