progress/log/eval_dflash_0407_1912.log

nohup: ignoring input

============================================
  Running DFlash eval: denoise_steps=1
  GPUs: 8, Samples: 500
============================================
W0407 19:12:42.495000 4584 site-packages/torch/distributed/run.py:803] 
W0407 19:12:42.495000 4584 site-packages/torch/distributed/run.py:803] *****************************************
W0407 19:12:42.495000 4584 site-packages/torch/distributed/run.py:803] Setting OMP_NUM_THREADS environment variable for each process to be 1 in default, to avoid your system being overloaded, please further tune the variable for optimal performance in your application as needed. 
W0407 19:12:42.495000 4584 site-packages/torch/distributed/run.py:803] *****************************************
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
Set TORCH_CUDA_ARCH_LIST to 9.0
Set TORCH_CUDA_ARCH_LIST to 9.0
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
Set TORCH_CUDA_ARCH_LIST to 9.0
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
`torch_dtype` is deprecated! Use `dtype` instead!

Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 155.80it/s]
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
============================================================
DFlash Evaluation (Multi-GPU Data Parallel)
============================================================
  Target model:       /workspace/models/Qwen3-8B
  Draft model:        /workspace/models/Qwen3-8B-DFlash-b16
  Dataset:            math500
  Max samples:        500
  Max new tokens:     512
  Denoise steps:      1
  Temperature:        0.0
  GPUs:               8
  Dtype:              bfloat16
============================================================

[1/4] Loading tokenizer...
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
[2/4] Loading target model on 8 GPUs...
`torch_dtype` is deprecated! Use `dtype` instead!
`torch_dtype` is deprecated! Use `dtype` instead!

Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 160.04it/s]

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 159.49it/s]
`torch_dtype` is deprecated! Use `dtype` instead!
`torch_dtype` is deprecated! Use `dtype` instead!
`torch_dtype` is deprecated! Use `dtype` instead!
`torch_dtype` is deprecated! Use `dtype` instead!
`torch_dtype` is deprecated! Use `dtype` instead!

Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
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Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 156.98it/s]

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 153.68it/s]

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 155.50it/s]

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 156.21it/s]

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 156.91it/s]
[3/4] Loading draft model on 8 GPUs...
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
  Draft layers:       5
  Draft block_size:   16
  Draft mask_token:   151669
  Draft layer_ids:    [1, 9, 17, 25, 33]
[4/4] Loading evaluation data...
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
  Total prompts: 500, ~63 per GPU

