Update Automated MNLP evaluation report (2026-05-29)

EVAL_REPORT.md

@@ -2,7 +2,7 @@
 
 - **Model repo:** [`cs-552-2026-vibe-trainers/math_model`](https://huggingface.co/cs-552-2026-vibe-trainers/math_model)
 - **Owner(s):** group **vibe-trainers**
-- **Generated at:** 2026-05-28T08:03:33+00:00 (UTC)
+- **Generated at:** 2026-05-29T06:54:15+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 | 0.3300 | ok |
+| Math | 0.3700 | ok |
 | Knowledge | — | not run |
 | Multilingual | — | not run |
 | Safety | — | not run |
@@ -24,84 +24,169 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
 **Correct** (1 shown)
 
-- **reference**: `\frac{448}{15625}`
-- **overall** (1/8 completions correct)
-- **extracted** (✓): `\frac{448}{15625}`
+- **reference**: `\frac{639}{40}`
+- **overall** (6/8 completions correct)
+- **extracted** (✓): `\frac{639}{40}`
 - **completion**:
 
     ```text
-    1. **Identify the probability of success and failure:**
-       Each island has a probability of \(\frac{1}{5}\) of containing treasure and a probability of \(\frac{4}{5}\) of not containing treasure.
-    
-    2. **Determine the number of successes:**
-       We need exactly 4 out of 7 islands to contain treasure. The number of ways to choose 4 islands out of 7 is given by the binomial coefficient \(\binom{7}{4}\).
-    
-    ... [truncated 125 chars] ...
-    
-    times 6 \times 5}{3 \times 2 \times 1} = 35
-       \]
-    
-    4. **Calculate the probability of one specific combination:**
-       The probability that any specific set of 4 islands contain treasure and the remaining 3 do not is \(\left(\frac{1}{5}\right)^4 \left(\frac{4}{5}\right)^3\).
-    
-    5. **Compute the probability of this specific combination occurring:**
-       \[
-       \left(\frac{1}{5}\right)^4 \left(\frac{4}{5}\right)^3 = \frac{1}{5^4} \cdot \frac{4^3}{5^3} = \frac{1}{5^7} \cdot 4^3 = \frac{64}{78125}
-       \]
-    
-    6. **Multiply by the number of combinations:**
-       Since there are 35 ways to choose which 4 islands contain treasure, we multiply the probability of one combination by 35:
-       \[
-       35 \cdot \frac{64}{78125} = \frac{35 \times 64}{78125} = \frac{2240}{78125}
-       \]
-    
-    7. **Simplify the fraction:**
-       To simplify \(\frac{2240}{78125}\), we find the greatest common divisor (GCD) of 2240 and 78125. Using the Euclidean algorithm, we find that the GCD is 5:
-       \[
-       \frac{2240}{78125} = \frac{2240 \div 5}{78125 \div 5} = \frac{448}{15625}
-       \]
-    
-    8. **Conclude with the final answer:**
-       Therefore, the probability that exactly 4 of the islands contain treasure is:
-       \[
-       \boxed{\frac{448}{15625}}
-       \]
+    We are given:
+    
+    - A **length of 3 inches** on the map represents **10 miles** in real life.
+    - The **actual distance** between two buildings is **53.25 miles**.
+    - We are to find the **distance on the map** (in inches) between the two buildings.
+    
+    ---
+    
+    ### Step 1: Find the scale factor
+    
+    The scale is:
+    
+    $$
+    \text{Scale} = \frac{3 \text{ inches}}{10 \text{ miles}} = \frac{3}{10} \text{ inches per mile}
+    $$
+    
+    So, **1 mile = 3/10 inches**.
+    
+    ---
+    
+    ### Step 2: Convert actual distance to map distance
+    
+    We are given:
+    
+    $$
+    \text{Actual distance} = 53.25 \text{ miles}
+    $$
+    
+    Use the scale to find the map distance:
+    
+    $$
+    \text{Map distance} = 53.25 \times \frac{3}{10}
+    $$
+    
+    First, multiply:
+    
+    $$
+    53.25 \times 3 = 159.75
+    $$
+    
+    Then divide by 10:
+    
+    $$
+    \frac{159.75}{10} = 15.975 \text{ inches}
+    $$
+    
+    ---
+    
+    ### Step 3: Express the result as a fraction
+    
+    $$
+    15.975 = \frac{15975}{1000}
+    $$
+    
+    Simplify the fraction:
+    
+    $$
+    \frac{15975}{1000} = \frac{639}{40} \quad \text{(divided numerator and denominator by 25)}
+    $$
+    
+    So, the distance between the buildings on the map is:
+    
+    $$
+    \boxed{\frac{639}{40}} \text{ inches}
+    $$
+    
+    ---
+    
+    ### ✅ Final Answer:
+    
+    $$
+    \boxed{\frac{639}{40}} \text{ inches}
+    $$
     ```
 
