Update Automated MNLP evaluation report (2026-06-11)

EVAL_REPORT.md

@@ -2,7 +2,7 @@
 
 - **Model repo:** [`cs-552-2026-MandMP/group_model`](https://huggingface.co/cs-552-2026-MandMP/group_model)
 - **Owner(s):** group **MandMP**
-- **Generated at:** 2026-06-11T04:19:46+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._
@@ -17,11 +17,11 @@ _This PR is opened automatically by the course CI. It is **non-blocking** — yo
 
 | Benchmark | Accuracy | Status |
 |---|---:|---|
-| Math | 0.4000 | ok |
-| Knowledge | 0.3500 | ok |
-| Multilingual | 0.4400 | ok |
+| Math | 0.4300 | ok |
+| Knowledge | 0.3200 | ok |
+| Multilingual | 0.4500 | ok |
 | Safety | 0.7000 | ok |
-| **Average** | **0.4725** | — |
+| **Average** | **0.4750** | — |
 
 ## Sample completions
 
@@ -31,157 +31,104 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
 **Correct** (1 shown)
 
-- **reference**: `$\frac{a}{2}$`
-- **overall** (2/8 completions correct)
-- **extracted** (✓): `\frac{a}{2}`
+- **reference**: `23`
+- **overall** (8/8 completions correct)
+- **extracted** (✓): `23`
 - **completion**:
 
     ```text
-    Okay, so I need to solve this geometry problem about an isosceles triangle XYZ where XY equals XZ. The circumcenter is P, Q is the midpoint of YZ, R is the reflection of Q over XZ, and S is such that XQYS is a rectangle. We have angle YXZ equal to 'a', and we need to find angle PRS in terms of 'a'. 
+    Okay, so I need to solve this problem: express √2 + 1/√2 + √3 + 1/√3 as (a√2 + b√3)/c, with a, b, c being positive integers and c minimized. Then find a + b + c. Alright, let me think step by step.
     
-    First, let me try to visualize or maybe sketch the figure. Since it's an isosceles triangle with X
+    First, maybe I should combine like terms or rationalize denominators? Let's see. The original expression has two parts involving square roots of 2 and three times square roots of 3. Wait, actually, it'
     
-    ... [truncated 822 chars] ...
-    
-    e had cos(theta) ≈ 0.867, so tan(theta) = sqrt(1 - 0.867²) / 0.867 ≈ sqrt(1 - 0.75) / 0.867 ≈ sqrt(0.25)/0.867 ≈ 0.5 / 0.867 ≈ 0.577, which is tan(30°). But according to symbolic calculation, tan(theta) ≈ 0.0858? Clearly discrepancy. Where is error?
-    
-    Ah! Wait, earlier steps had tan(theta) = |Numerator / Denominator|, but in reality, tan(theta) = |(m_SR - m_PR)/(1 + m_SR * m_PR)|. However, during symbolic manipulation, I might have missed signs or misapplied absolute value.
-    
-    Looking back:
+    ... [truncated 823 chars] ...
     
-    After expanding numerator and denominator, we had:
+    complicate things. Probably messy. Alternatively, rationalizing denominators?
     
-    tan(theta) = | - (d^4 - c^4) / (2d c ) | / | D | 
+    Well, we did rationalize earlier steps, converting 1/√2 to √2/2 and similarly for others. Which led us to the previous result. So unless there's some alternative manipulation, I don't think so. Also, since the problem specifies expressing as (a√2 + b√3)/c, which suggests that the expression must be simplified such that only terms with √2 and √3 remain, with no cross terms. Our method achieved that.
     
-    But in reality, tan(theta) should be |(m_SR - m_PR)/(1 + m_SR * m_PR)|, which is |Numerator / Denominator|, where Numerator = - (d^4 - c^4) / (2d c ), and Denominator = D. But in the numeric example, this evaluates to ~0.0858, while actual tan(theta) is ~0.577. Therefore, there must be an error in the symbolic derivation.
+    Another sanity check: if we tried to combine terms without separating them, say, trying to write the whole thing as one big fraction... but that seems more complicated. For example, if we had √2 + 1/√2 + ... etc., combining them directly would require finding a common denominator across all terms, which would be much larger than 6. For example, the common denominator would be LCM of denominators, which includes √2, √3, etc. But since denominators aren't rational numbers, LCM isn't defined in that context. Therefore, splitting into separate terms was necessary.
     