============================================================
Running evaluation...
============================================================
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
  [GPU 3] Sample 1/63 | tokens=512 | tau=1.48 | time=11.7s | <think> Okay, so I need to figure out how many positive whole-number divisors 19...
  [GPU 7] Sample 1/62 | tokens=512 | tau=1.57 | time=11.1s | <think> Okay, so I need to find the angle between two lines given by these equat...
  [GPU 0] Sample 1/63 | tokens=512 | tau=1.45 | time=12.0s | <think> Okay, so I need to convert the rectangular coordinates (0, 3) to polar c...
  [GPU 2] Sample 1/63 | tokens=512 | tau=1.68 | time=10.5s | <think> Okay, so I need to find the value of f(-2) + f(-1) + f(0) where the func...
  [GPU 4] Sample 1/62 | tokens=512 | tau=1.62 | time=10.7s | <think> Okay, so I need to figure out which student has the greatest average spe...
  [GPU 1] Sample 1/63 | tokens=512 | tau=1.60 | time=10.9s | <think> Okay, so I need to find a way to express the double sum $\sum_{j = 1}^\i...
  [GPU 5] Sample 1/62 | tokens=512 | tau=1.54 | time=11.3s | <think> Okay, so I need to figure out the perimeter of a regular hexagon when I ...
  [GPU 6] Sample 1/62 | tokens=512 | tau=1.50 | time=11.8s | <think> Okay, so I need to find the smallest positive perfect cube that can be w...
  [GPU 3] Sample 2/63 | tokens=512 | tau=1.48 | time=11.4s | <think> Okay, so I need to find p(8) where p(x) is a degree 5 polynomial that sa...
  [GPU 7] Sample 2/62 | tokens=512 | tau=1.50 | time=10.9s | <think> Okay, so I need to find the complex number w, which is the result of rot...
  [GPU 4] Sample 2/62 | tokens=512 | tau=1.68 | time=9.8s | <think> Okay, so I need to find the sum of the proper divisors of the sum of the...
  [GPU 2] Sample 2/63 | tokens=512 | tau=1.54 | time=10.8s | <think> Okay, so I need to find the least positive integer multiple of 30 that c...
  [GPU 0] Sample 2/63 | tokens=512 | tau=1.47 | time=11.3s | <think> Okay, so I need to find the distance between the two points (2, -6) and ...
  [GPU 1] Sample 2/63 | tokens=512 | tau=1.49 | time=11.0s | <think> Okay, so I need to figure out how many different values can be obtained ...
  [GPU 5] Sample 2/62 | tokens=512 | tau=1.43 | time=11.5s | <think> Okay, so I need to find the height of a cylinder when the volume is give...
  [GPU 6] Sample 2/62 | tokens=512 | tau=1.40 | time=12.0s | <think> Okay, so I need to find the length of DE in this diagram. Let me try to ...
  [GPU 7] Sample 3/62 | tokens=512 | tau=1.62 | time=10.1s | <think> Okay, so I need to solve the equation $ x = \sqrt{11 - 2x} + 4 $. Hmm, l...
  [GPU 3] Sample 3/63 | tokens=512 | tau=1.45 | time=11.5s | <think> Okay, so I need to find the smallest possible value of a positive real n...
  [GPU 4] Sample 3/62 | tokens=512 | tau=1.48 | time=11.2s | <think> Okay, so I need to evaluate the expression (1 + 2i) multiplied by 6, and...
  [GPU 2] Sample 3/63 | tokens=512 | tau=1.54 | time=10.8s | <think> Okay, let me try to figure out this geometry problem. So, we have a diag...
  [GPU 0] Sample 3/63 | tokens=512 | tau=1.54 | time=10.8s | <think> Okay, so I need to compute this series: 1 - 2 + 3 - 4 + 5 - ... + 99 - 1...
  [GPU 5] Sample 3/62 | tokens=512 | tau=1.65 | time=10.0s | <think> Okay, so I need to find the greatest integer less than $(\sqrt{7} + \sqr...
  [GPU 1] Sample 3/63 | tokens=512 | tau=1.49 | time=11.1s | <think> Okay, so I need to find the smallest possible value of c for the functio...
  [GPU 6] Sample 3/62 | tokens=512 | tau=1.55 | time=10.8s | <think> Okay, let me try to figure out this problem. So, Denali and Nate are dog...
  [GPU 7] Sample 4/62 | tokens=512 | tau=1.42 | time=11.6s | <think> Okay, so I need to simplify the square root of 242. Hmm, let me think. I...
  [GPU 3] Sample 4/63 | tokens=512 | tau=1.52 | time=10.9s | <think> Okay, let's see. The math club is having a bake sale to raise money for ...
  [GPU 0] Sample 4/63 | tokens=512 | tau=1.71 | time=9.8s | <think> Okay, so there's this worker who gets $20,000 every year and deposits it...
  [GPU 4] Sample 4/62 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to figure out what happens when I rotate the complex num...
  [GPU 1] Sample 4/63 | tokens=512 | tau=1.70 | time=9.8s | <think> Okay, so I need to solve this functional equation problem. The function ...
  [GPU 5] Sample 4/62 | tokens=512 | tau=1.55 | time=10.7s | <think> Okay, so I need to figure out how many different battalions can be sent ...
  [GPU 2] Sample 4/63 | tokens=512 | tau=1.40 | time=12.0s | <think> Okay, so I need to figure out how many ways 7 people can sit around a ro...
  [GPU 6] Sample 4/62 | tokens=512 | tau=1.47 | time=11.5s | <think> Okay, so I need to find the product of 6 base 8 and 7 base 8, and then e...
  [GPU 4] Sample 5/62 | tokens=512 | tau=1.91 | time=8.7s | <think> Okay, so I need to find the roots of the equation $(x - 3)^3 + (x - 7)^3...
  [GPU 7] Sample 5/62 | tokens=512 | tau=1.60 | time=10.3s | <think> Okay, so I need to find the greatest common factor (GCF) of 6432 and 132...
  [GPU 3] Sample 5/63 | tokens=512 | tau=1.64 | time=10.2s | <think> Okay, so I need to find the remainder when (n + 2)(n + 4)(n + 6) is divi...
  [GPU 0] Sample 5/63 | tokens=512 | tau=1.43 | time=11.6s | <think> Okay, so I need to figure out how many ways 8 people can sit around a ro...
  [GPU 1] Sample 5/63 | tokens=512 | tau=1.49 | time=11.1s | <think> Okay, so I need to find the eighth term of this geometric sequence: 125/...
  [GPU 2] Sample 5/63 | tokens=512 | tau=1.64 | time=10.2s | <think> Okay, so I need to find the constant term in the expansion of $\left(10x...
  [GPU 5] Sample 5/62 | tokens=512 | tau=1.45 | time=11.4s | <think> Okay, so I need to figure out the minimum number of degrees a regular pe...
  [GPU 6] Sample 5/62 | tokens=512 | tau=1.50 | time=11.2s | <think> Okay, so I need to figure out how many calories make up a person's daily...
  [GPU 3] Sample 6/63 | tokens=512 | tau=1.85 | time=9.3s | <think> Okay, so I need to find the minimum value of this expression:  $$ \sqrt{...
  [GPU 4] Sample 6/62 | tokens=512 | tau=1.61 | time=10.3s | <think> Okay, so Bill is walking in different directions, and I need to figure o...
  [GPU 7] Sample 6/62 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to find the vertical asymptotes and the horizontal asymp...
  [GPU 0] Sample 6/63 | tokens=512 | tau=1.56 | time=10.7s | <think> Okay, so I need to find the side length of a regular octagon that has th...
  [GPU 2] Sample 6/63 | tokens=512 | tau=1.58 | time=10.6s | <think> Okay, so I need to solve this inequality: -4 < 2(x - 1) < 8. And then ex...
  [GPU 1] Sample 6/63 | tokens=512 | tau=1.39 | time=11.9s | <think> Okay, so I need to find the coordinates (x, y) of the fourth vertex of a...
  [GPU 5] Sample 6/62 | tokens=512 | tau=1.45 | time=11.5s | <think> Okay, so I need to find tan A in this right triangle ABC where angle B i...
  [GPU 6] Sample 6/62 | tokens=512 | tau=1.45 | time=11.6s | <think> Okay, so I need to find the smallest positive integer n such that all th...
  [GPU 4] Sample 7/62 | tokens=512 | tau=1.63 | time=10.1s | <think> Okay, so I need to simplify this expression: the square root of (2.5 squ...
  [GPU 3] Sample 7/63 | tokens=512 | tau=1.53 | time=11.3s | <think> Okay, so I need to find the quotient when x⁶ - 3 is divided by x + 1. Hm...
  [GPU 7] Sample 7/62 | tokens=512 | tau=1.52 | time=10.8s | <think> Okay, so I need to figure out the degree of the polynomial f. The proble...
  [GPU 0] Sample 7/63 | tokens=512 | tau=1.47 | time=11.2s | <think> Okay, so I need to figure out what power of 4 equals 8. Hmm, let me thin...
  [GPU 2] Sample 7/63 | tokens=512 | tau=1.54 | time=10.9s | <think> Okay, let me try to figure out this problem. So, there are seven bags of...
  [GPU 1] Sample 7/63 | tokens=512 | tau=1.65 | time=9.9s | <think> Okay, so I need to solve this equation: Half the value of 3x minus 9 is ...
  [GPU 5] Sample 7/62 | tokens=512 | tau=1.50 | time=11.0s | <think> Okay, so I need to compute the arcsin of -1/2. Hmm, let me recall what a...
  [GPU 6] Sample 7/62 | tokens=512 | tau=1.38 | time=12.2s | <think> Okay, so I need to convert the fraction 3/20 into a decimal. Hmm, let me...
  [GPU 4] Sample 8/62 | tokens=512 | tau=1.64 | time=10.0s | <think> Okay, so I need to figure out the ordered triple (p, q, r) such that the...
  [GPU 3] Sample 8/63 | tokens=512 | tau=1.59 | time=10.7s | <think> Okay, so there's this problem about a class of 50 students. Some partici...
  [GPU 7] Sample 8/62 | tokens=512 | tau=1.59 | time=10.4s | <think> Okay, so I need to factor the polynomial $ x^8 + 3x^4 - 4 $ into monic p...
  [GPU 2] Sample 8/63 | tokens=512 | tau=1.74 | time=9.6s | <think> Okay, so I need to compute 99 squared plus 99 plus 1. Let me think about...
  [GPU 0] Sample 8/63 | tokens=512 | tau=1.60 | time=10.4s | <think> Okay, so I need to find the value of N where the sum of the first N posi...
  [GPU 1] Sample 8/63 | tokens=512 | tau=1.51 | time=11.0s | <think> Okay, so Ringo is trying to calculate the modulus of (1 - i) raised to t...
  [GPU 5] Sample 8/62 | tokens=512 | tau=1.71 | time=9.7s | <think> Okay, so I need to find the value of $ a $ given that the cubic equation...
  [GPU 4] Sample 9/62 | tokens=512 | tau=1.55 | time=10.5s | <think> Okay, so I need to solve this equation: tan 53° tan 81° tan x° = tan 53°...
  [GPU 6] Sample 8/62 | tokens=512 | tau=1.51 | time=11.1s | <think> Okay, so I need to find the smallest positive real number C such that th...
  [GPU 3] Sample 9/63 | tokens=512 | tau=1.55 | time=11.3s | <think> Okay, so I need to figure out by what percentage the area of a square de...
  [GPU 7] Sample 9/62 | tokens=512 | tau=1.47 | time=11.1s | <think> Okay, so I need to convert the binary number 10101001110₂ to octal. Hmm,...
  [GPU 2] Sample 9/63 | tokens=512 | tau=1.60 | time=10.5s | <think> Okay, so I need to expand and simplify this algebraic expression: x time...
  [GPU 5] Sample 9/62 | tokens=512 | tau=1.69 | time=9.8s | <think> Okay, so I need to compute the value of $ z + \frac{1}{z} + z^2 + \frac{...
  [GPU 0] Sample 9/63 | tokens=512 | tau=1.46 | time=11.4s | <think> Okay, so I need to find the constant $ d $ such that the equation $ (\si...
  [GPU 1] Sample 9/63 | tokens=512 | tau=1.40 | time=11.8s | <think> Okay, so I need to figure out what 1 raised to the power of 2 raised to ...
  [GPU 4] Sample 10/62 | tokens=512 | tau=1.46 | time=11.2s | <think> Okay, so I need to figure out the domain of the function log(x²) and the...
  [GPU 6] Sample 9/62 | tokens=512 | tau=1.52 | time=11.1s | <think> Okay, so I need to subtract two numbers in base 9: 58 base 9 minus 18 ba...
  [GPU 2] Sample 10/63 | tokens=512 | tau=1.70 | time=9.8s | <think> Okay, so I need to simplify this expression: $\frac{\sec x}{\sin x} - \f...
  [GPU 3] Sample 10/63 | tokens=512 | tau=1.51 | time=11.2s | <think> Okay, so I need to find the probability that when I throw two fair 6-sid...
  [GPU 7] Sample 10/62 | tokens=512 | tau=1.44 | time=11.3s | <think> Okay, so I need to find the value of x that makes the equation 2³ times ...
  [GPU 0] Sample 10/63 | tokens=512 | tau=1.52 | time=10.9s | <think> Okay, so I need to find the radius of a sphere where the volume and surf...
  [GPU 5] Sample 10/62 | tokens=512 | tau=1.46 | time=11.3s | <think> Okay, so I need to solve the equation $2^8 = 4^x$ and find the value of ...
  [GPU 1] Sample 10/63 | tokens=512 | tau=1.51 | time=11.0s | <think> Okay, so I need to figure out the value of 9 & 2 using this operation th...
  [GPU 4] Sample 11/62 | tokens=512 | tau=1.81 | time=9.1s | <think> Okay, so I need to find the values of 'a' and 'b' such that when I multi...
  [GPU 6] Sample 10/62 | tokens=512 | tau=1.72 | time=9.8s | <think> Okay, so I need to find real numbers a (which isn't zero) and b such tha...
  [GPU 2] Sample 11/63 | tokens=512 | tau=1.71 | time=9.8s | <think> Okay, so I need to find the greatest possible value of the slope of the ...
  [GPU 7] Sample 11/62 | tokens=512 | tau=1.62 | time=10.2s | <think> Okay, so I need to solve the equation |5x - 1| = x + 3 and find the larg...
  [GPU 0] Sample 11/63 | tokens=512 | tau=1.67 | time=9.9s | <think> Okay, so I need to find the number of integer values of k in the interva...
  [GPU 3] Sample 11/63 | tokens=512 | tau=1.40 | time=12.5s | <think> Okay, so I need to solve the equation $3^{2x} + 19 = 10^x$. Hmm, let me ...
  [GPU 5] Sample 11/62 | tokens=512 | tau=1.54 | time=10.8s | <think> Okay, so I need to find the radius of a right cylindrical tank. The prob...
  [GPU 1] Sample 11/63 | tokens=512 | tau=1.61 | time=10.2s | <think> Okay, let me try to figure out this problem. So, we have three different...
  [GPU 4] Sample 12/62 | tokens=512 | tau=1.50 | time=10.9s | <think> Okay, so I need to figure out the probability that exactly 4 out of 7 is...
  [GPU 6] Sample 11/62 | tokens=512 | tau=1.42 | time=11.8s | <think> Okay, so I need to figure out how many different outfits I can make with...
  [GPU 7] Sample 12/62 | tokens=512 | tau=1.70 | time=9.7s | <think> Okay, so I need to find the value of y such that the projection of the v...
  [GPU 2] Sample 12/63 | tokens=512 | tau=1.31 | time=12.9s | <think> Okay, so Remmy wants to divide 10 by 2/3, but he's confused about how to...
  [GPU 1] Sample 12/63 | tokens=512 | tau=1.94 | time=8.6s | <think> Okay, so I need to find the greatest common divisor (GCD) of three numbe...
  [GPU 5] Sample 12/62 | tokens=512 | tau=1.67 | time=10.0s | <think> Okay, so I need to find the value of $ c $ such that the circle given by...
  [GPU 0] Sample 12/63 | tokens=512 | tau=1.44 | time=11.5s | <think> Okay, so I need to find the largest value of 'a' such that the graph of ...
  [GPU 3] Sample 12/63 | tokens=512 | tau=1.52 | time=11.4s | <think> Okay, so I need to find the smallest integer value of x for which the fu...
  [GPU 4] Sample 13/62 | tokens=512 | tau=1.36 | time=12.0s | <think> Okay, so I need to find the measure of angle α in this hexagon inscribed...
  [GPU 6] Sample 12/62 | tokens=512 | tau=1.59 | time=10.6s | <think> Okay, so I need to find the measure of angle AFD in quadrilateral ABCD. ...
  [GPU 7] Sample 13/62 | tokens=512 | tau=1.55 | time=10.6s | <think> Okay, so I need to find the values of λ between 0 and 4 such that there'...
  [GPU 0] Sample 13/63 | tokens=512 | tau=1.81 | time=9.2s | <think> Okay, so I need to solve this equation:  $$\frac{( x+ 1)(x - 3)}{5(x + 2...
  [GPU 5] Sample 13/62 | tokens=512 | tau=1.66 | time=10.0s | <think> Okay, so I need to solve this equation: $x^{10} + (13x - 1)^{10} = 0$. T...
  [GPU 2] Sample 13/63 | tokens=512 | tau=1.53 | time=11.0s | <think> Okay, so I need to simplify this expression: (-k + 4) + (-2 + 3k). Let m...
  [GPU 1] Sample 13/63 | tokens=512 | tau=1.46 | time=11.3s | <think> Okay, so there's this figure skater who starts facing north, and she beg...
  [GPU 3] Sample 13/63 | tokens=512 | tau=1.64 | time=10.7s | <think> Okay, so I need to find a vector v such that when I take the dot product...
  [GPU 4] Sample 14/62 | tokens=512 | tau=1.57 | time=10.5s | <think> Okay, so I need to find the value of k for the ellipse given by the equa...
  [GPU 7] Sample 14/62 | tokens=512 | tau=1.58 | time=10.4s | <think> Okay, so Mr. Brennan has 7 boys and 4 girls in his statistics class, and...
  [GPU 6] Sample 13/62 | tokens=512 | tau=1.47 | time=11.5s | <think> Okay, so I need to factor the expression ab + 5b + 2a + 10. Hmm, factori...
  [GPU 0] Sample 14/63 | tokens=512 | tau=1.80 | time=9.3s | <think> Okay, so I need to find the sum of the distances from the four intersect...
  [GPU 5] Sample 14/62 | tokens=512 | tau=1.74 | time=9.6s | <think> Okay, so I need to find the degree measure of the least positive angle θ...
  [GPU 1] Sample 14/63 | tokens=512 | tau=1.82 | time=9.0s | <think> Okay, so I need to find the median number of students in 2005 for these ...
  [GPU 2] Sample 14/63 | tokens=512 | tau=1.58 | time=10.7s | <think> Okay, so I need to find the horizontal asymptote of the function y = (4x...
  [GPU 3] Sample 14/63 | tokens=512 | tau=1.87 | time=9.3s | <think> Okay, so I need to figure out how many elements are in the intersection ...
  [GPU 4] Sample 15/62 | tokens=512 | tau=1.55 | time=10.6s | <think> Okay, so I need to solve the equation $2^{2x} = 256^{\frac{1}{2}}$. Hmm,...
  [GPU 6] Sample 14/62 | tokens=512 | tau=1.68 | time=10.1s | <think> Okay, so I need to find the value of $ a_1 $ in a strictly increasing se...
  [GPU 7] Sample 15/62 | tokens=512 | tau=1.48 | time=11.1s | <think> Okay, so I need to figure out the minimum possible value of the expressi...
  [GPU 0] Sample 15/63 | tokens=512 | tau=1.55 | time=10.7s | <think> Okay, so I need to simplify the expression (1 + √2)/(2 + √3). The proble...
  [GPU 1] Sample 15/63 | tokens=512 | tau=1.57 | time=10.5s | <think> Okay, so I need to figure out the value of this expression: (26² - 24² -...
  [GPU 2] Sample 15/63 | tokens=512 | tau=1.68 | time=9.9s | <think> Okay, so I need to find the product CD where C and D are integers that s...
  [GPU 5] Sample 15/62 | tokens=512 | tau=1.47 | time=11.3s | <think> Okay, so I need to solve the equation √(3x - 5) = 2. Hmm, let me think. ...
  [GPU 3] Sample 15/63 | tokens=512 | tau=1.50 | time=11.2s | <think> Okay, so I need to figure out how many ways there are to arrange the let...
  [GPU 4] Sample 16/62 | tokens=512 | tau=1.63 | time=10.1s | <think> Okay, so I need to solve the equation |x + 5| - |3x - 6| = 0. Hmm, absol...
  [GPU 6] Sample 15/62 | tokens=512 | tau=1.60 | time=10.6s | <think> Okay, so I need to find the number of ordered pairs (a, b) of integers s...
  [GPU 7] Sample 16/62 | tokens=512 | tau=1.53 | time=10.7s | <think> Okay, so I need to convert the decimal number 555 into base 5. Hmm, let ...
  [GPU 5] Sample 16/62 | tokens=512 | tau=1.73 | time=9.6s | <think> Okay, so I need to evaluate this expression: the ceiling of (3.6 squared...
  [GPU 2] Sample 16/63 | tokens=512 | tau=1.71 | time=9.8s | <think> Okay, so Daniel says that the popularity of a television, which is measu...
