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values | status stringclasses 2
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values | metrics dict | trace_tree dict | problem_index int64 0 99 | generation_index int64 0 9 | level_num int64 1 1 | type stringclasses 7
values | ground_truth stringclasses 73
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18}
Insight: This is a simple algebraic equation; the key is to simplify the left-hand side first and then solve for \( x \) by cross-multiplication or reciprocal reasoning. | null | {
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"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 0 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
1 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18} | null | {
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"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 1 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
2 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18} | null | {
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"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 2 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
3 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18}
Insight: When solving equations of the form \(a - b = c/x\), first simplify the left-hand side, then isolate \(x\) by cross-multiplication or algebraic manipulation. | null | {
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"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 3 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
4 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{\frac{18}{5}}
Insight: When solving rational equations, simplifying one side first can streamline the process by reducing the number of fractions to manipulate. | null | {
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"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 4 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
5 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18}
Insight: Computing the left-hand side first simplifies the problem to solving a basic proportion, a common technique for such equations. | null | {
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"fragment": "\n\nI need to solve the equation \\(\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}\\) for \\(x\\). The left side is a difference of two fr... | 0 | 5 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
6 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18} | null | {
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"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 6 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
7 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18}
Insight: When solving rational equations, simplifying both sides first often makes the algebra straightforward. | null | {
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"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 7 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
8 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18} | null | {
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"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 8 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
9 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18} | null | {
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"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 9 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
10 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: Using the difference of squares identity simplifies mental multiplication when numbers are symmetric around a square. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 1 | 0 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
11 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: For mental multiplication, using difference of squares when numbers are symmetric around a round number can streamline the calculation. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I notice that... | 1 | 1 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
12 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: For numbers that sum to 100 or are symmetric around a round number, using the difference of squares is an efficient mental math strategy. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 1 | 2 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
13 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: When multiplying two numbers that are equidistant from a common center, the difference of squares trick provides a quick mental calculation. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 1 | 3 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
14 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: Recognizing numbers as a sum and difference around a common base allows efficient mental multiplication via the difference of squares. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I can compute... | 1 | 4 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
15 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: Using (a+b)(a-b) = a² - b² simplifies mental multiplication when numbers are symmetric around a round number. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I can compute... | 1 | 5 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
16 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2436}
Insight: Recognizing numbers as symmetric around a central value allows quick mental multiplication using the difference of squares identity. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I notice that... | 1 | 6 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
17 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: For numbers symmetric around a round number, using the difference of squares pattern simplifies mental multiplication. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I see that 54... | 1 | 7 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
18 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484} | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I notice that... | 1 | 8 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
19 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: Using the difference of squares pattern (a+b)(a-b) = a² - b² is a useful mental math trick for numbers symmetric around a round base. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I notice that... | 1 | 9 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
20 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150}
Insight: This demonstrates a direct proportionality where the number of paperclips is proportional to the volume, allowing simple scaling for similar containers. | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nThe problem involves direct proportionality between volume and the number of pa... | 2 | 0 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
21 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150}
Insight: For direct proportionality, scale factor = ratio of volumes. | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 1 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
22 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150} | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 2 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
23 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150} | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 3 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
24 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150}
Insight: When capacity is directly proportional to volume, scaling the volume by a factor scales the capacity by the same factor. | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 4 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
25 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150} | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 5 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