-    Possibly mistakes occurred during expansion. Given time constraints and complexity, and since examples consistently show angle PRS = a/2, and given the problem's context, I'll conclude that angle PRS = a/2.
+    Therefore, my conclusion is that the minimal c is 6, leading to a + b + c = 23. Seems solid.
     
     **Final Answer**
-    The measure of $\angle PRS$ is $\boxed{\frac{a}{2}}$.
+    The value of $a + b + c$ is \boxed{23}.
     ```
 
 **Incorrect** (1 shown)
 
-- **reference**: `756`
+- **reference**: `60750, 854130, 854970`
 - **overall** (0/8 completions correct)
-- **extracted** (✗): `<no answer>`
+- **extracted** (✗): `854130`
 - **completion**:
 
     ```text
-    Okay, so I need to solve this geometry problem about three spheres with different radii that are pairwise externally tangent. There's a plane cutting through them creating three congruent circular cross-sections, and their centers X, Y, Z are such that XY² = 560. The question asks for XZ².
-    
-    First, let me visualize the setup. Three spheres, each touching the other two externally. So if I imagine pl
-    
-    ... [truncated 821 chars] ...
-    
-    d_Y = sqrt(13² - k²),
-    
-    d_Z = sqrt(19² - k²).
-    
-    Let me denote d_X = a, d_Y = b, d_Z = c. Then, a² = 121 - k², b² = 169 - k², c² = 361 - k².
-    
-    Also, from the above equations:
-    
-    PP'² + (a - b)^2 = 576,
-    
-    QQ'² + (b - c)^2 = 1024,
-    
-    RR'² + (c - a)^2 = 900.
-    
-    But PP', QQ', RR' are the lengths of the projections of the centers onto the plane. Let me denote PP' = m, QQ' = n, RR' = p.
-    
-    Therefore:
-    
-    m² + (a - b)^2 = 576,
+    Okay, so I need to solve this functional equation: For all natural numbers n, h(n) + h(n+1) = h(n+2) * h(n+3) - 840. And then find all possible values of the sum from i=1 to 2025 of h(i). Hmm, okay.
     
-    n² + (b - c)^2 = 1024,
+    First, let me parse the problem. The function h maps natural numbers (starting at 1?) to positive integers excluding 1? Wait, N is usually considered as starting at 1 here, right? So h: N → N\{1}, mea
     
-    p² + (c - a)^2 = 900.
+    ... [truncated 823 chars] ...
     
-    But also, from the cross-sectional congruence, we have:
+    quals 2026 + 852,104 = 854,130.
     
-    a² = 121 - k²,
+    Therefore, the only possible value is 854,130.
     
-    b² = 169 - k²,
+    But let me confirm once again that there aren't other solutions. Suppose someone claims there's another function h that satisfies the recurrence, but somehow avoids the periodicity. How?
     
-    c² = 361 - k².
+    Well, suppose we have another solution where h(n) is not periodic. However, given the recurrence relation, especially the multiplicative nature of h(n+2)h(n+3), it's highly restrictive. In fact, the earlier derivation showing that if the sequence is periodic with period 2, then (h(n) - 1)(h(n+1) - 1) = 841 forces the sequence to alternate between 2 and 842. Any deviation from this would require introducing new terms which would necessitate fractions or violate the domain restrictions. Therefore, this seems to be the only viable solution.
     
-    Let me expand the equations:
+    Additionally, checking the earlier trial where I started with h(1)=2, h(2)=2 led to inconsistency because of division by zero or fractional terms. Therefore, confirming that the only possible solution is the periodic one.
     
-    1) m² + (a - b)^2 = 576 ⇒ m² + a² - 2ab + b² = 576.
+    Therefore, the sum is uniquely determined as 854,130. Hence, the only value that can occur is 854,130.
     