  [GPU 1] Sample 16/63 | tokens=512 | tau=1.50 | time=11.1s | <think> Okay, so I need to solve the equation (x/2) + (x/3) = 5. Hmm, let me thi...
  [GPU 0] Sample 16/63 | tokens=512 | tau=1.39 | time=11.9s | <think> Okay, so I need to figure out whether the composition of these functions...
  [GPU 3] Sample 16/63 | tokens=512 | tau=1.51 | time=11.3s | <think> Okay, so I need to find the area of quadrilateral DBEF. Let me first try...
  [GPU 4] Sample 17/62 | tokens=512 | tau=1.58 | time=10.4s | <think> Okay, so Rick is thinking of a positive factor of 14, and Steve is think...
  [GPU 6] Sample 16/62 | tokens=512 | tau=1.47 | time=11.5s | <think> Okay, so I need to find z_{2002} where each term is defined by iterating...
  [GPU 5] Sample 17/62 | tokens=512 | tau=1.54 | time=10.8s | <think> Okay, so I need to figure out the measure of the largest angle in this c...
  [GPU 7] Sample 17/62 | tokens=512 | tau=1.38 | time=11.9s | <think> Okay, so I need to figure out how many zeros are at the end of 42 factor...
  [GPU 1] Sample 17/63 | tokens=512 | tau=1.52 | time=10.9s | <think> Okay, so I need to find the area of triangle ACD in triangle ABC where A...
  [GPU 2] Sample 17/63 | tokens=512 | tau=1.41 | time=11.9s | <think> Okay, so I need to find an integer n between 0 and 17 (since 0 ≤ n < 18)...
  [GPU 0] Sample 17/63 | tokens=512 | tau=1.39 | time=12.0s | <think> Okay, so Suzanne walks four miles every third day. The question is askin...
  [GPU 3] Sample 17/63 | tokens=512 | tau=1.53 | time=11.2s | <think> Okay, so I need to find the value of f(3) given that f(-3) = 2 for the f...
  [GPU 4] Sample 18/62 | tokens=512 | tau=1.62 | time=10.1s | <think> Okay, so I need to find the greatest possible value of the greatest comm...
  [GPU 6] Sample 17/62 | tokens=512 | tau=1.57 | time=10.7s | <think> Okay, so I need to find the equation of a hyperbola given two foci, F₁ =...
  [GPU 7] Sample 18/62 | tokens=512 | tau=1.60 | time=10.1s | <think> Okay, so I need to find the area of triangle OAB, given the vectors OA a...
  [GPU 5] Sample 18/62 | tokens=512 | tau=1.52 | time=10.8s | <think> Okay, so Zach has three bags and a bunch of pencils. He needs to place t...
  [GPU 1] Sample 18/63 | tokens=512 | tau=1.59 | time=10.3s | <think> Okay, so I need to divide 413 base 5 by 2 base 5 and give the answer in ...
  [GPU 2] Sample 18/63 | tokens=512 | tau=1.49 | time=11.1s | <think> Okay, so Bob and Alice each have a bag with balls of five different colo...
  [GPU 0] Sample 18/63 | tokens=512 | tau=1.60 | time=10.3s | <think> Okay, so I need to find the sum of all possible values of n for a sequen...
  [GPU 3] Sample 18/63 | tokens=512 | tau=1.69 | time=9.7s | <think> Okay, so I need to find the maximum value of the function $ f(x, y) = x ...
  [GPU 4] Sample 19/62 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to solve the equation 2/3 equals 4 divided by (x minus 5...
  [GPU 7] Sample 19/62 | tokens=512 | tau=1.64 | time=10.0s | <think> Okay, so I need to find the square of the determinant of a 3x3 matrix wi...
  [GPU 5] Sample 19/62 | tokens=512 | tau=1.60 | time=10.4s | <think> Okay, let's try to figure out Rosa's age. The problem says that when her...
  [GPU 6] Sample 18/62 | tokens=512 | tau=1.46 | time=11.5s | <think> Okay, so I need to figure out how many ways the Senate committee can sit...
  [GPU 1] Sample 19/63 | tokens=512 | tau=1.57 | time=10.5s | <think> Okay, so I need to find $ z^{85} + \frac{1}{z^{85}} $ given that $ z + \...
  [GPU 0] Sample 19/63 | tokens=512 | tau=1.52 | time=10.9s | <think> Okay, so I need to find the point on the curve that's given by the param...
  [GPU 3] Sample 19/63 | tokens=512 | tau=1.48 | time=11.1s | <think> Okay, so I need to find the minimum value of the expression $ x^4 + 4y^2...
  [GPU 2] Sample 19/63 | tokens=512 | tau=1.38 | time=12.2s | <think> Okay, so I need to simplify the fraction 3 over the square root of 27. L...
  [GPU 4] Sample 20/62 | tokens=512 | tau=1.65 | time=9.9s | <think> Okay, so there's this problem about two runners, A and B, starting from ...
  [GPU 7] Sample 20/62 | tokens=512 | tau=1.60 | time=10.3s | <think> Okay, so I need to rewrite the quadratic equation $x^2 + 2.6x + 3.6$ in ...
  [GPU 5] Sample 20/62 | tokens=512 | tau=1.64 | time=10.1s | <think> Okay, so I need to find the value of a + b + c, where a, b, and c are th...
  [GPU 6] Sample 19/62 | tokens=512 | tau=1.67 | time=10.1s | <think> Okay, so I need to figure out what f(2015, 2) is based on this recursive...
  [GPU 1] Sample 20/63 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to find the probability that three randomly chosen point...
  [GPU 3] Sample 20/63 | tokens=512 | tau=1.56 | time=10.7s | <think> Okay, so I need to find the probability that a randomly selected point (...
  [GPU 0] Sample 20/63 | tokens=512 | tau=1.42 | time=11.6s | <think> Okay, so I need to find the area of triangle ENG in triangle ABC, where ...
  [GPU 2] Sample 20/63 | tokens=512 | tau=1.51 | time=11.1s | <think> Okay, so there's this gecko in a room, and it needs to get to a fly. The...
  [GPU 4] Sample 21/62 | tokens=512 | tau=1.43 | time=11.4s | <think> Okay, so I need to simplify the expression tan 100° + 4 sin 100°. Hmm, l...
  [GPU 5] Sample 21/62 | tokens=512 | tau=1.69 | time=9.8s | <think> Okay, let me try to figure out this problem. So, there's a bookcase with...
  [GPU 7] Sample 21/62 | tokens=512 | tau=1.45 | time=11.3s | <think> Okay, so I need to find the volume of a cone. The formula given is V equ...
  [GPU 6] Sample 20/62 | tokens=512 | tau=1.52 | time=11.1s | <think> Okay, so I need to find the sum of all multiples of 7 between 100 and 20...
  [GPU 1] Sample 21/63 | tokens=512 | tau=1.54 | time=10.8s | <think> Okay, so I need to evaluate log base 2 of 64. Hmm, let me think. Logarit...
  [GPU 3] Sample 21/63 | tokens=512 | tau=1.65 | time=10.5s | <think> Okay, so I need to find the greatest possible value of the expression $\...
  [GPU 0] Sample 21/63 | tokens=512 | tau=1.53 | time=10.8s | <think> Okay, so I need to find two consecutive positive even integers whose pro...
  [GPU 2] Sample 21/63 | tokens=512 | tau=1.53 | time=10.9s | <think> Okay, so I need to find the probability that a randomly selected integer...
  [GPU 4] Sample 22/62 | tokens=512 | tau=1.68 | time=9.7s | <think> Okay, so I need to find the sixth term of an arithmetic sequence where t...
  [GPU 5] Sample 22/62 | tokens=512 | tau=1.59 | time=10.4s | <think> Okay, so I need to find the smallest positive integer value of 'a' such ...
  [GPU 7] Sample 22/62 | tokens=512 | tau=1.72 | time=9.5s | <think> Okay, so I need to find the smallest possible value of |m - n| where m a...
  [GPU 6] Sample 21/62 | tokens=512 | tau=1.47 | time=11.5s | <think> Okay, so I need to find the measure of angle BAC, where there's a square...
  [GPU 1] Sample 22/63 | tokens=512 | tau=1.46 | time=11.3s | <think> Okay, so I need to find the area of a triangle with sides 5, 5, and 6 un...
  [GPU 2] Sample 22/63 | tokens=512 | tau=1.62 | time=10.3s | <think> Okay, so I need to find the product of the y-coordinates of all the dist...
  [GPU 0] Sample 22/63 | tokens=512 | tau=1.51 | time=11.0s | <think> Okay, so I need to figure out the value of n for a 3×n grid of points wh...
  [GPU 3] Sample 22/63 | tokens=512 | tau=1.45 | time=11.7s | <think> Okay, so Louis and Jack are sharing a pie, and I need to figure out how ...
  [GPU 4] Sample 23/62 | tokens=512 | tau=1.61 | time=10.2s | <think> Okay, so I need to figure out how many positive two-digit integers are f...
  [GPU 7] Sample 23/62 | tokens=512 | tau=1.65 | time=10.0s | <think> Okay, so I need to figure out how to write the expression √2 + 1/√2 + √3...
  [GPU 5] Sample 23/62 | tokens=512 | tau=1.59 | time=10.5s | <think> Okay, so I need to simplify this expression: the square root of the cube...
  [GPU 1] Sample 23/63 | tokens=512 | tau=1.64 | time=10.1s | <think> Okay, so I need to find the degree measure of the smallest angle in tria...
  [GPU 6] Sample 22/62 | tokens=512 | tau=1.54 | time=11.0s | <think> Okay, so I need to figure out how many y-intercepts the graph of the par...
  [GPU 4] Sample 24/62 | tokens=512 | tau=2.00 | time=8.2s | <think> Okay, so I need to find the largest x-value where the graphs of f(x) and...
  [GPU 2] Sample 23/63 | tokens=512 | tau=1.59 | time=10.6s | <think> Okay, so I need to find the positive square root of the product 10 times...
  [GPU 3] Sample 23/63 | tokens=512 | tau=1.61 | time=10.5s | <think> Okay, so I need to find the equation of the plane that contains the thre...
  [GPU 0] Sample 23/63 | tokens=512 | tau=1.42 | time=11.7s | <think> Okay, so I need to convert the fraction 21 divided by (2 squared times 5...
  [GPU 5] Sample 24/62 | tokens=512 | tau=1.59 | time=10.4s | <think> Okay, so I need to figure out the greatest length of rope that can be sa...
  [GPU 7] Sample 24/62 | tokens=512 | tau=1.48 | time=11.1s | <think> Okay, so I need to find the value of b when the point (a, b) is on the l...
  [GPU 6] Sample 23/62 | tokens=512 | tau=1.53 | time=11.1s | <think> Okay, so I need to figure out how many students are at Baker Middle Scho...
  [GPU 1] Sample 24/63 | tokens=512 | tau=1.45 | time=11.4s | <think> Okay, so I need to find the value of k such that (3^k)^6 equals 3^6. Let...
  [GPU 4] Sample 25/62 | tokens=512 | tau=1.50 | time=10.9s | <think> Okay, so I need to solve this equation: 441 plus 2 times 21 times 19 plu...
  [GPU 2] Sample 24/63 | tokens=512 | tau=1.50 | time=11.2s | <think> Okay, so I need to figure out for how many positive integers n > 1 it's ...
  [GPU 3] Sample 24/63 | tokens=512 | tau=1.58 | time=11.1s | <think> Okay, so Hillary has eleven coins, and they're all either dimes or nicke...
  [GPU 0] Sample 24/63 | tokens=512 | tau=1.61 | time=10.3s | <think> Okay, so I need to find all possible values of the expression $\frac{c}{...
  [GPU 5] Sample 25/62 | tokens=512 | tau=1.58 | time=10.5s | <think> Okay, so I need to figure out how many possible integer values of x ther...
  [GPU 7] Sample 25/62 | tokens=512 | tau=1.45 | time=11.3s | <think> Okay, so I need to find the value of x such that the arithmetic mean of ...
  [GPU 6] Sample 24/62 | tokens=512 | tau=1.66 | time=10.2s | <think> Okay, so Paul and Jesse each pick a number at random from the first six ...
  [GPU 1] Sample 25/63 | tokens=512 | tau=1.51 | time=11.1s | <think> Okay, so I need to find the number of different possible rational roots ...
  [GPU 4] Sample 26/62 | tokens=512 | tau=1.56 | time=10.6s | <think> Okay, so I need to find the maximum value of the product |(a + b)(a + c)...
  [GPU 3] Sample 25/63 | tokens=512 | tau=1.60 | time=10.5s | <think> Okay, so I need to find p(0) + p(4) where p(x) is a monic polynomial of ...
  [GPU 2] Sample 25/63 | tokens=512 | tau=1.50 | time=11.2s | <think> Okay, so I need to find the maximum value of the expression $\frac{x - y...
  [GPU 0] Sample 25/63 | tokens=512 | tau=1.46 | time=11.4s | <think> Okay, so I need to find the length of the median QM in triangle PQR wher...
  [GPU 5] Sample 26/62 | tokens=512 | tau=1.45 | time=11.4s | <think> Okay, so I need to find the matrix A multiplied by the vector (-13, 3, 4...
  [GPU 7] Sample 26/62 | tokens=512 | tau=1.41 | time=11.6s | <think> Okay, so Mikka wants to order a pizza with two different toppings, and h...
  [GPU 4] Sample 27/62 | tokens=512 | tau=1.65 | time=10.0s | <think> Okay, let's see. Frank took a 100-question test. Each correct answer giv...
  [GPU 1] Sample 26/63 | tokens=512 | tau=1.50 | time=11.1s | <think> Okay, so there's this problem about a group of N students, and N is less...
  [GPU 3] Sample 26/63 | tokens=512 | tau=1.76 | time=9.7s | <think> Okay, so I need to find the remainder when this big polynomial is divide...
  [GPU 6] Sample 25/62 | tokens=512 | tau=1.36 | time=12.5s | <think> Okay, so I need to figure out how many ways 6 girls and 2 boys can sit i...
  [GPU 0] Sample 26/63 | tokens=512 | tau=1.53 | time=10.8s | <think> Okay, so I need to figure out how many daps equal 42 baps. Let me start ...
  [GPU 2] Sample 26/63 | tokens=512 | tau=1.39 | time=12.0s | <think> Okay, so Alice and Bob are playing this game where they take turns flipp...
  [GPU 5] Sample 27/62 | tokens=512 | tau=2.02 | time=8.2s | <think> Okay, so I need to compute the infinite sum $\sum_{n = 1}^\infty \frac{F...
  [GPU 7] Sample 27/62 | tokens=512 | tau=1.57 | time=10.4s | <think> Okay, so I need to find the value of $ x^3 - 2x + 1 $ given that $ x^2 -...
  [GPU 1] Sample 27/63 | tokens=512 | tau=1.83 | time=9.1s | <think> Okay, so I need to find a two-digit integer AB such that when it's cubed...
  [GPU 4] Sample 28/62 | tokens=512 | tau=1.56 | time=10.6s | <think> Okay, so Sam is carrying a 2-gallon bucket of milk, and he needs to walk...
  [GPU 6] Sample 26/62 | tokens=512 | tau=1.66 | time=10.1s | <think> Okay, so I need to find the equation of a line given its parametric equa...
  [GPU 3] Sample 27/63 | tokens=512 | tau=1.50 | time=11.1s | <think> Okay, so I need to figure out how to compute this expression: 5^5 divide...
  [GPU 0] Sample 27/63 | tokens=512 | tau=1.57 | time=10.5s | <think> Okay, so I need to figure out how many numbers from 1 to 100 are divisib...
  [GPU 2] Sample 27/63 | tokens=512 | tau=1.50 | time=11.2s | <think> Okay, so I need to find the total area of the shaded region in this figu...
  [GPU 5] Sample 28/62 | tokens=512 | tau=1.55 | time=10.8s | <think> Okay, so I need to find the smallest positive integer k such that when I...
  [GPU 7] Sample 28/62 | tokens=512 | tau=1.69 | time=9.8s | <think> Okay, so I need to find the sum of the digits in the terminating decimal...
  [GPU 4] Sample 29/62 | tokens=512 | tau=1.91 | time=8.6s | <think> Okay, so I need to find the region of the volume enclosed by the set S, ...
  [GPU 1] Sample 28/63 | tokens=512 | tau=1.52 | time=10.8s | <think> Okay, so I need to find the smallest positive multiple of 450 where all ...
  [GPU 6] Sample 27/62 | tokens=512 | tau=1.54 | time=11.0s | <think> Okay, let's try to figure out how many students take physics. There are ...
  [GPU 3] Sample 28/63 | tokens=512 | tau=1.63 | time=10.6s | <think> Okay, so I need to figure out the probability that when I spin this whee...
  [GPU 0] Sample 28/63 | tokens=512 | tau=1.48 | time=11.2s | <think> Okay, so I need to figure out how much 56 Drinkets is worth in Trinkets....
  [GPU 2] Sample 28/63 | tokens=512 | tau=1.48 | time=11.2s | <think> Okay, so I need to find the midpoint between two points, (-5, 5) and (3,...
  [GPU 5] Sample 29/62 | tokens=512 | tau=1.47 | time=11.3s | <think> Okay, so Yann and Camille are going to a restaurant, and there are 10 it...
  [GPU 7] Sample 29/62 | tokens=512 | tau=1.56 | time=10.5s | <think> Okay, let's try to figure out how old Chris is now. The problem says tha...
  [GPU 4] Sample 30/62 | tokens=512 | tau=1.62 | time=10.1s | <think> Okay, so I need to compute the value of this expression: 1 over cos squa...
  [GPU 1] Sample 29/63 | tokens=512 | tau=1.76 | time=9.4s | <think> Okay, so I need to find the value of this expression when x is 4. The ex...
  [GPU 6] Sample 28/62 | tokens=512 | tau=1.54 | time=10.9s | <think> Okay, so I need to find the area of triangle CDE given that the area of ...
  [GPU 0] Sample 29/63 | tokens=512 | tau=1.67 | time=9.9s | <think> Okay, so I need to find the value of the product sin20° sin40° sin60° si...
  [GPU 3] Sample 29/63 | tokens=512 | tau=1.39 | time=12.3s | <think> Okay, so I need to figure out what shape the equation z = c represents i...
  [GPU 2] Sample 29/63 | tokens=512 | tau=1.51 | time=11.0s | <think> Okay, so I need to figure out how many ways there are to put 5 indisting...
  [GPU 5] Sample 30/62 | tokens=512 | tau=1.46 | time=11.3s | <think> Okay, so I need to find the value of x + y + z given that xy = 24, xz = ...
  [GPU 7] Sample 30/62 | tokens=512 | tau=1.52 | time=10.7s | <think> Okay, so I need to solve this problem about parallelograms bounded by li...
  [GPU 4] Sample 31/62 | tokens=512 | tau=1.64 | time=10.0s | <think> Okay, so I need to figure out how many sides a convex polygon has if the...
  [GPU 1] Sample 30/63 | tokens=512 | tau=1.50 | time=11.0s | <think> Okay, so I need to find the smallest possible angle between vectors a an...
  [GPU 6] Sample 29/62 | tokens=512 | tau=1.51 | time=11.2s | <think> Okay, so I need to find the maximum value of e given these two equations...
  [GPU 3] Sample 30/63 | tokens=512 | tau=1.61 | time=10.3s | <think> Okay, so I need to compute this expression: 0.7 repeating minus 0.4 repe...
  [GPU 0] Sample 30/63 | tokens=512 | tau=1.50 | time=11.0s | <think> Okay, so I need to evaluate the sum S = 1/(1 + ω) + 1/(1 + ω²) + ... + 1...
  [GPU 2] Sample 30/63 | tokens=512 | tau=1.63 | time=10.2s | <think> Okay, so I need to find the sum of the roots of the function g(x), which...
  [GPU 5] Sample 31/62 | tokens=512 | tau=1.48 | time=11.2s | <think> Okay, so I need to find the remainder when this big polynomial f(x) is d...
  [GPU 7] Sample 31/62 | tokens=512 | tau=1.59 | time=10.3s | <think> Okay, so I need to find the value of p(3)/p(4) where p(x) is a quadratic...
  [GPU 4] Sample 32/62 | tokens=512 | tau=1.62 | time=10.1s | <think> Okay, so I need to find the maximum value of the function $ 4(x + 7)(2 -...
  [GPU 1] Sample 31/63 | tokens=512 | tau=1.50 | time=11.0s | <think> Okay, so I need to find the smallest distance between the origin (0,0) a...
  [GPU 6] Sample 30/62 | tokens=512 | tau=1.73 | time=9.8s | <think> Okay, so I need to figure out the real values of x that are not in the d...
  [GPU 3] Sample 31/63 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to figure out the length of the third side of a triangle...
  [GPU 0] Sample 31/63 | tokens=512 | tau=1.53 | time=10.8s | <think> Okay, so I need to find the measure of angle PQR in this diagram. Let me...
  [GPU 2] Sample 31/63 | tokens=512 | tau=1.41 | time=11.9s | <think> Okay, so I need to figure out how much money will be in the investment a...
  [GPU 7] Sample 32/62 | tokens=512 | tau=1.60 | time=10.3s | <think> Okay, so I need to figure out what kind of curve is defined by the equat...
