Automated MNLP evaluation report (2026-05-16)

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:** 2026-05-13T23:30:17+00:00 (UTC)
+- **Generated at:** 2026-05-16T04:57:46+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 | 0.3500 | ok |
+| Math | 0.3400 | ok |
 | Knowledge | — | not run |
 | Multilingual | — | not run |
 | Safety | — | not run |
@@ -31,22 +31,19 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
     ```text
     <think>
-    The equation is given as:
-    \[ \frac{1}{x} + 5x^2 = 6x - 24 \]
+    To find the sum of the solutions \(a + b + c\), we first need to rewrite the given equation in the standard quadratic form \(ax^2 + bx + c = 0\). We do this by moving all terms to one side of the equation:
     
-    First, multiply both sides by \(x\) to eliminate the fraction:
-    \[ 1 + 5x^3 = 6x^2 - 24x \]
+    \[ \frac{1}{x} + 5x^2 = 6x - 24 \Rightarrow 5x^2 - 6x + 24 + \frac{1}{x} = 0 \]
+    
+    To eliminate the fraction, multiply every term by \(x\):
     
-    Rearrange the equation to get a standard cubic equation:
     \[ 5x^3 - 6x^2 + 24x + 1 = 0 \]
     
-    This is a cubic equation, and we are looking for the sum of its roots, which is given by Vieta's formulas as:
-    \[ a + b + c = -\frac{\text{coefficient of } x^2}{\text{coefficient of } x^3} \]
+    Now, we have a cubic equation. To find the sum of its roots, we can use Vieta's formulas, which state that for a polynomial of the form \(ax^3 + bx^2 + cx + d = 0\), the sum of the roots is given by \(-\frac{b}{a}\).
     
-    In this case, the coefficient of \(x^2\) is \(-6\) and the coefficient of \(x^3\) is \(5\).
+    In our case, \(a = 5\) and \(b = -6\), so the sum of the roots \(a + b + c\) is:
     
-    So, the sum of the roots is:
-    \[ a + b + c = -\frac{-6}{5} = \boxed{\frac{6}{5}} \]
+    \[ a + b + c = -\frac{b}{a} = -\frac{-6}{5} = \boxed{\frac{6}{5}} \]
     </think>
     
     \boxed{\frac{6}{5}}
@@ -56,7 +53,7 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
 - **reference**: `$(n-2)2^n +1$`
 - **overall** (0/8 completions correct)
-- **extracted** (✗): `2^n - 2`
+- **extracted** (✗): `2^{n-1} - 1`
 - **completion**:
 
     ```text
@@ -65,29 +62,26 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
     We are given a set C_n, which consists of numbers of the form 2^n - 2^i, where i is an integer and 0 ≤ i < n. We need to find the greatest positive integer that cannot be represented as a sum of elements from C_n, allowing repeated use of any element.
     
     ## Step 2: Analyze the set C_n
-    The set C_n contains numbers that are one less than a power of 2, starting
-    
-    ... [truncated 823 chars] ...
+    Let's analyze the set C_n. We can see that the elements of C_n are of the
     
-    ents of C_n is 2^n - 2. This is because 2^n - 2 is one less than a power of 2, and it cannot be represented as a sum of elements of C_n.
+    ... [truncated 207 chars] ...
     
-    ## Step 6: Determine the greatest positive integer that cannot be represented as a sum of elements of C_n
-    The greatest positive integer that cannot be represented as a sum of elements of C_n is 2^n - 2.
+    cause when i = n-1, the expression 2^n - 2^i becomes 2^n - 2^{n-1} = 2^{n-1}(2 - 1) = 2^{n-1}.
     
-    ## Step 7: Find the largest positive integer that cannot be represented as a sum of elements of C_n
-    The largest positive integer that cannot be represented as a sum of elements of C_n is 2^n - 2.
+    ## Step 4: Consider the binary representation of the largest element
+    The largest element in C_n, which is 2^{n-1}, can be represented in binary as a 1 followed by n-1 zeros. This means that when we add up elements of C_n, we can only get numbers that have a binary representation with at most n-1 zeros.
     
-    ## Step 8: Find the greatest positive integer that cannot be represented as a sum of elements of C_n
-    The greatest positive integer that cannot be represented as a sum of elements of C_n is 2^n - 2.
+    ## Step 5: Determine the largest positive integer that cannot be represented as a sum of elements of C_n
+    Based on the analysis above, we can see that the largest positive integer that cannot be represented as a sum of elements of C_n is 2^n - 1 - 2^{n-1} = 2^{n-1} - 1. This is because we can always subtract 2^{n-1} from 2^n - 1 to get a number that cannot be represented as a sum of elements of C_n.
     
-    ## Step 9: Find the greatest positive integer that cannot be represented as a sum of elements of C_n
-    The greatest positive integer that cannot be represented as a sum of elements of C_n is 2^n - 2.
+    ## Step 6: Find the greatest positive integer that is not representable as a sum of elements of C_n
+    The greatest positive integer that is not representable as a sum of elements of C_n is 2^n - 1 - 2^{n-1} = 2^{n-1} - 1.
     
-    ## Step 10: Find the greatest positive integer that cannot be represented as a sum of elements of C_n
-    The greatest positive integer that cannot be represented as a sum of elements of C_n is 2^n - 2.
+    ## Step 7: Simplify the expression
+    We can simplify the expression 2^{n-1} - 1 to get the final answer.
     
-    The final answer is: $\boxed{2^n - 2}
+    The final answer is: $\boxed{2^{n-1} - 1}
     </think>
     
-    \boxed{2^n - 2}
+    \boxed{2^{n-1} - 1}
     ```