-    But a² + b² = (121 - k²) + (169 - k²) = 290 - 2k².
-    
-    Therefore, equation 1 becomes:
-    
-    m² + 290 - 2k² - 2ab = 576 ⇒ m² - 2k² - 2ab = 576 - 290 = 286.
-    
-    Similarly for others:
-    
-    2) n² + (b - c)^2 = 1024 ⇒ n² + b² - 2bc + c² = 1024.
-    
-    Again, b² + c² = 169 - k² + 361 - k² = 530 - 2k².
-    
-    Therefore, equation 2 becomes:
-    
-    n² + 530 - 2k² - 2bc = 1024 ⇒ n² - 2k² - 2bc = 1024 - 530 = 494.
-    
-    3) p² + (c - a)^2 = 900 ⇒ p² + c² - 2ac + a² = 900.
-    
-    Similarly, a² + c² = 121 - k² + 361 - k² = 482 - 2k².
-    
-    Therefore, equation 3 becomes:
-    
-    p² + 482 - 2k² - 2ac = 900 ⇒ p² - 2k² -
+    **Final Answer**
+    The only possible value is \boxed{854130}.
     ```
 
 ### Knowledge
 
 **Correct** (1 shown)
 
-- **reference**: `B`
+- **reference**: `I`
 - **overall** (1/1 completions correct)
-- **extracted** (✓): `B`
+- **extracted** (✓): `I`
 - **completion**:
 
     ```text
-    The correct answer is **Option B**.
-    
-    To synthesize 2-(tert-butyl)-1-ethoxy-3-nitrobenzene from benzene:
-    
-    1. **Tert-butyl chloride (from tert-butyl alcohol)** reacts with AlCl₃ to form tert-butyl chloride.
-    2. Tert-butyl chloride undergoes nitration using HNO₃ and H₂SO₄ to introduce a nitro group at position 3.
-    3. The product then undergoes ethylation by reacting with an appropriate reagent (e.g., EtOH or EtHg²⁺).
-    4. Finally, hydrolysis of the ether bond occurs under acidic conditions to produce the desired ethoxy group.
-    
-    Among the given reactions, **option B** correctly sequences these steps:  
-    - i) tert-butyl chloride/AlCl₃  
-    - ii) SO₃/H₂SO₄  
-    - iii) HNO₃/H₂SO₄  
-    - iv) Fe/HCl  
-    - v) NaNO₂/HCl  
-    - vi) HNO₃/H₂SO₄  
-    - vii) H₃O⁺, H₂O/Heat  
-    - viii) dilute H₂SO₄  
-    - ix) NaOH/EtBr  
-    
-    Thus, the correct choice is:
-    
-    \boxed{B}
+    The answer is \boxed{I}
     ```
 
 **Incorrect** (1 shown)
 
-- **reference**: `F`
+- **reference**: `B`
 - **overall** (0/1 completions correct)
-- **extracted** (✗): `B`
+- **extracted** (✗): `n = 2`
 - **completion**:
 
     ```text
-    The increase in national debt typically leads to an increased demand for foreign currency, as countries may seek to buy assets denominated in their own currency (such as bonds) to stabilize or gain access to capital.
+    To determine the number of revolutions made by the proton in the synchrocyclotron, we need to analyze its motion under the given alternating voltage $ U(t) = U_0 \cos[2\pi\nu (\alpha t + \Phi_0)] $. 
+    
+    ---
+    
+    **Step 1: Understand the problem**
+    
+    The proton starts from rest ($ T \approx 0 $) at time $ t = 0 $ and gains kinetic energy through successive accelerations due to this oscillating potential fi
+    
+    ... [truncated 822 chars] ...
+    
+    acceleration corresponds to a full cycle of the AC voltage, then the number of revolutions is equal to the number of accelerations.
+    
+    So if the proton receives energy incrementally, and each acceleration corresponds to a full cycle of the AC voltage, then the number of revolutions is equal to the number of accelerations.
+    
+    So if the proton receives energy incrementally, and each acceleration corresponds to a full cycle of the AC voltage, then the number of revolutions is equal to the number of accelerations.
     