  [GPU 4] Sample 33/62 | tokens=512 | tau=1.59 | time=10.3s | <think> Okay, so I need to find the angle ABC, which is the angle at point B for...
  [GPU 5] Sample 32/62 | tokens=512 | tau=1.42 | time=11.7s | <think> Okay, so I need to figure out what fraction of 2 feet is 3 inches. Hmm, ...
  [GPU 1] Sample 32/63 | tokens=512 | tau=1.52 | time=10.9s | <think> Okay, so I need to find an odd integer t between 0 and 23 such that t + ...
  [GPU 6] Sample 31/62 | tokens=512 | tau=1.56 | time=10.8s | <think> Okay, so there's this problem about twelve friends who went to dinner, a...
  [GPU 3] Sample 32/63 | tokens=512 | tau=1.60 | time=10.3s | <think> Okay, so there's this problem about six cars pulling up to a red light o...
  [GPU 0] Sample 32/63 | tokens=512 | tau=1.67 | time=9.9s | <think> Okay, so I need to compute A^27 + A^31 + A^40 where A is the matrix [[3,...
  [GPU 7] Sample 33/62 | tokens=512 | tau=1.56 | time=10.5s | <think> Okay, so I need to figure out how many sides a regular polygon has if it...
  [GPU 4] Sample 34/62 | tokens=512 | tau=1.57 | time=10.3s | <think> Okay, so I need to find the remainder when the sum of numbers from 1 to ...
  [GPU 2] Sample 32/63 | tokens=512 | tau=1.51 | time=11.1s | <think> Okay, so I need to find the x-intercept (a), the y-intercept (b), and th...
  [GPU 5] Sample 33/62 | tokens=512 | tau=1.43 | time=11.6s | <think> Okay, so I need to find the measure of angle B in triangle ABC, where an...
  [GPU 1] Sample 33/63 | tokens=512 | tau=1.54 | time=10.6s | <think> Okay, so I need to find the total surface area of a cube that has a volu...
  [GPU 6] Sample 32/62 | tokens=512 | tau=1.44 | time=11.7s | <think> Okay, so Pat wants to select six cookies from a tray that has chocolate ...
  [GPU 0] Sample 33/63 | tokens=512 | tau=1.55 | time=10.6s | <think> Okay, so I need to simplify this expression: (1/5) multiplied by (8/7) d...
  [GPU 3] Sample 33/63 | tokens=512 | tau=1.47 | time=11.3s | <think> Okay, so I need to compute the product of the number 5 plus the square r...
  [GPU 7] Sample 34/62 | tokens=512 | tau=1.64 | time=9.9s | <think> Okay, so I need to find the inverse of 997 modulo 1000. That means I nee...
  [GPU 4] Sample 35/62 | tokens=512 | tau=1.55 | time=10.6s | <think> Okay, so I need to figure out for how many real values of x the expressi...
  [GPU 2] Sample 33/63 | tokens=512 | tau=1.55 | time=10.7s | <think> Okay, so I need to figure out how many blue marbles were in the bag orig...
  [GPU 5] Sample 34/62 | tokens=512 | tau=1.54 | time=10.7s | <think> Okay, so I need to figure out how many distinct arrangements there are f...
  [GPU 1] Sample 34/63 | tokens=512 | tau=1.71 | time=9.8s | <think> Okay, so I need to find the 2003rd term of the sequence of odd numbers: ...
  [GPU 6] Sample 33/62 | tokens=512 | tau=1.62 | time=10.4s | <think> Okay, so I need to solve the equation $10^x - 10 = 9990$. Let me think a...
  [GPU 0] Sample 34/63 | tokens=512 | tau=1.50 | time=10.9s | <think> Okay, so I need to find the length of BH in this figure. Let me try to v...
  [GPU 3] Sample 34/63 | tokens=512 | tau=1.43 | time=11.6s | <think> Okay, so I need to find the sum of the measures of angle J and angle H i...
  [GPU 4] Sample 36/62 | tokens=512 | tau=1.82 | time=9.0s | <think> Okay, so I need to solve the equation:  $$ \sin \left( \tan^{-1} (x) + \...
  [GPU 7] Sample 35/62 | tokens=512 | tau=1.52 | time=10.8s | <think> Okay, so I need to figure out the difference between the area of the reg...
  [GPU 2] Sample 34/63 | tokens=512 | tau=1.49 | time=11.2s | <think> Okay, so I need to find the probability that a randomly selected number ...
  [GPU 1] Sample 35/63 | tokens=512 | tau=1.59 | time=10.4s | <think> Okay, so I need to figure out how many dollars are equivalent to 1,000,0...
  [GPU 5] Sample 35/62 | tokens=512 | tau=1.43 | time=11.5s | <think> Okay, so I need to figure out what the square root of 53 is in its simpl...
  [GPU 4] Sample 37/62 | tokens=512 | tau=2.07 | time=7.9s | <think> Okay, so I need to find the value of $ x_{531} + x_{753} + x_{975} $ giv...
  [GPU 6] Sample 34/62 | tokens=512 | tau=1.53 | time=11.1s | <think> Okay, so I need to figure out how many more dollars Pam pays than Susan ...
  [GPU 0] Sample 35/63 | tokens=512 | tau=1.67 | time=9.9s | <think> Okay, so I need to convert the repeating decimal 0.133113311331... into ...
  [GPU 3] Sample 35/63 | tokens=512 | tau=1.56 | time=10.6s | <think> Okay, so I need to find the value of g(f(5) - 1). Let me start by recall...
  [GPU 7] Sample 36/62 | tokens=512 | tau=1.50 | time=10.9s | <think> Okay, so I need to figure out after how many seconds both gears will hav...
  [GPU 2] Sample 35/63 | tokens=512 | tau=1.42 | time=11.7s | <think> Okay, so I need to find the perimeter of this set S. Let me try to visua...
  [GPU 1] Sample 36/63 | tokens=512 | tau=1.54 | time=10.7s | <think> Okay, so I need to find the measure of angle A in this regular pentagon ...
  [GPU 5] Sample 36/62 | tokens=512 | tau=1.65 | time=10.0s | <think> Okay, so Steve is thinking of a polynomial with all positive integer roo...
  [GPU 0] Sample 36/63 | tokens=512 | tau=1.70 | time=9.7s | <think> Okay, so I need to figure out how many whole-number divisors the express...
  [GPU 6] Sample 35/62 | tokens=512 | tau=1.53 | time=11.0s | <think> Okay, so I need to figure out the largest eight-digit number in base 2, ...
  [GPU 4] Sample 38/62 | tokens=512 | tau=1.43 | time=11.4s | <think> Okay, so I need to figure out the maximum number of points where at leas...
  [GPU 3] Sample 36/63 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to figure out what (4 5/8)^55 multiplied by (8/37)^55 is...
  [GPU 7] Sample 37/62 | tokens=512 | tau=1.62 | time=10.1s | <think> Okay, so I need to solve this equation: $ z^4 + 4z^3i - 6z^2 - 4zi - i =...
  [GPU 2] Sample 36/63 | tokens=512 | tau=1.97 | time=8.5s | <think> Okay, let me try to figure out this sequence problem. The sequence start...
  [GPU 1] Sample 37/63 | tokens=512 | tau=1.50 | time=11.0s | <think> Okay, so I need to find the minimum value of the expression $(a + b + c ...
  [GPU 5] Sample 37/62 | tokens=512 | tau=1.53 | time=10.9s | <think> Okay, so I need to find all values of p that satisfy both inequalities: ...
  [GPU 0] Sample 37/63 | tokens=512 | tau=1.67 | time=9.9s | <think> Okay, so I need to find the distance between two parallel lines. Let me ...
  [GPU 6] Sample 36/62 | tokens=512 | tau=1.54 | time=11.0s | <think> Okay, so I need to compute the sum over all triples (a, b, c) of positiv...
  [GPU 4] Sample 39/62 | tokens=512 | tau=1.43 | time=11.4s | <think> Okay, so I need to find the surface area of one of the pieces created wh...
  [GPU 3] Sample 37/63 | tokens=512 | tau=1.50 | time=11.0s | <think> Okay, so I need to figure out how many integer coordinate points are str...
  [GPU 2] Sample 37/63 | tokens=512 | tau=1.73 | time=9.6s | <think> Okay, so I need to find the value of r that satisfies the equation (6r² ...
  [GPU 7] Sample 38/62 | tokens=512 | tau=1.41 | time=11.6s | <think> Okay, so I need to find the area of triangle ACD in this trapezoid ABCD ...
  [GPU 5] Sample 38/62 | tokens=512 | tau=1.57 | time=10.4s | <think> Okay, so I need to figure out the average price of Juan's stamps from th...
  [GPU 1] Sample 38/63 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to figure out the smallest number of leaves in a book wh...
  [GPU 0] Sample 38/63 | tokens=512 | tau=1.55 | time=10.6s | <think> Okay, so I need to figure out which of these equations has the largest s...
  [GPU 6] Sample 37/62 | tokens=512 | tau=1.60 | time=10.6s | <think> Okay, so I need to find three consecutive positive integers where their ...
  [GPU 4] Sample 40/62 | tokens=512 | tau=1.58 | time=10.3s | <think> Okay, so I need to factor the quadratic expression $10x^2 - x - 24$ into...
  [GPU 2] Sample 38/63 | tokens=512 | tau=1.81 | time=9.2s | <think> Okay, so I need to compute the cross product (2b - a) × (3c + a). The pr...
  [GPU 3] Sample 38/63 | tokens=512 | tau=1.60 | time=10.3s | <think> Okay, so I need to figure out how many integer coordinates are strictly ...
  [GPU 7] Sample 39/62 | tokens=512 | tau=1.63 | time=10.0s | <think> Okay, so I need to find the value of n where the sum 1 + 12 + 123 + 1234...
  [GPU 1] Sample 39/63 | tokens=512 | tau=1.58 | time=10.4s | <think> Okay, so I need to solve the equation √(2x)/√(3x - 1) = 3/2. Hmm, let me...
  [GPU 5] Sample 39/62 | tokens=512 | tau=1.44 | time=11.5s | <think> Okay, so I need to find the least possible sum of a set of distinct posi...
  [GPU 0] Sample 39/63 | tokens=512 | tau=1.81 | time=9.2s | <think> Okay, so I need to find the minimum value of the function $\frac{(x + 5)...
  [GPU 6] Sample 38/62 | tokens=512 | tau=1.57 | time=10.7s | <think> Okay, so I need to figure out how many digits repeat in the decimal expa...
  [GPU 2] Sample 39/63 | tokens=512 | tau=1.66 | time=10.1s | <think> Okay, so I need to find the number of quadratic equations of the form $x...
  [GPU 4] Sample 41/62 | tokens=512 | tau=1.43 | time=11.4s | <think> Okay, so I need to find the measure of angle ADC in this diagram with tw...
  [GPU 3] Sample 39/63 | tokens=512 | tau=1.45 | time=11.4s | <think> Okay, so I need to find the range of the function y = log base 2 of the ...
  [GPU 7] Sample 40/62 | tokens=512 | tau=1.58 | time=10.4s | <think> Okay, so I need to solve the equation |x - 4| - 10 = 2 and find the prod...
  [GPU 1] Sample 40/63 | tokens=512 | tau=1.46 | time=11.4s | <think> Okay, so Charlie is riding his unicycle, and I need to figure out the sp...
  [GPU 0] Sample 40/63 | tokens=512 | tau=1.55 | time=10.7s | <think> Okay, so I need to solve the inequality 1 divided by (x minus 5) is grea...
  [GPU 5] Sample 40/62 | tokens=512 | tau=1.47 | time=11.3s | <think> Okay, so I need to find the degree of the polynomial p(x) given by that ...
  [GPU 2] Sample 40/63 | tokens=512 | tau=1.60 | time=10.5s | <think> Okay, so I need to figure out where the point (0,0) ends up after two re...
  [GPU 6] Sample 39/62 | tokens=512 | tau=1.42 | time=11.9s | <think> Okay, so I need to figure out the value of this operation @ between two ...
  [GPU 4] Sample 42/62 | tokens=512 | tau=1.48 | time=11.1s | <think> Okay, so I need to find the minimum value of (x + y)(y + z) given that x...
  [GPU 3] Sample 40/63 | tokens=512 | tau=1.60 | time=10.4s | <think> Okay, so I need to find positive integers a, b, and 2009, where a < b < ...
  [GPU 7] Sample 41/62 | tokens=512 | tau=1.47 | time=11.2s | <think> Okay, so I need to find P(5) where P(x) is a monic cubic polynomial. Let...
  [GPU 0] Sample 41/63 | tokens=512 | tau=1.53 | time=10.9s | <think> Okay, so I need to find cos(angle RPS) given that sin(angle RPQ) is 7/25...
  [GPU 5] Sample 41/62 | tokens=512 | tau=1.57 | time=10.6s | <think> Okay, so I need to figure out how many cylindrical beakers it takes to f...
  [GPU 1] Sample 41/63 | tokens=512 | tau=1.39 | time=11.9s | <think> Okay, so there's this robot that moves at a constant speed. It takes 2.5...
  [GPU 2] Sample 41/63 | tokens=512 | tau=1.60 | time=10.5s | <think> Okay, so I need to find the value of $ b $ given the functions $ f(x) = ...
  [GPU 4] Sample 43/62 | tokens=512 | tau=1.59 | time=10.4s | <think> Okay, so I need to find the angle between vectors a and a - b. The probl...
  [GPU 6] Sample 40/62 | tokens=512 | tau=1.58 | time=10.7s | <think> Okay, so I need to combine these two fractions into a single fraction. T...
  [GPU 7] Sample 42/62 | tokens=512 | tau=1.67 | time=9.8s | <think> Okay, so I need to find the remainder when the 100th term of the Fibonac...
  [GPU 3] Sample 41/63 | tokens=512 | tau=1.47 | time=11.3s | <think> Okay, so I need to find the probability that two segments AB and CD inte...
  [GPU 5] Sample 42/62 | tokens=512 | tau=1.68 | time=10.0s | <think> Okay, so I need to find the value of $ b $ in the continued fraction exp...
  [GPU 0] Sample 42/63 | tokens=512 | tau=1.57 | time=10.7s | <think> Okay, so I need to figure out how many distinct values the function $ f(...
  [GPU 1] Sample 42/63 | tokens=512 | tau=1.43 | time=11.5s | <think> Okay, so I need to figure out the bicycle's speed in inches per second w...
  [GPU 2] Sample 42/63 | tokens=512 | tau=1.49 | time=11.3s | <think> Okay, so I need to figure out how many ways we can form a subcommittee o...
  [GPU 4] Sample 44/62 | tokens=512 | tau=1.63 | time=10.1s | <think> Okay, so I need to compute the binomial coefficient $\dbinom{31}{28}$. H...
  [GPU 6] Sample 41/62 | tokens=512 | tau=1.56 | time=10.8s | <think> Okay, so I need to evaluate this expression: sin(arcsin 0.4 + arcsin 0.5...
  [GPU 7] Sample 43/62 | tokens=512 | tau=1.47 | time=11.2s | <think> Okay, so I need to figure out how many different license plates can be m...
  [GPU 3] Sample 42/63 | tokens=512 | tau=1.46 | time=11.3s | <think> Okay, so I need to simplify this expression: the square root of a fracti...
  [GPU 5] Sample 43/62 | tokens=512 | tau=1.52 | time=10.9s | <think> Okay, so I need to find the smallest number that is one less than twice ...
  [GPU 0] Sample 43/63 | tokens=512 | tau=1.51 | time=11.0s | <think> Okay, so I need to find the value of 513 squared minus 487 squared. Hmm,...
  [GPU 1] Sample 43/63 | tokens=512 | tau=1.50 | time=11.1s | <think> Okay, so I need to find three consecutive integers whose product is 120,...
  [GPU 4] Sample 45/62 | tokens=512 | tau=1.56 | time=10.6s | <think> Okay, so I need to find all real numbers x such that -4 < x⁴ + 4x² < 21....
  [GPU 2] Sample 43/63 | tokens=512 | tau=1.51 | time=11.0s | <think> Okay, so I need to figure out what 999 in base 10 is in base six. Hmm, l...
  [GPU 6] Sample 42/62 | tokens=512 | tau=1.56 | time=10.8s | <think> Okay, so I need to find the value of the product abc given these three e...
  [GPU 7] Sample 44/62 | tokens=512 | tau=1.63 | time=10.1s | <think> Okay, so I need to simplify this product of cosines: cos(2π/15) * cos(4π...
  [GPU 3] Sample 43/63 | tokens=512 | tau=1.42 | time=11.6s | <think> Okay, so I need to figure out how to express a + b + c + d + e + f in te...
  [GPU 0] Sample 44/63 | tokens=512 | tau=1.50 | time=11.1s | <think> Okay, so I need to find the value of 'a' that makes the function f(n) co...
  [GPU 5] Sample 44/62 | tokens=512 | tau=1.40 | time=11.8s | <think> Okay, so I need to figure out how many ways 8 people can be seated aroun...
  [GPU 1] Sample 44/63 | tokens=512 | tau=1.58 | time=10.6s | <think> Okay, let me try to figure out this problem. So, the question is: If t(x...
  [GPU 4] Sample 46/62 | tokens=512 | tau=1.62 | time=10.2s | <think> Okay, so I need to figure out the equation of the set of image points af...
  [GPU 2] Sample 44/63 | tokens=512 | tau=1.61 | time=10.4s | <think> Okay, so I need to solve this equation: the cube root of (x squared minu...
  [GPU 7] Sample 45/62 | tokens=512 | tau=1.73 | time=9.5s | <think> Okay, so I need to find the value of $ xy + yz + zx $ given these three ...
  [GPU 6] Sample 43/62 | tokens=512 | tau=1.59 | time=10.7s | <think> Okay, so I need to find an integer x that satisfies the inequality 1/4 <...
  [GPU 3] Sample 44/63 | tokens=512 | tau=1.76 | time=9.3s | <think> Okay, so I need to simplify this algebraic expression: 4 times (3r³ + 5r...
  [GPU 0] Sample 45/63 | tokens=512 | tau=1.52 | time=10.9s | <think> Okay, so I need to find the perimeter of triangle ABC, which is isoscele...
  [GPU 5] Sample 45/62 | tokens=512 | tau=1.55 | time=10.8s | <think> Okay, so I need to figure out how many possible values of x there are wh...
  [GPU 1] Sample 45/63 | tokens=512 | tau=1.40 | time=11.8s | <think> Okay, so I need to figure out how many ways I can stack my 6 different b...
  [GPU 4] Sample 47/62 | tokens=512 | tau=1.48 | time=11.1s | <think> Okay, so I need to find the measure of angle BAC in this diagram. Let me...
  [GPU 2] Sample 45/63 | tokens=512 | tau=1.51 | time=11.1s | <think> Okay, so I need to find the median of 27 consecutive positive integers w...
  [GPU 7] Sample 46/62 | tokens=512 | tau=1.57 | time=10.5s | <think> Okay, so I need to find $ f^{-1}(f^{-1}(6)) $. Let me start by recalling...
  [GPU 3] Sample 45/63 | tokens=512 | tau=1.77 | time=9.4s | <think> Okay, so I need to find the minimum value of this expression:   $$ \frac...
  [GPU 6] Sample 44/62 | tokens=512 | tau=1.57 | time=10.8s | <think> Okay, so I need to find the units digit of 18 raised to the 6th power. H...
  [GPU 5] Sample 46/62 | tokens=512 | tau=1.80 | time=9.3s | <think> Okay, so I need to figure out how many possible values there are for $ a...
  [GPU 0] Sample 46/63 | tokens=512 | tau=1.67 | time=9.9s | <think> Okay, so I need to find the value of b in the direction vector of the li...
  [GPU 1] Sample 46/63 | tokens=512 | tau=1.63 | time=10.3s | <think> Okay, so I need to find the side length of an equilateral triangle inscr...
  [GPU 4] Sample 48/62 | tokens=512 | tau=1.60 | time=10.3s | <think> Okay, so I need to solve the inequality $\frac{|x^2 - 81|}{x^2 - 36x} < ...
  [GPU 7] Sample 47/62 | tokens=512 | tau=1.61 | time=10.2s | <think> Okay, so I need to find the sum of the positive divisors of 500, which i...
  [GPU 2] Sample 46/63 | tokens=512 | tau=1.60 | time=10.5s | <think> Okay, so there's this problem about two candidates running for class pre...
  [GPU 6] Sample 45/62 | tokens=512 | tau=1.61 | time=10.5s | <think> Okay, so I need to figure out what kind of graph the equation $\left(\fr...
  [GPU 3] Sample 46/63 | tokens=512 | tau=1.44 | time=11.5s | <think> Okay, so I need to solve this equation: Three plus the reciprocal of a n...
  [GPU 5] Sample 47/62 | tokens=512 | tau=1.63 | time=10.3s | <think> Okay, so William Sydney Porter tried to calculate (-3 + 4i) divided by (...
  [GPU 0] Sample 47/63 | tokens=512 | tau=1.53 | time=10.9s | <think> Okay, so I need to find the greatest possible perimeter of a triangle wh...
  [GPU 1] Sample 47/63 | tokens=512 | tau=1.60 | time=10.3s | <think> Okay, so I need to find the area of this trapezoid. Let me recall the fo...
  [GPU 4] Sample 49/62 | tokens=512 | tau=1.59 | time=10.3s | <think> Okay, so I need to find the smallest real number x in the domain of the ...
  [GPU 7] Sample 48/62 | tokens=512 | tau=1.61 | time=10.2s | <think> Okay, so I need to solve the inequality $ x^2 - 5x - 4 \leq 10 $. Let me...
