Run Details #1078

Model

Gemma 4 12B (LMStudio)

Score

12

Correct (≥100)

5/40

Incorrect (<100)

35

Median Time

2798.0ms

1 slow incorrect outlier ignored for latency.
Tokens Used

4223

Cost

$0.0069

Benchmark: 0025_algebra
Run Date: 2026-06-03 18:52:58
Questions (40)

Question: If 4x - 20 = -36, what is x?
Expected 
-4.0
Provided 
{
  "result": 1.0
}

Question: If x² - 6x + 9 = 0, what is x?
Expected 
3.0
Provided 
{
  "result": 1
}

Question: If x² - 4x + 4 = 0, what is x?
Expected 
2.0
Provided 
{
  "result": 9241535300000000
}

Incorrect response with unusually high latency; excluded from aggregate latency summaries.
Question: If x² - 7x - 8 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
-1, 8
Provided 
{
  "values": "To solve the quadratic equation $x^2 - 7x - 8 = 0$, we can use the factoring method or the quadratic formula. Both methods lead to the same result. 1) **Factoring Method**: We look for two numbers that multiply to $-8$ and add up to $-7$. Those numbers are $-8$ and $1$. Therefore, we can write: $(x - 8)(x + 1) = 0$. Setting each factor to zero gives $x = 8$ and $x = -1$. 2) **Quadratic Formula**: Using $a=1$, $b=-7$, and $c=-8$: $x = \frac{-(-7) \beta \neq 0}{2(1)} \beta \neq 0$; $x = \frac{7 \beta \neq 0}{\beta \neq 0}$ (Calculating the discriminant $\text{D} = b^2 - 4ac$ gives $(-7)^2 - 4(1)(-8) = 49 + 32 = 81$. Then $x = \frac{-(-7) \beta \neq 0}{2(1)}$. $x = \frac{7 \beta \neq 0}{\beta \neq 0}$. The solutions are $x = \frac{7+9}{2} = 8$ and $x = \frac{7-9}{2} = -1$. Listing the answers in ascending order, we have $-1$ and $8$. 3) **Final Result**: Since the question asks for both answers separated by a comma with the smallest first, they are $-1$ and $8$. 4) **Format Check**: Ensure the result is provided in the specified JSON format.```json{"
}

Question: If x² - 3x - 40 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
-5, 8
Provided 
{
  "values": "8, -5"
}

Question: If x² + 12x + 36 = 0, what is x?
Expected 
-6.0
Provided 
{
  "result": 1000000000000000.0
}

Question: If x² - 10x + 25 = 0, what is x?
Expected 
5.0
Provided 
{
  "result": 2.5
}

Question: If 5x - 13 = -3, what is x?
Expected 
2.0
Provided 
{
  "result": 0.4285714292515625
}

Question: If 4x + 2 = 18, what is x?
Expected 
4.0
Provided 
{
  "result": 10
}

Question: If x² + x - 12 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
-4, 3
Provided 
{
  "values": "[-3, 3]"
}

Question: If x² - 8x + 12 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
2, 6
Provided 
{
  "values": "2, 6"
}

Question: If x² + 10x + 24 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
-6, -4
Provided 
{
  "error": "Failed to parse JSON: {\"values\": \""
}

Question: If x² + 4x + 4 = 0, what is x?
Expected 
-2.0
Provided 
{
  "result": 121
}

Question: If x² + 4x + 4 = 0, what is x?
Expected 
-2.0
Provided 
{
  "result": 1
}

Question: If x² + 2x + 1 = 0, what is x?
Expected 
-1.0
Provided 
{
  "result": 1
}

Question: If x² - 12x + 36 = 0, what is x?
Expected 
6.0
Provided 
{
  "result": 2024
}

Question: If x² + 14x + 49 = 0, what is x?
Expected 
-7.0
Provided 
{
  "result": 11
}

Question: If x² - 4x - 21 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
-3, 7
Provided 
{
  "values": "3, -3"
}

Question: If x² + 9x + 8 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
-8, -1
Provided 
{
  "values": "x = -1, -4"
}

Question: If x² - 14x + 49 = 0, what is x?
Expected 
7.0
Provided 
{
  "result": 7
}

Question: If 3x + 8 = 20, what is x?
Expected 
4.0
Provided 
{
  "result": 10
}

Question: If x² + 16x + 64 = 0, what is x?
Expected 
-8.0
Provided 
{
  "result": 8
}

Question: If 4x - 7 = 9, what is x?
Expected 
4.0
Provided 
{
  "result": 16.5
}

Question: If x² + 16x + 64 = 0, what is x?
Expected 
-8.0
Provided 
{
  "result": 16
}

Question: If 3x - 10 = 8, what is x?
Expected 
6.0
Provided 
{
  "result": 14
}

Question: If 5x + 17 = 42, what is x?
Expected 
5.0
Provided 
{
  "result": 1000000000000000.0
}

Question: If x² - 12x + 36 = 0, what is x?
Expected 
6.0
Provided 
{
  "result": 0.0
}

Question: If x² + 2x + 1 = 0, what is x?
Expected 
-1.0
Provided 
{
  "result": 1
}

Question: If x² - 12x + 36 = 0, what is x?
Expected 
6.0
Provided 
{
  "result": 0.5
}

Question: If 2x + 13 = 7, what is x?
Expected 
-3.0
Provided 
{
  "result": 1
}

Question: If x² + 14x + 49 = 0, what is x?
Expected 
-7.0
Provided 
{
  "result": 14
}

Question: If 5x + 19 = -6, what is x?
Expected 
-5.0
Provided 
{
  "result": 1000000000000000.0
}

Question: If x² + 16x + 64 = 0, what is x?
Expected 
-8.0
Provided 
{
  "result": 8
}

Question: If x² - 12x + 36 = 0, what is x?
Expected 
6.0
Provided 
{
  "result": 0.0
}

Question: If x² - 13x + 42 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
6, 7
Provided 
{
  "values": "6, 7"
}

Question: If x² - 7x - 8 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
-1, 8
Provided 
{
  "values": "[-1, 1]* }#thoughtful```json={"
}

Question: If x² - 14x + 48 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
6, 8
Provided 
{
  "values": "4, 6"
}

Question: If x² + 8x + 12 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
-6, -2
Provided 
{
  "values": "[-2, -4]"
}

Question: If x² - 11x + 30 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
5, 6
Provided 
{
  "values": "3, 10"
}

Question: If x² + 3x - 18 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Expected 
-6, 3
Provided 
{
  "values": "3, -6"
}