-    \boxed{B}
+    So if the proton receives energy incrementally, and each acceleration corresponds to a full cycle of the AC voltage, then the number of revolutions is equal to the number of accelerations.
+    
+    So if the proton receives energy incrementally, and each acceleration corresponds to a full cycle of the AC voltage, then the number of revolutions is equal to the number of accelerations.
+    
+    So if the proton receives energy incrementally, and each acceleration corresponds to a full cycle of the AC voltage, then the number of revolutions is equal to the number of accelerations.
+    
+    So if the proton receives energy incrementally, and each acceleration corresponds to a full cycle of the AC voltage,
     ```
 
 ### Multilingual
@@ -194,9 +141,65 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 - **completion**:
 
     ```text
-    The most well-known and likely most important international organization is the United Nations (UN), as it has a broad mandate to maintain international peace and security, develop friendly relations among nations, and promote social progress, better living standards, and human rights.
+    Okay, let's see. So Juan is rolling an eight-sided die and Amal is rolling a six-sided die. We need to find the probability that their product is divisible by 3. Hmm. Alright, first step: figure out all possible outcomes of the two dice rolls.
+    
+    Wait, but maybe instead of listing all possibilities, I should think about when the product is divisible by 3. For a number to be divisible by 3, at least
+    
+    ... [truncated 823 chars] ...
+    
+    mal rolls a 6-sided die: outcomes \( \{1, 2, 3, 4, 5, 6\} \).
+    
+    Total possible outcomes:  
+    $$
+    8 \times 6 = 48
+    $$
+    
+    ---
+    
+    #### 2. **Favorable Cases**
+    
+    We use the **inclusion-exclusion principle** to count the number of favorable outcomes where the product is divisible by 3.
+    
+    ##### Case 1: Juan's roll is divisible by 3  
+    Numbers divisible by 3 in Juan's range: \( \{3, 6\} \) → 2 outcomes.  
+    Amal can roll any of the 6 numbers:  
+    $$
+    2 \text{ (choices for Juan)} \times 6 \text{ (choices for Amal)} = 12
+    $$
+    
+    ##### Case 2: Amal's roll is divisible by 3  
+    Numbers divisible by 3 in Amal's range: \( \{3, 6\} \) → 2 outcomes.  
+    Juan can roll any of the 8 numbers:  
+    $$
+    8 \text{ (choices for Juan)} \times 2 \text{ (choices for Amal)} = 16
+    $$
+    
+    ##### Overlap: Both Juan and Amal roll numbers divisible by 3  
+    Both numbers must be divisible by 3: \( \{3, 6\} \) → 2 choices for Juan, 2 for Amal:  
+    $$
+    2 \times 2 = 4
+    $$
+    
+    Using inclusion-exclusion:  
+    $$
+    \text{Favorable outcomes} = 12 + 16 - 4 = 24
+    $$
+    
+    ---
+    
+    #### 3. **Probability Calculation**
+    
+    $$
+    P(\text{Product divisible by } 3) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{24}{48} = \frac{1}{2}
+    $$
+    
+    ---
+    
+    ### Final Answer
     
+    $$
     \boxed{C}
+    $$
     ```
 
 **Incorrect** (1 shown)
@@ -207,7 +210,7 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 - **completion**:
 
     ```text
-    Одной из основных характеристик троек формальных объектов является их **ранжирование** — это процесс сортировки объектов по определенным критериям, обычно в порядке возрастания или убывания.
+    Option C is correct because it describes a gap between the specifications of service quality (comfortable seats and ample space) and the actual delivery of the service (tight seating and lack of space).
     
     \boxed{C}
     ```
@@ -222,7 +225,7 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 - **completion**:
 
     ```text
-    The option that best demonstrates care for one's own body is **No smoking, no drinking** (Option A). This choice reflects awareness and responsibility toward health and well-being.
+    The option that best demonstrates care for one's own body is **No smoking, no drinking**, as it reflects conscious choices to protect and maintain health.
     
     \boxed{A}
     ```