  [GPU 2] Sample 47/63 | tokens=512 | tau=1.46 | time=11.5s | <think> Okay, so I need to find the dot product of these two vectors: the first ...
  [GPU 6] Sample 46/62 | tokens=512 | tau=1.46 | time=11.6s | <think> Okay, so I need to find the modulo 7 remainder of the sum of all the odd...
  [GPU 3] Sample 47/63 | tokens=512 | tau=1.48 | time=11.1s | <think> Okay, so I need to find the largest possible value of |a| + |b| + |c| gi...
  [GPU 5] Sample 48/62 | tokens=512 | tau=1.57 | time=10.5s | <think> Okay, so I need to find the probability that a triangle with sides of le...
  [GPU 0] Sample 48/63 | tokens=512 | tau=1.76 | time=9.4s | <think> Okay, so I need to find the coordinates of point P on the line y = -x + ...
  [GPU 7] Sample 49/62 | tokens=512 | tau=1.61 | time=10.2s | <think> Okay, so I need to find the inverse function values for f(x) at 0 and 6,...
  [GPU 1] Sample 48/63 | tokens=512 | tau=1.43 | time=11.5s | <think> Okay, so I need to find the units digit of 4$, which is defined as a sup...
  [GPU 4] Sample 50/62 | tokens=512 | tau=1.56 | time=10.5s | <think> Okay, so I need to find the area of the gray piece in this tangram puzzl...
  [GPU 2] Sample 48/63 | tokens=512 | tau=1.67 | time=9.9s | <think> Okay, so I need to figure out how many two-digit prime numbers have digi...
  [GPU 3] Sample 48/63 | tokens=512 | tau=1.55 | time=10.6s | <think> Okay, so I need to figure out for which grade the number of male bus rid...
  [GPU 6] Sample 47/62 | tokens=512 | tau=1.57 | time=10.8s | <think> Okay, so I need to figure out the difference between the positive square...
  [GPU 5] Sample 49/62 | tokens=512 | tau=1.48 | time=11.2s | <think> Okay, so I need to find sin T in triangle RST. They told me that sin R i...
  [GPU 0] Sample 49/63 | tokens=512 | tau=1.41 | time=11.7s | <think> Okay, so I need to simplify this expression: 19x plus 1 minus 4x minus 8...
  [GPU 1] Sample 49/63 | tokens=512 | tau=1.59 | time=10.4s | <think> Okay, let's see. Kathy has $300 in the bank, and she wants to withdraw h...
  [GPU 4] Sample 51/62 | tokens=512 | tau=1.52 | time=10.7s | <think> Okay, so Roslyn has ten boxes total. Let me try to figure out how many b...
  [GPU 7] Sample 50/62 | tokens=512 | tau=1.46 | time=11.2s | <think> Okay, so I need to add 313.9 and 12.6 together. Let me think about how t...
  [GPU 2] Sample 49/63 | tokens=512 | tau=1.57 | time=10.6s | <think> Okay, so I need to figure out how many integers satisfy the inequality |...
  [GPU 6] Sample 48/62 | tokens=512 | tau=1.61 | time=10.6s | <think> Okay, so I need to find the largest possible area of a rectangular field...
  [GPU 3] Sample 49/63 | tokens=512 | tau=1.47 | time=11.2s | <think> Okay, so I need to find the value of f(-2) for the function f(x) = 5x² +...
  [GPU 0] Sample 50/63 | tokens=512 | tau=1.67 | time=9.9s | <think> Okay, so I need to find the distance from point P to the sixth vertex of...
  [GPU 5] Sample 50/62 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to solve this equation: 3x + 2(1 + x) = 17, and then fin...
  [GPU 1] Sample 50/63 | tokens=512 | tau=1.65 | time=10.0s | <think> Okay, so I need to figure out the ratio of the acceleration of Jen's sof...
  [GPU 4] Sample 52/62 | tokens=512 | tau=1.60 | time=10.2s | <think> Okay, so I need to find P(16) where P(x) is a quadratic polynomial that'...
  [GPU 2] Sample 50/63 | tokens=512 | tau=1.61 | time=10.4s | <think> Okay, so I need to figure out the value of x that Archimedes should choo...
  [GPU 7] Sample 51/62 | tokens=512 | tau=1.47 | time=11.2s | <think> Okay, so I need to find the value of the inverse function of f at 1/5, w...
  [GPU 6] Sample 49/62 | tokens=512 | tau=1.72 | time=9.9s | <think> Okay, so I need to find the smallest distance between the origin and a p...
  [GPU 3] Sample 50/63 | tokens=512 | tau=1.43 | time=11.4s | <think> Okay, so I need to find the value of this expression: (16 times the cube...
  [GPU 0] Sample 51/63 | tokens=512 | tau=1.52 | time=10.9s | <think> Okay, so I need to find the radius of the smaller semicircle in this cir...
  [GPU 5] Sample 51/62 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to figure out how many ways 3 people can be assigned to ...
  [GPU 1] Sample 51/63 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to find the maximum value of the expression |1 + z| + |1...
  [GPU 4] Sample 53/62 | tokens=512 | tau=1.56 | time=10.6s | <think> Okay, so I need to find the projection of vector a onto vector b. The pr...
  [GPU 7] Sample 52/62 | tokens=512 | tau=1.54 | time=10.7s | <think> Okay, so I need to find the remainder when $129^{34} + 96^{38}$ is divid...
  [GPU 6] Sample 50/62 | tokens=512 | tau=1.62 | time=10.4s | <think> Okay, so Navin, Luka, and Ian are talking about their part-time jobs, an...
  [GPU 2] Sample 51/63 | tokens=512 | tau=1.39 | time=12.1s | <think> Okay, so I need to figure out what happens when I rotate the complex num...
  [GPU 3] Sample 51/63 | tokens=512 | tau=1.56 | time=10.5s | <think> Okay, so I need to figure out how many of the same digits are found in t...
  [GPU 0] Sample 52/63 | tokens=512 | tau=1.68 | time=9.9s | <think> Okay, so I need to figure out where the reflection takes the vector $\be...
  [GPU 5] Sample 52/62 | tokens=512 | tau=1.45 | time=11.5s | <think> Okay, so I need to simplify this expression: (10r³)(4r⁶) divided by 8r⁴....
  [GPU 1] Sample 52/63 | tokens=512 | tau=1.70 | time=9.7s | <think> Okay, so I need to find the distance between the foci of a hyperbola. Th...
  [GPU 4] Sample 54/62 | tokens=512 | tau=1.55 | time=10.6s | <think> Okay, so I need to find the minimum value of the expression $\frac{1}{a}...
  [GPU 7] Sample 53/62 | tokens=512 | tau=1.61 | time=10.2s | <think> Okay, so I need to find the largest integer less than 2010 that satisfie...
  [GPU 2] Sample 52/63 | tokens=512 | tau=1.64 | time=10.3s | <think> Okay, so I need to figure out the units digit N of the number 21420N suc...
  [GPU 6] Sample 51/62 | tokens=512 | tau=1.53 | time=11.1s | <think> Okay, so I need to find the remainder when 2004 is divided by 12. Hmm, l...
  [GPU 3] Sample 52/63 | tokens=512 | tau=1.48 | time=11.1s | <think> Okay, so there's this problem about six witches and ten sorcerers at an ...
  [GPU 0] Sample 53/63 | tokens=512 | tau=1.36 | time=12.2s | <think> Okay, so I need to compute the value of sin³18° + sin²18°. Hmm, let me t...
  [GPU 5] Sample 53/62 | tokens=512 | tau=1.57 | time=10.6s | <think> Okay, so I need to solve this equation: arccos x + arccos 2x + arccos 3x...
  [GPU 1] Sample 53/63 | tokens=512 | tau=1.57 | time=10.5s | <think> Okay, so I need to find the sum of the coefficients of the polynomial g(...
  [GPU 7] Sample 54/62 | tokens=512 | tau=1.79 | time=9.2s | <think> Okay, so I need to find the range of the function $ f(x) = (\arccos x)^2...
  [GPU 4] Sample 55/62 | tokens=512 | tau=1.49 | time=11.0s | <think> Okay, so I need to find the number of dice, n, such that when you roll n...
  [GPU 2] Sample 53/63 | tokens=512 | tau=1.64 | time=10.3s | <think> Okay, so I need to find the shortest distance from the point (6, 0) to t...
  [GPU 6] Sample 52/62 | tokens=512 | tau=1.56 | time=10.9s | <think> Okay, so I need to solve this equation: (3)5² - 4(5 - a)² ÷ 3 = 63. Hmm,...
  [GPU 3] Sample 53/63 | tokens=512 | tau=1.62 | time=10.3s | <think> Okay, so I need to find a vector v such that when I take the cross produ...
  [GPU 5] Sample 54/62 | tokens=512 | tau=1.76 | time=9.4s | <think> Okay, so I need to find the minimum value of $ a^4 + b^8 $ given that $ ...
  [GPU 0] Sample 54/63 | tokens=512 | tau=1.51 | time=11.0s | <think> Okay, so I need to solve this problem where y varies inversely as the sq...
  [GPU 7] Sample 55/62 | tokens=512 | tau=1.54 | time=10.6s | <think> Okay, so I need to find the quotient when x^9 + 1 is divided by x - 1. H...
  [GPU 1] Sample 54/63 | tokens=512 | tau=1.40 | time=11.8s | <think> Okay, so I need to find an expression for AF² + BF² + CF² in terms of th...
  [GPU 4] Sample 56/62 | tokens=512 | tau=1.45 | time=11.3s | <think> Okay, so I need to find the probability that a randomly chosen point ins...
  [GPU 6] Sample 53/62 | tokens=512 | tau=1.75 | time=9.6s | <think> Okay, so I need to find the unordered set containing the three expressio...
  [GPU 2] Sample 54/63 | tokens=512 | tau=1.53 | time=10.9s | <think> Okay, so I need to find the length of the diagonal of a square when it h...
  [GPU 3] Sample 54/63 | tokens=512 | tau=1.75 | time=9.4s | <think> Okay, so I need to figure out the cost of a pencil in cents. The problem...
  [GPU 5] Sample 55/62 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to figure out the value of the square symbol, which is r...
  [GPU 0] Sample 55/63 | tokens=512 | tau=1.58 | time=10.5s | <think> Okay, so I need to solve this recurrence relation problem. Let me first ...
  [GPU 7] Sample 56/62 | tokens=512 | tau=1.58 | time=10.4s | <think> Okay, so there's this problem about thirty-five students attending a mat...
  [GPU 4] Sample 57/62 | tokens=512 | tau=1.64 | time=10.0s | <think> Okay, so I need to solve this problem about a two-digit number. Let me r...
  [GPU 1] Sample 55/63 | tokens=512 | tau=1.43 | time=11.7s | <think> Okay, so I need to convert the fraction 57/160 into a terminating decima...
  [GPU 2] Sample 55/63 | tokens=512 | tau=1.50 | time=11.1s | <think> Okay, so I need to find the area of an isosceles right triangle where th...
  [GPU 3] Sample 55/63 | tokens=512 | tau=1.57 | time=10.4s | <think> Okay, so I need to find the domain of the function f(x) = (2x - 7)/√(x² ...
  [GPU 6] Sample 54/62 | tokens=512 | tau=1.42 | time=11.8s | <think> Okay, so I need to figure out what 9 divided by 2 is as a decimal. Hmm, ...
  [GPU 5] Sample 56/62 | tokens=512 | tau=1.57 | time=10.6s | <think> Okay, so I need to find the area of the quadrilateral formed by the four...
  [GPU 0] Sample 56/63 | tokens=512 | tau=1.67 | time=9.9s | <think> Okay, so I need to simplify this expression: (u + 4)(u - 1) minus (u - 3...
  [GPU 7] Sample 57/62 | tokens=512 | tau=1.45 | time=11.4s | <think> Okay, so I need to figure out how many ways 5 students can be selected f...
  [GPU 1] Sample 56/63 | tokens=512 | tau=1.70 | time=9.8s | <think> Okay, so Karla drove her vehicle 12,000 miles last year. The question is...
  [GPU 4] Sample 58/62 | tokens=512 | tau=1.59 | time=10.3s | <think> Okay, so I need to find the measure of angle STR in this diagram. Let me...
  [GPU 2] Sample 56/63 | tokens=512 | tau=1.57 | time=10.8s | <think> Okay, so I need to find the square root of f(f(f(f(1)))) where f(x) is 2...
  [GPU 6] Sample 55/62 | tokens=512 | tau=1.59 | time=10.6s | <think> Okay, so I need to find the last nonzero digit to the right of the decim...
  [GPU 3] Sample 56/63 | tokens=512 | tau=1.53 | time=10.7s | <think> Okay, so I need to find the integer value of x in the arithmetic sequenc...
  [GPU 5] Sample 57/62 | tokens=512 | tau=1.55 | time=10.7s | <think> Okay, so I need to figure out how many representatives the 8th grade sho...
  [GPU 0] Sample 57/63 | tokens=512 | tau=1.44 | time=11.4s | <think> Okay, so I need to find the inverse of 17 modulo 83. That means I need t...
  [GPU 7] Sample 58/62 | tokens=512 | tau=1.53 | time=10.7s | <think> Okay, so I need to figure out for how many values of x the expression (x...
  [GPU 4] Sample 59/62 | tokens=512 | tau=1.49 | time=11.0s | <think> Okay, so I need to figure out how many integer values of t satisfy the c...
  [GPU 1] Sample 57/63 | tokens=512 | tau=1.48 | time=11.2s | <think> Okay, so I need to figure out the value of 5 star 1, where the operation...
  [GPU 6] Sample 56/62 | tokens=512 | tau=1.61 | time=10.5s | <think> Okay, so I need to find the value of n such that the sum of the first n ...
  [GPU 3] Sample 57/63 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to figure out how many inches on the map correspond to 5...
  [GPU 2] Sample 57/63 | tokens=512 | tau=1.50 | time=11.3s | <think> Okay, so I need to find the average of the two smallest positive integer...
  [GPU 5] Sample 58/62 | tokens=512 | tau=1.59 | time=10.4s | <think> Okay, so I need to find the value of this function f(n) at three differe...
  [GPU 0] Sample 58/63 | tokens=512 | tau=1.64 | time=10.2s | <think> Okay, so I need to find all the integer roots of the polynomial equation...
  [GPU 7] Sample 59/62 | tokens=512 | tau=1.60 | time=10.3s | <think> Okay, so I need to find the class average for this test. Let me think. T...
  [GPU 4] Sample 60/62 | tokens=512 | tau=1.51 | time=10.8s | <think> Okay, so Jim and Martha are at the corner of a rectangular field. The fi...
  [GPU 1] Sample 58/63 | tokens=512 | tau=1.43 | time=11.6s | <think> Okay, so I need to figure out the remainder when 54 is divided by 6. Let...
  [GPU 6] Sample 57/62 | tokens=512 | tau=1.72 | time=9.8s | <think> Okay, so I need to find the image of the line y = 2x + 1 under the matri...
  [GPU 3] Sample 58/63 | tokens=512 | tau=1.66 | time=9.9s | <think> Okay, so I need to figure out the cost of a 3-inch cube made of fake gol...
  [GPU 2] Sample 58/63 | tokens=512 | tau=1.45 | time=11.6s | <think> Okay, let me try to figure out this problem. So, the question is about h...
  [GPU 5] Sample 59/62 | tokens=512 | tau=1.60 | time=10.4s | <think> Okay, so I need to evaluate the ceiling of the square root of 20, and th...
  [GPU 0] Sample 59/63 | tokens=512 | tau=1.54 | time=10.8s | <think> Okay, so I need to solve this system of logarithmic equations:  First eq...
  [GPU 7] Sample 60/62 | tokens=512 | tau=1.56 | time=10.6s | <think> Okay, so I need to figure out for which prime numbers p the congruence 8...
  [GPU 4] Sample 61/62 | tokens=512 | tau=1.61 | time=10.2s | <think> Okay, so I need to solve this equation: √(x + √(3x + 6)) + √(x - √(3x + ...
  [GPU 6] Sample 58/62 | tokens=512 | tau=1.77 | time=9.6s | <think> Okay, so Linda, Sherry, June, and Connie sold cookies and earned differe...
  [GPU 1] Sample 59/63 | tokens=512 | tau=1.53 | time=10.9s | <think> Okay, so I need to figure out the fifth number in the list of positive i...
  [GPU 3] Sample 59/63 | tokens=512 | tau=1.61 | time=10.2s | <think> Okay, so I need to find the area of the shaded triangle in the diagram. ...
  [GPU 2] Sample 59/63 | tokens=512 | tau=1.69 | time=10.0s | <think> Okay, so I need to find the sum of all possible values of θ where re^{iθ...
  [GPU 5] Sample 60/62 | tokens=512 | tau=1.55 | time=10.8s | <think> Okay, so I need to figure out how many distinct possible values there ar...
  [GPU 0] Sample 60/63 | tokens=512 | tau=1.48 | time=11.2s | <think> Okay, so I need to figure out how far a car would travel if it's going 5...
  [GPU 7] Sample 61/62 | tokens=512 | tau=1.47 | time=11.2s | <think> Okay, so I need to figure out the remainder when the sum of numbers from...
  [GPU 4] Sample 62/62 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to find the equation of a line that consists of all vect...
  [GPU 6] Sample 59/62 | tokens=512 | tau=1.50 | time=11.3s | <think> Okay, so I need to find the maximum value of the expression $ ab^2 c^3 d...
  [GPU 1] Sample 60/63 | tokens=512 | tau=1.50 | time=11.1s | <think> Okay, so I need to figure out the value of n in this magic square. Let m...
  [GPU 3] Sample 60/63 | tokens=512 | tau=1.54 | time=10.7s | <think> Okay, so I need to solve this problem about an unfair six-sided die. Let...
  [GPU 2] Sample 60/63 | tokens=512 | tau=1.53 | time=11.0s | <think> Okay, so I need to find the value of this product of logarithms: log bas...
  [GPU 5] Sample 61/62 | tokens=512 | tau=1.59 | time=10.4s | <think> Okay, so I need to figure out the shortest distance you can travel if yo...
  [GPU 0] Sample 61/63 | tokens=512 | tau=1.52 | time=10.9s | <think> Okay, so I need to find all possible values of the expression $\frac{1}{...
  [GPU 7] Sample 62/62 | tokens=512 | tau=1.62 | time=10.1s | <think> Okay, so I need to find the domain of the function f(x) = (2 - x) / log(...
  [GPU 6] Sample 60/62 | tokens=512 | tau=1.75 | time=9.6s | <think> Okay, so I need to find the sum of all complex solutions to this equatio...
  [GPU 1] Sample 61/63 | tokens=512 | tau=1.76 | time=9.4s | <think> Okay, so I need to simplify this big fraction where the numerator is the...
  [GPU 3] Sample 61/63 | tokens=512 | tau=1.64 | time=10.0s | <think> Okay, so I need to find tan A for triangle ABC, given that the area of t...
  [GPU 2] Sample 61/63 | tokens=512 | tau=1.44 | time=11.6s | <think> Okay, so I need to find the probability that the reciprocal of a randoml...
  [GPU 5] Sample 62/62 | tokens=512 | tau=1.83 | time=9.0s | <think> Okay, so I need to figure out the value of $(\sqrt{2} + \sqrt{3})^3$ and...
  [GPU 0] Sample 62/63 | tokens=512 | tau=1.55 | time=10.6s | <think> Okay, so I need to figure out the original price of the shirt when the s...
  [GPU 1] Sample 62/63 | tokens=512 | tau=1.51 | time=10.9s | <think> Okay, so I need to find the minimum value of the function f(x) = |x - p|...
  [GPU 6] Sample 61/62 | tokens=512 | tau=1.46 | time=11.5s | <think> Okay, so I need to figure out the volume of a cube from which a steel sp...
  [GPU 3] Sample 62/63 | tokens=512 | tau=1.51 | time=10.8s | <think> Okay, so Tom has this Mr. Potato Head, and he wants to figure out how ma...
  [GPU 2] Sample 62/63 | tokens=512 | tau=1.57 | time=10.6s | <think> Okay, so I need to find the least possible value of |a_{n-1}| for a poly...
  [GPU 0] Sample 63/63 | tokens=512 | tau=1.62 | time=10.1s | <think> Okay, so I need to find the modulus of this complex number w, which is g...
  [GPU 6] Sample 62/62 | tokens=512 | tau=1.62 | time=10.3s | <think> Okay, so I need to find the area of the set S, which consists of points ...
  [GPU 1] Sample 63/63 | tokens=512 | tau=1.43 | time=11.5s | <think> Okay, so I need to find the area of an equiangular octagon that has four...
  [GPU 3] Sample 63/63 | tokens=512 | tau=1.37 | time=12.0s | <think> Okay, so I need to find the measure of angle AHB in triangle ABC where A...
  [GPU 2] Sample 63/63 | tokens=512 | tau=1.71 | time=9.9s | <think> Okay, so I need to solve this problem where there's a sequence defined b...