 **Incorrect** (1 shown)
 
-- **reference**: `756`
+- **reference**: `279`
 - **overall** (0/8 completions correct)
-- **extracted** (✗): `<no answer>`
+- **extracted** (✗): `12`
 - **completion**:
 
     ```text
-    Let the centers of the balloons be \(A\), \(B\), and \(C\) with radii \(r_A = 11\), \(r_B = 13\), and \(r_C = 19\). Let the centers of the circular cross-sections be \(X\), \(Y\), and \(Z\), respectively. The centers of the cross-section circles are the incenters of triangles \(ABC\), \(AXB\), and \(AXC\).
-    
-    The distances between the centers of the balloons are \(AB = 11 + 13 = 24\), \(BC = 13 + 19
-    
-    ... [truncated 822 chars] ...
-    
-    30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \frac{24^2 (32^2 - 30^2)}{24^2 + 32^2 - 30^2} \]
-    \[ XY^2 = \
+    We are given a function $ f(n) $ defined as follows:
+    
+    - For a positive integer $ n < 1000 $, take its base-ten digits (e.g., $ n = 72 $ has digits $ 7 $ and $ 2 $).
+    - Let $ b $ be the **smallest integer strictly larger than every digit** in $ n $.
+    - Interpret the digit string of $ n $ as a number in base $ b $, and call that value $ f(n) $.
+    
+    We are to count how many such numbers $ n < 1000 $ satis
+    
+    ... [truncated 467 chars] ...
+    
+    o the maximum digit is $ 7 $, so $ b = 8 $.
+    
+    Then, interpret the digits $ d_1 d_2 \dots d_k $ as a base-$ b $ number:
+    
+    $$
+    f(n) = d_1 \cdot b^{k-1} + d_2 \cdot b^{k-2} + \dots + d_k \cdot b^0
+    $$
+    
+    We are to find all $ n < 1000 $ such that:
+    
+    $$
+    f(n) = n
+    $$
+    
+    ---
+    
+    ### Step 2: Consider all $ n < 1000 $
+    
+    We are to count all $ n < 1000 $ such that $ f(n) = n $.
+    
+    Let’s consider all numbers $ n < 1000 $, i.e., all numbers from 1 to 999 (inclusive).
+    
+    We'll use a **brute-force approach** to compute $ f(n) $ for each $ n $, and count how many satisfy $ f(n) = n $.
+    
+    ---
+    
+    ### Step 3: Implement the function $ f(n) $ for $ n < 1000 $
+    
+    We can define a helper function:
+    
+    ```python
+    def f(n):
+        digits = list(map(int, str(n)))
+        max_digit = max(digits)
+        b = max_digit + 1
+        value = 0
+        for d in digits:
+            value = value * b + d
+        return value
+    ```
+    
+    Now, we'll iterate over all $ n < 1000 $ and check if $ f(n) = n $.
+    
+    ---
+    
+    ### Step 4: Count the valid numbers
+    
+    Let’s compute this:
+    
+    ```python
+    count = 0
+    for n in range(1, 1000):
+        if f(n) == n:
+            count += 1
+    print(count)
+    ```
+    
+    ---
+    
+    ### ✅ Final Answer:
+    
+    $$
+    \boxed{12}
+    $$
+    
+    There are **12** positive integers $ n < 1000 $ such that $ f(n) = n $.
     ```