26 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150}
Insight: For direct proportionality, scaling the input by a factor scales the output by the same factor. This can be verified using either a constant ratio or a multiplicative scaling factor. | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 6 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
27 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150} | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 7 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
28 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150} | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 8 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
29 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | FAILED | Tree generation failed. Reason: Maximum recursion depth (5) reached. | {
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"total_llm_calls": 5,
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\nThis is a problem of direct proportionality: the number of paperclips a box can h... | 2 | 9 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | |
30 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20} | null | {
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} | {
"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 0 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
31 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20}
Insight: For constant speed, time = distance / speed; ensure consistent units (convert hours to minutes as needed). | null | {
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"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 1 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
32 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20}
Insight: When speed is constant, time is proportional to distance; 20 miles is one-third of 60 miles, so time is one-third of 60 minutes. | null | {
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"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 2 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
33 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20}
Insight: When speed is given in miles per hour, converting to miles per minute by dividing by 60 simplifies time calculation for distances in miles. | null | {
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"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 3 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
34 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20}
Insight: When speed is given in miles per hour, converting to miles per minute by dividing by 60 can simplify time calculations for distances. | null | {
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"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 4 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
35 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20} | null | {
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"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 5 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
36 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20} | null | {
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} | {
"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 6 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
37 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20}
Insight: When speed is given in miles per hour, the time in minutes for a distance in miles can be found by (distance / speed) * 60. | null | {
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"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 7 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
38 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20}
Insight: For constant speed, time is directly proportional to distance and inversely proportional to speed. Converting units (hours to minutes) is essential. | null | {
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"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 8 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
39 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20}
Insight: For constant speed problems, converting to desired time units first (e.g., minutes) can simplify calculation by setting a per-unit-time rate. | null | {
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"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 9 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
40 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1} | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate ... | 4 | 0 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
41 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1} | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I notice that this ... | 4 | 1 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
42 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1}
Insight: Recognizing patterns like \((x-1)(x+1) = x^2 - 1\) can simplify calculations involving consecutive numbers, avoiding direct multiplication of large numbers. | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nWe are asked to evaluate the expression $(723)(723) - (722)(724)$. At first glance, it looks like a direct arithmetic multiplication and subtraction, but the numbers are close to eac... | 4 | 2 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
43 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | FAILED | Tree generation failed. Reason: Maximum recursion depth (5) reached. | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nComputing (723)(723) and (722)(724) directly is straightforward but prone to arithmetic errors. Notice that the numbers are centered around 723: 722 = 723 - 1 and 724 = 723 + 1. This... | 4 | 3 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | |
44 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1}
Insight: For any integer a, (a+1)^2 - a(a+2) = 1, which shows that the square of the middle number exceeds the product of the two numbers that differ by 2 from it by exactly 1. | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nWe notice that 722 = 723 - 1 and 724 = 723 + 1, so the expression is of the form (n+1)(n+1) - (n)(n+2) with n=722. This pattern simplifies nicely using algebraic identities. To confi... | 4 | 4 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
45 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1}
Insight: Recognizing patterns like (n-1)(n+1) = n²-1 allows quick evaluation of such expressions without direct multiplication. | null | {
"actual_latency_seconds": 9.49308705329895,
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I notice that the e... | 4 | 5 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
46 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1} | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "We are to evaluate ... | 4 | 6 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
47 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1}
Insight: This algebraic pattern simplifies many similar computations. | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "This expression is ... | 4 | 7 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
48 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1}
Insight: The difference of squares identity (a-b)(a+b) = a^2 - b^2 simplifies such expressions: (723)^2 - (722)(724) = (723)^2 - (723^2 - 1) = 1. | null | {
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"theoretical_parallel_latency": 8.528428316116333
} | {
"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "We need to compute ... | 4 | 8 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
49 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1} | null | {
"actual_latency_seconds": 4.676428556442261,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 219,
"theoretical_parallel_latency": 4.675795316696167
} | {
"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "This expression can... | 4 | 9 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