============================================================
RESULTS SUMMARY
============================================================
  Denoise steps:              1
  GPUs used:                  8
  Samples evaluated:          500
  Total blocks:               164810
  Total generated tokens:     256000
  Total GPU-time:             5343.68s
  Wall-clock time (approx):   12.86s
  ---
  Avg acceptance length (tau): 1.55
  Median acceptance length:    1.0
  Per-sample avg tau:          ['1.45', '1.47', '1.54', '1.71', '1.43', '1.56', '1.47', '1.60', '1.46', '1.52', '1.67', '1.44', '1.81', '1.80', '1.55', '1.39', '1.39', '1.60', '1.52', '1.42', '1.53', '1.51', '1.42', '1.61', '1.46', '1.53', '1.57', '1.48', '1.67', '1.50', '1.53', '1.67', '1.55', '1.50', '1.67', '1.70', '1.67', '1.55', '1.81', '1.55', '1.53', '1.57', '1.51', '1.50', '1.52', '1.67', '1.53', '1.76', '1.41', '1.67', '1.52', '1.68', '1.36', '1.51', '1.58', '1.67', '1.44', '1.64', '1.54', '1.48', '1.52', '1.55', '1.62', '1.60', '1.49', '1.49', '1.70', '1.49', '1.39', '1.65', '1.51', '1.40', '1.51', '1.61', '1.94', '1.46', '1.82', '1.57', '1.50', '1.52', '1.59', '1.57', '1.51', '1.54', '1.46', '1.64', '1.45', '1.51', '1.50', '1.83', '1.52', '1.76', '1.50', '1.50', '1.52', '1.54', '1.71', '1.59', '1.54', '1.50', '1.51', '1.58', '1.46', '1.39', '1.43', '1.50', '1.58', '1.40', '1.63', '1.60', '1.43', '1.59', '1.65', '1.51', '1.70', '1.57', '1.40', '1.43', '1.70', '1.48', '1.43', '1.53', '1.50', '1.76', '1.51', '1.43', '1.68', '1.54', '1.54', '1.40', '1.64', '1.58', '1.54', '1.74', '1.60', '1.70', '1.71', '1.31', '1.53', '1.58', '1.68', '1.71', '1.41', '1.49', '1.38', '1.51', '1.53', '1.62', '1.59', '1.50', '1.50', '1.39', '1.50', '1.48', '1.51', '1.63', '1.41', '1.51', '1.55', '1.49', '1.42', '1.97', '1.73', '1.81', '1.66', '1.60', '1.60', '1.49', '1.51', '1.61', '1.51', '1.60', '1.46', '1.67', '1.57', '1.61', '1.39', '1.64', '1.64', '1.53', '1.50', '1.57', '1.50', '1.45', '1.69', '1.53', '1.44', '1.57', '1.71', '1.48', '1.48', '1.45', '1.52', '1.64', '1.85', '1.53', '1.59', '1.55', '1.51', '1.40', '1.52', '1.64', '1.87', '1.50', '1.51', '1.53', '1.69', '1.48', '1.56', '1.65', '1.45', '1.61', '1.58', '1.60', '1.76', '1.50', '1.63', '1.39', '1.61', '1.51', '1.60', '1.47', '1.43', '1.56', '1.51', '1.50', '1.60', '1.45', '1.60', '1.47', '1.46', '1.42', '1.76', '1.77', '1.44', '1.48', '1.55', '1.47', '1.43', '1.56', '1.48', '1.62', '1.75', '1.57', '1.53', '1.51', '1.66', '1.61', '1.54', '1.64', '1.51', '1.37', '1.62', '1.68', '1.48', '1.51', '1.91', '1.61', '1.63', '1.64', '1.55', '1.46', '1.81', '1.50', '1.36', '1.57', '1.55', '1.63', '1.58', '1.62', '1.51', '1.65', '1.43', '1.68', '1.61', '2.00', '1.50', '1.56', '1.65', '1.56', '1.91', '1.62', '1.64', '1.62', '1.59', '1.57', '1.55', '1.82', '2.07', '1.43', '1.43', '1.58', '1.43', '1.48', '1.59', '1.63', '1.56', '1.62', '1.48', '1.60', '1.59', '1.56', '1.52', '1.60', '1.56', '1.55', '1.49', '1.45', '1.64', '1.59', '1.49', '1.51', '1.61', '1.51', '1.54', '1.43', '1.65', '1.55', '1.45', '1.45', '1.50', '1.71', '1.69', '1.46', '1.54', '1.67', '1.66', '1.74', '1.47', '1.73', '1.54', '1.52', '1.60', '1.64', '1.69', '1.59', '1.59', '1.59', '1.58', '1.45', '2.02', '1.55', '1.47', '1.46', '1.48', '1.42', '1.43', '1.54', '1.43', '1.65', '1.53', '1.57', '1.44', '1.47', '1.57', '1.68', '1.52', '1.40', '1.55', '1.80', '1.63', '1.57', '1.48', '1.51', '1.51', '1.45', '1.57', '1.76', '1.51', '1.57', '1.55', '1.59', '1.60', '1.55', '1.59', '1.83', '1.50', '1.40', '1.55', '1.47', '1.50', '1.45', '1.38', '1.51', '1.52', '1.72', '1.42', '1.59', '1.47', '1.68', '1.60', '1.47', '1.57', '1.46', '1.67', '1.52', '1.47', '1.54', '1.53', '1.66', '1.36', '1.66', '1.54', '1.54', '1.51', '1.73', '1.56', '1.44', '1.62', '1.53', '1.53', '1.54', '1.60', '1.57', '1.42', '1.58', '1.56', '1.56', '1.59', '1.57', '1.61', '1.46', '1.57', '1.61', '1.72', '1.62', '1.53', '1.56', '1.75', '1.42', '1.59', '1.61', '1.72', '1.77', '1.50', '1.75', '1.46', '1.62', '1.57', '1.50', '1.62', '1.42', '1.60', '1.51', '1.52', '1.59', '1.47', '1.44', '1.62', '1.70', '1.55', '1.58', '1.48', '1.53', '1.38', '1.60', '1.64', '1.60', '1.45', '1.72', '1.65', '1.48', '1.45', '1.41', '1.57', '1.69', '1.56', '1.52', '1.59', '1.60', '1.56', '1.64', '1.52', '1.50', '1.62', '1.41', '1.63', '1.58', '1.47', '1.67', '1.47', '1.63', '1.73', '1.57', '1.61', '1.61', '1.61', '1.46', '1.47', '1.54', '1.61', '1.79', '1.54', '1.58', '1.45', '1.53', '1.60', '1.56', '1.47', '1.62']
  Min per-sample tau:          1.31
  Max per-sample tau:          2.07
============================================================

Results saved to /workspace/hanrui/idea1/results/dflash_eval/math500_steps1.json

============================================
  Running DFlash eval: denoise_steps=2
  GPUs: 8, Samples: 500
============================================
W0407 19:24:52.186000 5428 site-packages/torch/distributed/run.py:803] 
W0407 19:24:52.186000 5428 site-packages/torch/distributed/run.py:803] *****************************************
W0407 19:24:52.186000 5428 site-packages/torch/distributed/run.py:803] Setting OMP_NUM_THREADS environment variable for each process to be 1 in default, to avoid your system being overloaded, please further tune the variable for optimal performance in your application as needed. 
W0407 19:24:52.186000 5428 site-packages/torch/distributed/run.py:803] *****************************************
Set TORCH_CUDA_ARCH_LIST to 9.0
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
Set TORCH_CUDA_ARCH_LIST to 9.0
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
Set TORCH_CUDA_ARCH_LIST to 9.0
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
`torch_dtype` is deprecated! Use `dtype` instead!

Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]`torch_dtype` is deprecated! Use `dtype` instead!

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 155.71it/s]

Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 158.49it/s]
`torch_dtype` is deprecated! Use `dtype` instead!

Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 147.05it/s]
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
============================================================
DFlash Evaluation (Multi-GPU Data Parallel)
============================================================
  Target model:       /workspace/models/Qwen3-8B
  Draft model:        /workspace/models/Qwen3-8B-DFlash-b16
  Dataset:            math500
  Max samples:        500
  Max new tokens:     512
  Denoise steps:      2
  Temperature:        0.0
  GPUs:               8
  Dtype:              bfloat16
============================================================

[1/4] Loading tokenizer...
`torch_dtype` is deprecated! Use `dtype` instead!
`torch_dtype` is deprecated! Use `dtype` instead!
`torch_dtype` is deprecated! Use `dtype` instead!
[2/4] Loading target model on 8 GPUs...
`torch_dtype` is deprecated! Use `dtype` instead!
`torch_dtype` is deprecated! Use `dtype` instead!

Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
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Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 141.17it/s]

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 154.82it/s]

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 141.03it/s]

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 155.45it/s]

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 155.21it/s]
[3/4] Loading draft model on 8 GPUs...
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
  Draft layers:       5
  Draft block_size:   16
  Draft mask_token:   151669
  Draft layer_ids:    [1, 9, 17, 25, 33]
[4/4] Loading evaluation data...
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
  Total prompts: 500, ~63 per GPU