50 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3} | null | {
"actual_latency_seconds": 2.826476573944092,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 157,
"theoretical_parallel_latency": 2.825556993484497
} | {
"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate log base 3 of 27. This is ... | 5 | 0 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
51 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3}
Insight: This is a basic logarithmic evaluation where the argument is a power of the base. | null | {
"actual_latency_seconds": 3.8655428886413574,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 234,
"theoretical_parallel_latency": 3.8648650646209717
} | {
"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "The logarithm $\\log_3 27$ asks for the expon... | 5 | 1 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
52 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3} | null | {
"actual_latency_seconds": 2.9161393642425537,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 157,
"theoretical_parallel_latency": 2.915440797805786
} | {
"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "The expression $\\log_327$ asks for the expon... | 5 | 2 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
53 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3}
Insight: Recognizing powers of the base is a fundamental technique for evaluating logarithms. | null | {
"actual_latency_seconds": 4.367711544036865,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 240,
"theoretical_parallel_latency": 4.366911172866821
} | {
"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "To evaluate \\(\\log_3 27\\), recall the loga... | 5 | 3 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
54 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3}
Insight: Recognizing powers of the base simplifies logarithmic evaluation to a trivial arithmetic step. | null | {
"actual_latency_seconds": 5.453336954116821,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 390,
"theoretical_parallel_latency": 5.452615737915039
} | {
"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "To evaluate \\(\\log_3 27\\), recall that the... | 5 | 4 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
55 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3}
Insight: The logarithm \(\log_b b^k\) simplifies directly to \(k\), a fundamental property useful for solving similar problems efficiently. | null | {
"actual_latency_seconds": 5.053048372268677,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 338,
"theoretical_parallel_latency": 5.0522003173828125
} | {
"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate the logarithmic expression... | 5 | 5 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
56 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3} | null | {
"actual_latency_seconds": 3.154845952987671,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 131,
"theoretical_parallel_latency": 3.154191017150879
} | {
"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I recall that 27 is a power of 3: 27 = 3^3. U... | 5 | 6 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
57 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
3
Insight: The logarithm of a number to the base of that number's root or power simplifies directly using exponent rules. | null | {
"actual_latency_seconds": 5.535104274749756,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 356,
"theoretical_parallel_latency": 5.534256219863892
} | {
"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate \\(\\log_3 27\\). This is ... | 5 | 7 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
58 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3}
Insight: Recognizing powers simplifies logarithmic evaluation. | null | {
"actual_latency_seconds": 3.4444382190704346,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 188,
"theoretical_parallel_latency": 3.4438281059265137
} | {
"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "We need to compute log base 3 of 27. Recogniz... | 5 | 8 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
59 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3}
Insight: Recognizing powers of the base simplifies logarithmic evaluation. | null | {
"actual_latency_seconds": 4.08177924156189,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 220,
"theoretical_parallel_latency": 4.081089496612549
} | {
"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate \\(\\log_3 27\\). Since \\... | 5 | 9 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
60 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181}
Insight: For polynomial evaluation with specific values, direct substitution and arithmetic simplification is efficient. | null | {
"actual_latency_seconds": 6.478240728378296,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 419,
"theoretical_parallel_latency": 6.477556228637695
} | {
"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate the expr... | 6 | 0 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
61 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | FAILED | Tree generation failed. Reason: Maximum recursion depth (5) reached. | {
"actual_latency_seconds": 34.72103452682495,
"total_llm_calls": 5,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 319,
"theoretical_parallel_latency": 34.71848917007446
} | {
"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\nI need to evaluate the expression \\(3x^2+5x-1\\) at \\(x=7\\). First, compute \\(x^2 = 7^2 = 49\\). Then multiply by 3: \\(3 \\times 49 = 147\\). Next, compute \\(5x = 5 \\times 7 = 35\\)... | 6 | 1 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | |
62 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181} | null | {
"actual_latency_seconds": 5.894273281097412,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 256,
"theoretical_parallel_latency": 5.893728256225586
} | {
"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "To evaluate $3x^2+5x-1$ whe... | 6 | 2 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
63 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181}
Insight: Breaking down polynomial evaluation into independent term calculations allows for parallel delegation, which can improve efficiency in more complex expressions. | null | {
"actual_latency_seconds": 19.869704484939575,
"total_llm_calls": 5,
"max_tree_depth": 1,
"max_subproblems": 3,
"max_output_chars": 604,
"theoretical_parallel_latency": 19.867945909500122
} | {
"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nTo evaluate the expression $3x^2+5x-1$ at $x=7$, I can compute each term separately to ensure accuracy. The terms $3 \\cdot 7^2$, $5 \\cdot 7$, and $-1$ are independent and can be calcul... | 6 | 3 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
64 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181}
Insight: The evaluation involves basic arithmetic operations and order of operations; no deeper mathematical insights are needed for this specific computation. | null | {
"actual_latency_seconds": 7.056891441345215,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 452,
"theoretical_parallel_latency": 7.056337594985962
} | {
"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "Evaluating the expression $... | 6 | 4 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
65 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181}
Insight: For evaluating a polynomial at a given value, direct substitution with careful arithmetic is efficient and minimizes error when the expression is simple. | null | {
"actual_latency_seconds": 5.8351521492004395,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 331,
"theoretical_parallel_latency": 5.834414720535278
} | {
"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "This is a straightforward s... | 6 | 5 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
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