============================================================
Running evaluation...
============================================================
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
  [GPU 7] Sample 1/62 | tokens=512 | tau=1.44 | time=13.4s | <think> Okay, so I need to find the angle between two lines given by these equat...
  [GPU 1] Sample 1/63 | tokens=512 | tau=1.51 | time=13.1s | <think> Okay, so I need to find a way to express the double sum $\sum_{j = 1}^\i...
  [GPU 5] Sample 1/62 | tokens=512 | tau=1.45 | time=13.2s | <think> Okay, so I need to figure out the perimeter of a regular hexagon when I ...
  [GPU 2] Sample 1/63 | tokens=512 | tau=1.56 | time=12.8s | <think> Okay, so I need to find the value of f(-2) + f(-1) + f(0) where the func...
  [GPU 6] Sample 1/62 | tokens=512 | tau=1.49 | time=13.0s | <think> Okay, so I need to find the smallest positive perfect cube that can be w...
  [GPU 3] Sample 1/63 | tokens=512 | tau=1.43 | time=14.3s | <think> Okay, so I need to figure out how many positive whole-number divisors 19...
  [GPU 4] Sample 1/62 | tokens=512 | tau=1.54 | time=13.1s | <think> Okay, so I need to figure out which student has the greatest average spe...
  [GPU 0] Sample 1/63 | tokens=512 | tau=1.38 | time=14.5s | <think> Okay, so I need to convert the rectangular coordinates (0, 3) to polar c...
  [GPU 7] Sample 2/62 | tokens=512 | tau=1.50 | time=12.2s | <think> Okay, so I need to find the complex number w, which is the result of rot...
  [GPU 1] Sample 2/63 | tokens=512 | tau=1.46 | time=13.0s | <think> Okay, so I need to figure out how many different values can be obtained ...
  [GPU 5] Sample 2/62 | tokens=512 | tau=1.38 | time=13.4s | <think> Okay, so I need to find the height of a cylinder when the volume is give...
  [GPU 4] Sample 2/62 | tokens=512 | tau=1.58 | time=12.3s | <think> Okay, so I need to find the sum of the proper divisors of the sum of the...
  [GPU 2] Sample 2/63 | tokens=512 | tau=1.44 | time=13.2s | <think> Okay, so I need to find the least positive integer multiple of 30 that c...
  [GPU 6] Sample 2/62 | tokens=512 | tau=1.38 | time=13.4s | <think> Okay, so I need to find the length of DE in this diagram. Let me try to ...
  [GPU 3] Sample 2/63 | tokens=512 | tau=1.42 | time=14.0s | <think> Okay, so I need to find p(8) where p(x) is a degree 5 polynomial that sa...
  [GPU 0] Sample 2/63 | tokens=512 | tau=1.42 | time=13.5s | <think> Okay, so I need to find the distance between the two points (2, -6) and ...
  [GPU 7] Sample 3/62 | tokens=512 | tau=1.51 | time=12.1s | <think> Okay, so I need to solve the equation $ x = \sqrt{11 - 2x} + 4 $. Hmm, l...
  [GPU 1] Sample 3/63 | tokens=512 | tau=1.45 | time=13.1s | <think> Okay, so I need to find the smallest possible value of c for the functio...
  [GPU 5] Sample 3/62 | tokens=512 | tau=1.50 | time=12.3s | <think> Okay, so I need to find the greatest integer less than $(\sqrt{7} + \sqr...
  [GPU 6] Sample 3/62 | tokens=512 | tau=1.48 | time=12.4s | <think> Okay, let me try to figure out this problem. So, Denali and Nate are dog...
  [GPU 2] Sample 3/63 | tokens=512 | tau=1.44 | time=13.2s | <think> Okay, let me try to figure out this geometry problem. So, we have a diag...
  [GPU 4] Sample 3/62 | tokens=512 | tau=1.40 | time=13.7s | <think> Okay, so I need to evaluate the expression (1 + 2i) multiplied by 6, and...
  [GPU 3] Sample 3/63 | tokens=512 | tau=1.42 | time=13.8s | <think> Okay, so I need to find the smallest possible value of a positive real n...
  [GPU 0] Sample 3/63 | tokens=512 | tau=1.43 | time=13.4s | <think> Okay, so I need to compute this series: 1 - 2 + 3 - 4 + 5 - ... + 99 - 1...
  [GPU 7] Sample 4/62 | tokens=512 | tau=1.39 | time=13.2s | <think> Okay, so I need to simplify the square root of 242. Hmm, let me think. I...
  [GPU 1] Sample 4/63 | tokens=512 | tau=1.54 | time=12.3s | <think> Okay, so I need to solve this functional equation problem. The function ...
  [GPU 5] Sample 4/62 | tokens=512 | tau=1.48 | time=12.5s | <think> Okay, so I need to figure out how many different battalions can be sent ...
  [GPU 6] Sample 4/62 | tokens=512 | tau=1.40 | time=13.2s | <think> Okay, so I need to find the product of 6 base 8 and 7 base 8, and then e...
  [GPU 4] Sample 4/62 | tokens=512 | tau=1.43 | time=13.4s | <think> Okay, so I need to figure out what happens when I rotate the complex num...
  [GPU 0] Sample 4/63 | tokens=512 | tau=1.62 | time=11.8s | <think> Okay, so there's this worker who gets $20,000 every year and deposits it...
  [GPU 2] Sample 4/63 | tokens=512 | tau=1.33 | time=14.3s | <think> Okay, so I need to figure out how many ways 7 people can sit around a ro...
  [GPU 3] Sample 4/63 | tokens=512 | tau=1.44 | time=13.5s | <think> Okay, let's see. The math club is having a bake sale to raise money for ...
  [GPU 7] Sample 5/62 | tokens=512 | tau=1.50 | time=12.3s | <think> Okay, so I need to find the greatest common factor (GCF) of 6432 and 132...
  [GPU 1] Sample 5/63 | tokens=512 | tau=1.43 | time=13.3s | <think> Okay, so I need to find the eighth term of this geometric sequence: 125/...
  [GPU 5] Sample 5/62 | tokens=512 | tau=1.38 | time=13.4s | <think> Okay, so I need to figure out the minimum number of degrees a regular pe...
  [GPU 4] Sample 5/62 | tokens=512 | tau=1.75 | time=11.1s | <think> Okay, so I need to find the roots of the equation $(x - 3)^3 + (x - 7)^3...
  [GPU 6] Sample 5/62 | tokens=512 | tau=1.43 | time=12.9s | <think> Okay, so I need to figure out how many calories make up a person's daily...
  [GPU 2] Sample 5/63 | tokens=512 | tau=1.55 | time=12.3s | <think> Okay, so I need to find the constant term in the expansion of $\left(10x...
  [GPU 3] Sample 5/63 | tokens=512 | tau=1.58 | time=12.4s | <think> Okay, so I need to find the remainder when (n + 2)(n + 4)(n + 6) is divi...
  [GPU 0] Sample 5/63 | tokens=512 | tau=1.36 | time=14.1s | <think> Okay, so I need to figure out how many ways 8 people can sit around a ro...
  [GPU 7] Sample 6/62 | tokens=512 | tau=1.45 | time=12.7s | <think> Okay, so I need to find the vertical asymptotes and the horizontal asymp...
  [GPU 1] Sample 6/63 | tokens=512 | tau=1.31 | time=14.5s | <think> Okay, so I need to find the coordinates (x, y) of the fourth vertex of a...
  [GPU 5] Sample 6/62 | tokens=512 | tau=1.40 | time=13.2s | <think> Okay, so I need to find tan A in this right triangle ABC where angle B i...
  [GPU 4] Sample 6/62 | tokens=512 | tau=1.51 | time=12.8s | <think> Okay, so Bill is walking in different directions, and I need to figure o...
  [GPU 6] Sample 6/62 | tokens=512 | tau=1.41 | time=13.1s | <think> Okay, so I need to find the smallest positive integer n such that all th...
  [GPU 3] Sample 6/63 | tokens=512 | tau=1.69 | time=11.6s | <think> Okay, so I need to find the minimum value of this expression:  $$ \sqrt{...
  [GPU 2] Sample 6/63 | tokens=512 | tau=1.42 | time=13.4s | <think> Okay, so I need to solve this inequality: -4 < 2(x - 1) < 8. And then ex...
  [GPU 0] Sample 6/63 | tokens=512 | tau=1.44 | time=13.4s | <think> Okay, so I need to find the side length of a regular octagon that has th...
  [GPU 7] Sample 7/62 | tokens=512 | tau=1.45 | time=12.7s | <think> Okay, so I need to figure out the degree of the polynomial f. The proble...
  [GPU 1] Sample 7/63 | tokens=512 | tau=1.52 | time=12.5s | <think> Okay, so I need to solve this equation: Half the value of 3x minus 9 is ...
  [GPU 4] Sample 7/62 | tokens=512 | tau=1.51 | time=12.8s | <think> Okay, so I need to simplify this expression: the square root of (2.5 squ...
  [GPU 5] Sample 7/62 | tokens=512 | tau=1.41 | time=13.0s | <think> Okay, so I need to compute the arcsin of -1/2. Hmm, let me recall what a...
  [GPU 6] Sample 7/62 | tokens=512 | tau=1.33 | time=13.9s | <think> Okay, so I need to convert the fraction 3/20 into a decimal. Hmm, let me...
  [GPU 3] Sample 7/63 | tokens=512 | tau=1.44 | time=13.6s | <think> Okay, so I need to find the quotient when x⁶ - 3 is divided by x + 1. Hm...
  [GPU 2] Sample 7/63 | tokens=512 | tau=1.43 | time=13.4s | <think> Okay, let me try to figure out this problem. So, there are seven bags of...
  [GPU 0] Sample 7/63 | tokens=512 | tau=1.41 | time=13.7s | <think> Okay, so I need to figure out what power of 4 equals 8. Hmm, let me thin...
  [GPU 7] Sample 8/62 | tokens=512 | tau=1.47 | time=12.6s | <think> Okay, so I need to factor the polynomial $ x^8 + 3x^4 - 4 $ into monic p...
  [GPU 5] Sample 8/62 | tokens=512 | tau=1.58 | time=11.7s | <think> Okay, so I need to find the value of $ a $ given that the cubic equation...
  [GPU 1] Sample 8/63 | tokens=512 | tau=1.43 | time=13.3s | <think> Okay, so Ringo is trying to calculate the modulus of (1 - i) raised to t...
  [GPU 4] Sample 8/62 | tokens=512 | tau=1.52 | time=12.8s | <think> Okay, so I need to figure out the ordered triple (p, q, r) such that the...
  [GPU 2] Sample 8/63 | tokens=512 | tau=1.69 | time=11.3s | <think> Okay, so I need to compute 99 squared plus 99 plus 1. Let me think about...
  [GPU 6] Sample 8/62 | tokens=512 | tau=1.48 | time=12.4s | <think> Okay, so I need to find the smallest positive real number C such that th...
  [GPU 3] Sample 8/63 | tokens=512 | tau=1.50 | time=13.0s | <think> Okay, so there's this problem about a class of 50 students. Some partici...
  [GPU 0] Sample 8/63 | tokens=512 | tau=1.48 | time=12.9s | <think> Okay, so I need to find the value of N where the sum of the first N posi...
  [GPU 7] Sample 9/62 | tokens=512 | tau=1.48 | time=12.4s | <think> Okay, so I need to convert the binary number 10101001110₂ to octal. Hmm,...
  [GPU 5] Sample 9/62 | tokens=512 | tau=1.60 | time=11.4s | <think> Okay, so I need to compute the value of $ z + \frac{1}{z} + z^2 + \frac{...
  [GPU 4] Sample 9/62 | tokens=512 | tau=1.48 | time=13.0s | <think> Okay, so I need to solve this equation: tan 53° tan 81° tan x° = tan 53°...
  [GPU 1] Sample 9/63 | tokens=512 | tau=1.38 | time=13.8s | <think> Okay, so I need to figure out what 1 raised to the power of 2 raised to ...
  [GPU 2] Sample 9/63 | tokens=512 | tau=1.52 | time=12.5s | <think> Okay, so I need to expand and simplify this algebraic expression: x time...
  [GPU 6] Sample 9/62 | tokens=512 | tau=1.44 | time=12.7s | <think> Okay, so I need to subtract two numbers in base 9: 58 base 9 minus 18 ba...
  [GPU 3] Sample 9/63 | tokens=512 | tau=1.47 | time=13.3s | <think> Okay, so I need to figure out by what percentage the area of a square de...
  [GPU 0] Sample 9/63 | tokens=512 | tau=1.43 | time=13.4s | <think> Okay, so I need to find the constant $ d $ such that the equation $ (\si...
  [GPU 7] Sample 10/62 | tokens=512 | tau=1.39 | time=13.3s | <think> Okay, so I need to find the value of x that makes the equation 2³ times ...
  [GPU 5] Sample 10/62 | tokens=512 | tau=1.40 | time=13.1s | <think> Okay, so I need to solve the equation $2^8 = 4^x$ and find the value of ...
  [GPU 2] Sample 10/63 | tokens=512 | tau=1.60 | time=11.9s | <think> Okay, so I need to simplify this expression: $\frac{\sec x}{\sin x} - \f...
  [GPU 6] Sample 10/62 | tokens=512 | tau=1.61 | time=11.5s | <think> Okay, so I need to find real numbers a (which isn't zero) and b such tha...
  [GPU 4] Sample 10/62 | tokens=512 | tau=1.41 | time=13.7s | <think> Okay, so I need to figure out the domain of the function log(x²) and the...
  [GPU 1] Sample 10/63 | tokens=512 | tau=1.43 | time=13.3s | <think> Okay, so I need to figure out the value of 9 & 2 using this operation th...
  [GPU 3] Sample 10/63 | tokens=512 | tau=1.45 | time=13.4s | <think> Okay, so I need to find the probability that when I throw two fair 6-sid...
  [GPU 0] Sample 10/63 | tokens=512 | tau=1.49 | time=12.8s | <think> Okay, so I need to find the radius of a sphere where the volume and surf...
  [GPU 7] Sample 11/62 | tokens=512 | tau=1.52 | time=12.1s | <think> Okay, so I need to solve the equation |5x - 1| = x + 3 and find the larg...
  [GPU 5] Sample 11/62 | tokens=512 | tau=1.49 | time=12.4s | <think> Okay, so I need to find the radius of a right cylindrical tank. The prob...
  [GPU 2] Sample 11/63 | tokens=512 | tau=1.58 | time=12.0s | <think> Okay, so I need to find the greatest possible value of the slope of the ...
  [GPU 4] Sample 11/62 | tokens=512 | tau=1.66 | time=11.6s | <think> Okay, so I need to find the values of 'a' and 'b' such that when I multi...
  [GPU 1] Sample 11/63 | tokens=512 | tau=1.54 | time=12.2s | <think> Okay, let me try to figure out this problem. So, we have three different...
  [GPU 6] Sample 11/62 | tokens=512 | tau=1.36 | time=13.5s | <think> Okay, so I need to figure out how many different outfits I can make with...
  [GPU 3] Sample 11/63 | tokens=512 | tau=1.35 | time=14.4s | <think> Okay, so I need to solve the equation $3^{2x} + 19 = 10^x$. Hmm, let me ...
  [GPU 0] Sample 11/63 | tokens=512 | tau=1.52 | time=12.6s | <think> Okay, so I need to find the number of integer values of k in the interva...
  [GPU 7] Sample 12/62 | tokens=512 | tau=1.53 | time=12.0s | <think> Okay, so I need to find the value of y such that the projection of the v...
  [GPU 5] Sample 12/62 | tokens=512 | tau=1.52 | time=12.0s | <think> Okay, so I need to find the value of $ c $ such that the circle given by...
  [GPU 1] Sample 12/63 | tokens=512 | tau=1.71 | time=11.0s | <think> Okay, so I need to find the greatest common divisor (GCD) of three numbe...
  [GPU 4] Sample 12/62 | tokens=512 | tau=1.42 | time=13.6s | <think> Okay, so I need to figure out the probability that exactly 4 out of 7 is...
  [GPU 6] Sample 12/62 | tokens=512 | tau=1.45 | time=12.6s | <think> Okay, so I need to find the measure of angle AFD in quadrilateral ABCD. ...
  [GPU 2] Sample 12/63 | tokens=512 | tau=1.28 | time=14.8s | <think> Okay, so Remmy wants to divide 10 by 2/3, but he's confused about how to...
  [GPU 3] Sample 12/63 | tokens=512 | tau=1.46 | time=13.3s | <think> Okay, so I need to find the smallest integer value of x for which the fu...
  [GPU 0] Sample 12/63 | tokens=512 | tau=1.38 | time=14.0s | <think> Okay, so I need to find the largest value of 'a' such that the graph of ...
  [GPU 7] Sample 13/62 | tokens=512 | tau=1.43 | time=12.8s | <think> Okay, so I need to find the values of λ between 0 and 4 such that there'...
  [GPU 5] Sample 13/62 | tokens=512 | tau=1.52 | time=12.1s | <think> Okay, so I need to solve this equation: $x^{10} + (13x - 1)^{10} = 0$. T...
  [GPU 1] Sample 13/63 | tokens=512 | tau=1.42 | time=13.3s | <think> Okay, so there's this figure skater who starts facing north, and she beg...
  [GPU 6] Sample 13/62 | tokens=512 | tau=1.38 | time=13.4s | <think> Okay, so I need to factor the expression ab + 5b + 2a + 10. Hmm, factori...
  [GPU 2] Sample 13/63 | tokens=512 | tau=1.42 | time=13.4s | <think> Okay, so I need to simplify this expression: (-k + 4) + (-2 + 3k). Let m...
  [GPU 4] Sample 13/62 | tokens=512 | tau=1.32 | time=14.5s | <think> Okay, so I need to find the measure of angle α in this hexagon inscribed...
  [GPU 0] Sample 13/63 | tokens=512 | tau=1.65 | time=11.6s | <think> Okay, so I need to solve this equation:  $$\frac{( x+ 1)(x - 3)}{5(x + 2...
  [GPU 3] Sample 13/63 | tokens=512 | tau=1.50 | time=13.0s | <think> Okay, so I need to find a vector v such that when I take the dot product...
  [GPU 7] Sample 14/62 | tokens=512 | tau=1.48 | time=12.4s | <think> Okay, so Mr. Brennan has 7 boys and 4 girls in his statistics class, and...
  [GPU 5] Sample 14/62 | tokens=512 | tau=1.69 | time=10.9s | <think> Okay, so I need to find the degree measure of the least positive angle θ...
  [GPU 1] Sample 14/63 | tokens=512 | tau=1.67 | time=11.3s | <think> Okay, so I need to find the median number of students in 2005 for these ...
  [GPU 6] Sample 14/62 | tokens=512 | tau=1.57 | time=11.8s | <think> Okay, so I need to find the value of $ a_1 $ in a strictly increasing se...
  [GPU 2] Sample 14/63 | tokens=512 | tau=1.49 | time=12.9s | <think> Okay, so I need to find the horizontal asymptote of the function y = (4x...
  [GPU 4] Sample 14/62 | tokens=512 | tau=1.50 | time=12.8s | <think> Okay, so I need to find the value of k for the ellipse given by the equa...
  [GPU 0] Sample 14/63 | tokens=512 | tau=1.60 | time=12.1s | <think> Okay, so I need to find the sum of the distances from the four intersect...
  [GPU 3] Sample 14/63 | tokens=512 | tau=1.63 | time=12.0s | <think> Okay, so I need to figure out how many elements are in the intersection ...
  [GPU 7] Sample 15/62 | tokens=512 | tau=1.43 | time=12.9s | <think> Okay, so I need to figure out the minimum possible value of the expressi...
  [GPU 5] Sample 15/62 | tokens=512 | tau=1.41 | time=13.0s | <think> Okay, so I need to solve the equation √(3x - 5) = 2. Hmm, let me think. ...
  [GPU 1] Sample 15/63 | tokens=512 | tau=1.51 | time=12.6s | <think> Okay, so I need to figure out the value of this expression: (26² - 24² -...
  [GPU 6] Sample 15/62 | tokens=512 | tau=1.50 | time=12.3s | <think> Okay, so I need to find the number of ordered pairs (a, b) of integers s...
  [GPU 2] Sample 15/63 | tokens=512 | tau=1.58 | time=12.1s | <think> Okay, so I need to find the product CD where C and D are integers that s...
  [GPU 4] Sample 15/62 | tokens=512 | tau=1.44 | time=13.4s | <think> Okay, so I need to solve the equation $2^{2x} = 256^{\frac{1}{2}}$. Hmm,...
  [GPU 0] Sample 15/63 | tokens=512 | tau=1.46 | time=13.3s | <think> Okay, so I need to simplify the expression (1 + √2)/(2 + √3). The proble...
  [GPU 3] Sample 15/63 | tokens=512 | tau=1.48 | time=13.1s | <think> Okay, so I need to figure out how many ways there are to arrange the let...
  [GPU 7] Sample 16/62 | tokens=512 | tau=1.48 | time=12.4s | <think> Okay, so I need to convert the decimal number 555 into base 5. Hmm, let ...
  [GPU 5] Sample 16/62 | tokens=512 | tau=1.59 | time=11.5s | <think> Okay, so I need to evaluate this expression: the ceiling of (3.6 squared...
  [GPU 1] Sample 16/63 | tokens=512 | tau=1.37 | time=13.8s | <think> Okay, so I need to solve the equation (x/2) + (x/3) = 5. Hmm, let me thi...
  [GPU 6] Sample 16/62 | tokens=512 | tau=1.43 | time=13.0s | <think> Okay, so I need to find z_{2002} where each term is defined by iterating...
  [GPU 2] Sample 16/63 | tokens=512 | tau=1.58 | time=12.1s | <think> Okay, so Daniel says that the popularity of a television, which is measu...
  [GPU 4] Sample 16/62 | tokens=512 | tau=1.50 | time=12.8s | <think> Okay, so I need to solve the equation |x + 5| - |3x - 6| = 0. Hmm, absol...
  [GPU 5] Sample 17/62 | tokens=512 | tau=1.44 | time=12.7s | <think> Okay, so I need to figure out the measure of the largest angle in this c...
  [GPU 0] Sample 16/63 | tokens=512 | tau=1.38 | time=13.9s | <think> Okay, so I need to figure out whether the composition of these functions...
  [GPU 3] Sample 16/63 | tokens=512 | tau=1.40 | time=13.9s | <think> Okay, so I need to find the area of quadrilateral DBEF. Let me first try...
  [GPU 7] Sample 17/62 | tokens=512 | tau=1.34 | time=13.7s | <think> Okay, so I need to figure out how many zeros are at the end of 42 factor...
  [GPU 1] Sample 17/63 | tokens=512 | tau=1.46 | time=13.0s | <think> Okay, so I need to find the area of triangle ACD in triangle ABC where A...
  [GPU 6] Sample 17/62 | tokens=512 | tau=1.48 | time=12.4s | <think> Okay, so I need to find the equation of a hyperbola given two foci, F₁ =...
  [GPU 2] Sample 17/63 | tokens=512 | tau=1.38 | time=13.8s | <think> Okay, so I need to find an integer n between 0 and 17 (since 0 ≤ n < 18)...
  [GPU 4] Sample 17/62 | tokens=512 | tau=1.51 | time=12.9s | <think> Okay, so Rick is thinking of a positive factor of 14, and Steve is think...
  [GPU 5] Sample 18/62 | tokens=512 | tau=1.43 | time=12.8s | <think> Okay, so Zach has three bags and a bunch of pencils. He needs to place t...
  [GPU 7] Sample 18/62 | tokens=512 | tau=1.55 | time=12.0s | <think> Okay, so I need to find the area of triangle OAB, given the vectors OA a...
  [GPU 3] Sample 17/63 | tokens=512 | tau=1.48 | time=13.3s | <think> Okay, so I need to find the value of f(3) given that f(-3) = 2 for the f...
  [GPU 0] Sample 17/63 | tokens=512 | tau=1.34 | time=14.4s | <think> Okay, so Suzanne walks four miles every third day. The question is askin...
  [GPU 1] Sample 18/63 | tokens=512 | tau=1.48 | time=12.7s | <think> Okay, so I need to divide 413 base 5 by 2 base 5 and give the answer in ...
  [GPU 6] Sample 18/62 | tokens=512 | tau=1.43 | time=12.8s | <think> Okay, so I need to figure out how many ways the Senate committee can sit...
  [GPU 2] Sample 18/63 | tokens=512 | tau=1.44 | time=13.3s | <think> Okay, so Bob and Alice each have a bag with balls of five different colo...
  [GPU 4] Sample 18/62 | tokens=512 | tau=1.47 | time=13.1s | <think> Okay, so I need to find the greatest possible value of the greatest comm...
  [GPU 5] Sample 19/62 | tokens=512 | tau=1.59 | time=11.6s | <think> Okay, let's try to figure out Rosa's age. The problem says that when her...
  [GPU 7] Sample 19/62 | tokens=512 | tau=1.56 | time=11.7s | <think> Okay, so I need to find the square of the determinant of a 3x3 matrix wi...
  [GPU 3] Sample 18/63 | tokens=512 | tau=1.54 | time=12.7s | <think> Okay, so I need to find the maximum value of the function $ f(x, y) = x ...
  [GPU 0] Sample 18/63 | tokens=512 | tau=1.51 | time=12.7s | <think> Okay, so I need to find the sum of all possible values of n for a sequen...
  [GPU 1] Sample 19/63 | tokens=512 | tau=1.47 | time=12.9s | <think> Okay, so I need to find $ z^{85} + \frac{1}{z^{85}} $ given that $ z + \...
  [GPU 6] Sample 19/62 | tokens=512 | tau=1.49 | time=12.3s | <think> Okay, so I need to figure out what f(2015, 2) is based on this recursive...
  [GPU 2] Sample 19/63 | tokens=512 | tau=1.30 | time=14.6s | <think> Okay, so I need to simplify the fraction 3 over the square root of 27. L...
  [GPU 5] Sample 20/62 | tokens=512 | tau=1.51 | time=12.1s | <think> Okay, so I need to find the value of a + b + c, where a, b, and c are th...
  [GPU 4] Sample 19/62 | tokens=512 | tau=1.41 | time=13.6s | <think> Okay, so I need to solve the equation 2/3 equals 4 divided by (x minus 5...
  [GPU 7] Sample 20/62 | tokens=512 | tau=1.44 | time=12.7s | <think> Okay, so I need to rewrite the quadratic equation $x^2 + 2.6x + 3.6$ in ...
  [GPU 3] Sample 19/63 | tokens=512 | tau=1.38 | time=14.2s | <think> Okay, so I need to find the minimum value of the expression $ x^4 + 4y^2...
  [GPU 0] Sample 19/63 | tokens=512 | tau=1.41 | time=13.6s | <think> Okay, so I need to find the point on the curve that's given by the param...
  [GPU 1] Sample 20/63 | tokens=512 | tau=1.46 | time=13.0s | <think> Okay, so I need to find the probability that three randomly chosen point...
  [GPU 6] Sample 20/62 | tokens=512 | tau=1.41 | time=13.1s | <think> Okay, so I need to find the sum of all multiples of 7 between 100 and 20...
  [GPU 5] Sample 21/62 | tokens=512 | tau=1.58 | time=11.6s | <think> Okay, let me try to figure out this problem. So, there's a bookcase with...
  [GPU 2] Sample 20/63 | tokens=512 | tau=1.48 | time=12.8s | <think> Okay, so there's this gecko in a room, and it needs to get to a fly. The...
  [GPU 4] Sample 20/62 | tokens=512 | tau=1.53 | time=12.6s | <think> Okay, so there's this problem about two runners, A and B, starting from ...
  [GPU 7] Sample 21/62 | tokens=512 | tau=1.36 | time=13.5s | <think> Okay, so I need to find the volume of a cone. The formula given is V equ...
  [GPU 3] Sample 20/63 | tokens=512 | tau=1.47 | time=13.4s | <think> Okay, so I need to find the probability that a randomly selected point (...
  [GPU 0] Sample 20/63 | tokens=512 | tau=1.36 | time=14.2s | <think> Okay, so I need to find the area of triangle ENG in triangle ABC, where ...
  [GPU 6] Sample 21/62 | tokens=512 | tau=1.46 | time=12.6s | <think> Okay, so I need to find the measure of angle BAC, where there's a square...
  [GPU 1] Sample 21/63 | tokens=512 | tau=1.45 | time=13.2s | <think> Okay, so I need to evaluate log base 2 of 64. Hmm, let me think. Logarit...
  [GPU 5] Sample 22/62 | tokens=512 | tau=1.48 | time=12.4s | <think> Okay, so I need to find the smallest positive integer value of 'a' such ...
  [GPU 2] Sample 21/63 | tokens=512 | tau=1.49 | time=12.8s | <think> Okay, so I need to find the probability that a randomly selected integer...
  [GPU 7] Sample 22/62 | tokens=512 | tau=1.66 | time=11.1s | <think> Okay, so I need to find the smallest possible value of |m - n| where m a...
  [GPU 4] Sample 21/62 | tokens=512 | tau=1.38 | time=14.0s | <think> Okay, so I need to simplify the expression tan 100° + 4 sin 100°. Hmm, l...
  [GPU 3] Sample 21/63 | tokens=512 | tau=1.53 | time=12.9s | <think> Okay, so I need to find the greatest possible value of the expression $\...
  [GPU 0] Sample 21/63 | tokens=512 | tau=1.51 | time=12.8s | <think> Okay, so I need to find two consecutive positive even integers whose pro...
  [GPU 6] Sample 22/62 | tokens=512 | tau=1.45 | time=12.7s | <think> Okay, so I need to figure out how many y-intercepts the graph of the par...
  [GPU 1] Sample 22/63 | tokens=512 | tau=1.39 | time=13.6s | <think> Okay, so I need to find the area of a triangle with sides 5, 5, and 6 un...
  [GPU 5] Sample 23/62 | tokens=512 | tau=1.50 | time=12.2s | <think> Okay, so I need to simplify this expression: the square root of the cube...
  [GPU 7] Sample 23/62 | tokens=512 | tau=1.52 | time=12.1s | <think> Okay, so I need to figure out how to write the expression √2 + 1/√2 + √3...
  [GPU 2] Sample 22/63 | tokens=512 | tau=1.50 | time=12.7s | <think> Okay, so I need to find the product of the y-coordinates of all the dist...
  [GPU 4] Sample 22/62 | tokens=512 | tau=1.54 | time=12.5s | <think> Okay, so I need to find the sixth term of an arithmetic sequence where t...
  [GPU 0] Sample 22/63 | tokens=512 | tau=1.45 | time=13.2s | <think> Okay, so I need to figure out the value of n for a 3×n grid of points wh...
  [GPU 3] Sample 22/63 | tokens=512 | tau=1.39 | time=14.1s | <think> Okay, so Louis and Jack are sharing a pie, and I need to figure out how ...
  [GPU 6] Sample 23/62 | tokens=512 | tau=1.47 | time=12.7s | <think> Okay, so I need to figure out how many students are at Baker Middle Scho...
  [GPU 1] Sample 23/63 | tokens=512 | tau=1.53 | time=12.4s | <think> Okay, so I need to find the degree measure of the smallest angle in tria...
  [GPU 5] Sample 24/62 | tokens=512 | tau=1.51 | time=12.1s | <think> Okay, so I need to figure out the greatest length of rope that can be sa...
  [GPU 7] Sample 24/62 | tokens=512 | tau=1.45 | time=12.7s | <think> Okay, so I need to find the value of b when the point (a, b) is on the l...
  [GPU 2] Sample 23/63 | tokens=512 | tau=1.51 | time=12.6s | <think> Okay, so I need to find the positive square root of the product 10 times...
  [GPU 4] Sample 23/62 | tokens=512 | tau=1.46 | time=13.2s | <think> Okay, so I need to figure out how many positive two-digit integers are f...
  [GPU 3] Sample 23/63 | tokens=512 | tau=1.51 | time=13.0s | <think> Okay, so I need to find the equation of the plane that contains the thre...
  [GPU 6] Sample 24/62 | tokens=512 | tau=1.59 | time=11.7s | <think> Okay, so Paul and Jesse each pick a number at random from the first six ...
  [GPU 0] Sample 23/63 | tokens=512 | tau=1.36 | time=14.2s | <think> Okay, so I need to convert the fraction 21 divided by (2 squared times 5...
  [GPU 1] Sample 24/63 | tokens=512 | tau=1.39 | time=13.6s | <think> Okay, so I need to find the value of k such that (3^k)^6 equals 3^6. Let...
  [GPU 5] Sample 25/62 | tokens=512 | tau=1.50 | time=12.3s | <think> Okay, so I need to figure out how many possible integer values of x ther...
  [GPU 7] Sample 25/62 | tokens=512 | tau=1.43 | time=12.9s | <think> Okay, so I need to find the value of x such that the arithmetic mean of ...
  [GPU 4] Sample 24/62 | tokens=512 | tau=1.78 | time=10.7s | <think> Okay, so I need to find the largest x-value where the graphs of f(x) and...
  [GPU 2] Sample 24/63 | tokens=512 | tau=1.45 | time=13.1s | <think> Okay, so I need to figure out for how many positive integers n > 1 it's ...
  [GPU 3] Sample 24/63 | tokens=512 | tau=1.53 | time=12.8s | <think> Okay, so Hillary has eleven coins, and they're all either dimes or nicke...
  [GPU 0] Sample 24/63 | tokens=512 | tau=1.51 | time=12.7s | <think> Okay, so I need to find all possible values of the expression $\frac{c}{...
  [GPU 6] Sample 25/62 | tokens=512 | tau=1.35 | time=13.8s | <think> Okay, so I need to figure out how many ways 6 girls and 2 boys can sit i...
  [GPU 1] Sample 25/63 | tokens=512 | tau=1.45 | time=13.0s | <think> Okay, so I need to find the number of different possible rational roots ...
  [GPU 5] Sample 26/62 | tokens=512 | tau=1.40 | time=13.1s | <think> Okay, so I need to find the matrix A multiplied by the vector (-13, 3, 4...
  [GPU 7] Sample 26/62 | tokens=512 | tau=1.41 | time=13.0s | <think> Okay, so Mikka wants to order a pizza with two different toppings, and h...
  [GPU 4] Sample 25/62 | tokens=512 | tau=1.42 | time=13.5s | <think> Okay, so I need to solve this equation: 441 plus 2 times 21 times 19 plu...
  [GPU 2] Sample 25/63 | tokens=512 | tau=1.41 | time=13.5s | <think> Okay, so I need to find the maximum value of the expression $\frac{x - y...
  [GPU 3] Sample 25/63 | tokens=512 | tau=1.51 | time=13.0s | <think> Okay, so I need to find p(0) + p(4) where p(x) is a monic polynomial of ...
  [GPU 6] Sample 26/62 | tokens=512 | tau=1.54 | time=12.0s | <think> Okay, so I need to find the equation of a line given its parametric equa...
  [GPU 5] Sample 27/62 | tokens=512 | tau=1.80 | time=10.2s | <think> Okay, so I need to compute the infinite sum $\sum_{n = 1}^\infty \frac{F...
  [GPU 0] Sample 25/63 | tokens=512 | tau=1.43 | time=13.5s | <think> Okay, so I need to find the length of the median QM in triangle PQR wher...
  [GPU 1] Sample 26/63 | tokens=512 | tau=1.40 | time=13.5s | <think> Okay, so there's this problem about a group of N students, and N is less...
  [GPU 7] Sample 27/62 | tokens=512 | tau=1.44 | time=12.7s | <think> Okay, so I need to find the value of $ x^3 - 2x + 1 $ given that $ x^2 -...
  [GPU 4] Sample 26/62 | tokens=512 | tau=1.43 | time=13.5s | <think> Okay, so I need to find the maximum value of the product |(a + b)(a + c)...
  [GPU 2] Sample 26/63 | tokens=512 | tau=1.35 | time=14.0s | <think> Okay, so Alice and Bob are playing this game where they take turns flipp...
  [GPU 3] Sample 26/63 | tokens=512 | tau=1.65 | time=11.9s | <think> Okay, so I need to find the remainder when this big polynomial is divide...
  [GPU 6] Sample 27/62 | tokens=512 | tau=1.49 | time=12.3s | <think> Okay, let's try to figure out how many students take physics. There are ...
  [GPU 5] Sample 28/62 | tokens=512 | tau=1.48 | time=12.4s | <think> Okay, so I need to find the smallest positive integer k such that when I...
  [GPU 1] Sample 27/63 | tokens=512 | tau=1.76 | time=10.7s | <think> Okay, so I need to find a two-digit integer AB such that when it's cubed...
  [GPU 0] Sample 26/63 | tokens=512 | tau=1.47 | time=13.1s | <think> Okay, so I need to figure out how many daps equal 42 baps. Let me start ...
  [GPU 7] Sample 28/62 | tokens=512 | tau=1.61 | time=11.5s | <think> Okay, so I need to find the sum of the digits in the terminating decimal...
  [GPU 4] Sample 27/62 | tokens=512 | tau=1.50 | time=12.9s | <think> Okay, let's see. Frank took a 100-question test. Each correct answer giv...
  [GPU 2] Sample 27/63 | tokens=512 | tau=1.47 | time=13.0s | <think> Okay, so I need to find the total area of the shaded region in this figu...
  [GPU 6] Sample 28/62 | tokens=512 | tau=1.45 | time=12.7s | <think> Okay, so I need to find the area of triangle CDE given that the area of ...
  [GPU 3] Sample 27/63 | tokens=512 | tau=1.40 | time=14.0s | <think> Okay, so I need to figure out how to compute this expression: 5^5 divide...
  [GPU 5] Sample 29/62 | tokens=512 | tau=1.40 | time=13.2s | <think> Okay, so Yann and Camille are going to a restaurant, and there are 10 it...
  [GPU 1] Sample 28/63 | tokens=512 | tau=1.49 | time=12.6s | <think> Okay, so I need to find the smallest positive multiple of 450 where all ...
  [GPU 0] Sample 27/63 | tokens=512 | tau=1.49 | time=12.9s | <think> Okay, so I need to figure out how many numbers from 1 to 100 are divisib...
  [GPU 7] Sample 29/62 | tokens=512 | tau=1.48 | time=12.6s | <think> Okay, let's try to figure out how old Chris is now. The problem says tha...
  [GPU 4] Sample 28/62 | tokens=512 | tau=1.51 | time=12.8s | <think> Okay, so Sam is carrying a 2-gallon bucket of milk, and he needs to walk...
  [GPU 2] Sample 28/63 | tokens=512 | tau=1.39 | time=13.7s | <think> Okay, so I need to find the midpoint between two points, (-5, 5) and (3,...
  [GPU 6] Sample 29/62 | tokens=512 | tau=1.43 | time=12.9s | <think> Okay, so I need to find the maximum value of e given these two equations...
  [GPU 5] Sample 30/62 | tokens=512 | tau=1.45 | time=12.7s | <think> Okay, so I need to find the value of x + y + z given that xy = 24, xz = ...
  [GPU 3] Sample 28/63 | tokens=512 | tau=1.51 | time=13.0s | <think> Okay, so I need to figure out the probability that when I spin this whee...
  [GPU 1] Sample 29/63 | tokens=512 | tau=1.54 | time=12.3s | <think> Okay, so I need to find the value of this expression when x is 4. The ex...
  [GPU 0] Sample 28/63 | tokens=512 | tau=1.43 | time=13.5s | <think> Okay, so I need to figure out how much 56 Drinkets is worth in Trinkets....
  [GPU 7] Sample 30/62 | tokens=512 | tau=1.48 | time=12.4s | <think> Okay, so I need to solve this problem about parallelograms bounded by li...
  [GPU 4] Sample 29/62 | tokens=512 | tau=1.76 | time=11.0s | <think> Okay, so I need to find the region of the volume enclosed by the set S, ...
  [GPU 2] Sample 29/63 | tokens=512 | tau=1.48 | time=12.8s | <think> Okay, so I need to figure out how many ways there are to put 5 indisting...
  [GPU 6] Sample 30/62 | tokens=512 | tau=1.64 | time=11.2s | <think> Okay, so I need to figure out the real values of x that are not in the d...
  [GPU 5] Sample 31/62 | tokens=512 | tau=1.45 | time=12.7s | <think> Okay, so I need to find the remainder when this big polynomial f(x) is d...
  [GPU 1] Sample 30/63 | tokens=512 | tau=1.43 | time=13.1s | <think> Okay, so I need to find the smallest possible angle between vectors a an...
  [GPU 0] Sample 29/63 | tokens=512 | tau=1.60 | time=12.0s | <think> Okay, so I need to find the value of the product sin20° sin40° sin60° si...
  [GPU 3] Sample 29/63 | tokens=512 | tau=1.35 | time=14.6s | <think> Okay, so I need to figure out what shape the equation z = c represents i...
  [GPU 7] Sample 31/62 | tokens=512 | tau=1.55 | time=11.9s | <think> Okay, so I need to find the value of p(3)/p(4) where p(x) is a quadratic...
  [GPU 4] Sample 30/62 | tokens=512 | tau=1.48 | time=13.1s | <think> Okay, so I need to compute the value of this expression: 1 over cos squa...
  [GPU 2] Sample 30/63 | tokens=512 | tau=1.55 | time=12.3s | <think> Okay, so I need to find the sum of the roots of the function g(x), which...
  [GPU 6] Sample 31/62 | tokens=512 | tau=1.53 | time=12.1s | <think> Okay, so there's this problem about twelve friends who went to dinner, a...
  [GPU 5] Sample 32/62 | tokens=512 | tau=1.38 | time=13.3s | <think> Okay, so I need to figure out what fraction of 2 feet is 3 inches. Hmm, ...
  [GPU 1] Sample 31/63 | tokens=512 | tau=1.40 | time=13.5s | <think> Okay, so I need to find the smallest distance between the origin (0,0) a...
  [GPU 3] Sample 30/63 | tokens=512 | tau=1.56 | time=12.6s | <think> Okay, so I need to compute this expression: 0.7 repeating minus 0.4 repe...
  [GPU 7] Sample 32/62 | tokens=512 | tau=1.50 | time=12.3s | <think> Okay, so I need to figure out what kind of curve is defined by the equat...
  [GPU 0] Sample 30/63 | tokens=512 | tau=1.45 | time=13.3s | <think> Okay, so I need to evaluate the sum S = 1/(1 + ω) + 1/(1 + ω²) + ... + 1...
  [GPU 4] Sample 31/62 | tokens=512 | tau=1.51 | time=12.9s | <think> Okay, so I need to figure out how many sides a convex polygon has if the...
  [GPU 2] Sample 31/63 | tokens=512 | tau=1.39 | time=13.7s | <think> Okay, so I need to figure out how much money will be in the investment a...
  [GPU 6] Sample 32/62 | tokens=512 | tau=1.43 | time=12.9s | <think> Okay, so Pat wants to select six cookies from a tray that has chocolate ...
  [GPU 5] Sample 33/62 | tokens=512 | tau=1.38 | time=13.3s | <think> Okay, so I need to find the measure of angle B in triangle ABC, where an...
  [GPU 7] Sample 33/62 | tokens=512 | tau=1.50 | time=12.2s | <think> Okay, so I need to figure out how many sides a regular polygon has if it...
  [GPU 1] Sample 32/63 | tokens=512 | tau=1.42 | time=13.2s | <think> Okay, so I need to find an odd integer t between 0 and 23 such that t + ...
  [GPU 0] Sample 31/63 | tokens=512 | tau=1.45 | time=13.2s | <think> Okay, so I need to find the measure of angle PQR in this diagram. Let me...
  [GPU 3] Sample 31/63 | tokens=512 | tau=1.44 | time=13.6s | <think> Okay, so I need to figure out the length of the third side of a triangle...
  [GPU 4] Sample 32/62 | tokens=512 | tau=1.50 | time=12.9s | <think> Okay, so I need to find the maximum value of the function $ 4(x + 7)(2 -...
  [GPU 6] Sample 33/62 | tokens=512 | tau=1.58 | time=11.6s | <think> Okay, so I need to solve the equation $10^x - 10 = 9990$. Let me think a...
  [GPU 2] Sample 32/63 | tokens=512 | tau=1.43 | time=13.2s | <think> Okay, so I need to find the x-intercept (a), the y-intercept (b), and th...
  [GPU 5] Sample 34/62 | tokens=512 | tau=1.49 | time=12.2s | <think> Okay, so I need to figure out how many distinct arrangements there are f...
  [GPU 7] Sample 34/62 | tokens=512 | tau=1.53 | time=12.1s | <think> Okay, so I need to find the inverse of 997 modulo 1000. That means I nee...
  [GPU 1] Sample 33/63 | tokens=512 | tau=1.48 | time=12.7s | <think> Okay, so I need to find the total surface area of a cube that has a volu...
  [GPU 0] Sample 32/63 | tokens=512 | tau=1.57 | time=12.3s | <think> Okay, so I need to compute A^27 + A^31 + A^40 where A is the matrix [[3,...
  [GPU 3] Sample 32/63 | tokens=512 | tau=1.52 | time=12.9s | <think> Okay, so there's this problem about six cars pulling up to a red light o...
  [GPU 4] Sample 33/62 | tokens=512 | tau=1.51 | time=12.8s | <think> Okay, so I need to find the angle ABC, which is the angle at point B for...
  [GPU 6] Sample 34/62 | tokens=512 | tau=1.42 | time=12.9s | <think> Okay, so I need to figure out how many more dollars Pam pays than Susan ...
  [GPU 2] Sample 33/63 | tokens=512 | tau=1.45 | time=13.1s | <think> Okay, so I need to figure out how many blue marbles were in the bag orig...
  [GPU 7] Sample 35/62 | tokens=512 | tau=1.50 | time=12.3s | <think> Okay, so I need to figure out the difference between the area of the reg...
  [GPU 5] Sample 35/62 | tokens=512 | tau=1.39 | time=13.2s | <think> Okay, so I need to figure out what the square root of 53 is in its simpl...
  [GPU 1] Sample 34/63 | tokens=512 | tau=1.60 | time=11.8s | <think> Okay, so I need to find the 2003rd term of the sequence of odd numbers: ...
  [GPU 0] Sample 33/63 | tokens=512 | tau=1.49 | time=12.8s | <think> Okay, so I need to simplify this expression: (1/5) multiplied by (8/7) d...
  [GPU 3] Sample 33/63 | tokens=512 | tau=1.42 | time=13.8s | <think> Okay, so I need to compute the product of the number 5 plus the square r...
  [GPU 4] Sample 34/62 | tokens=512 | tau=1.46 | time=13.2s | <think> Okay, so I need to find the remainder when the sum of numbers from 1 to ...
  [GPU 6] Sample 35/62 | tokens=512 | tau=1.49 | time=12.4s | <think> Okay, so I need to figure out the largest eight-digit number in base 2, ...
  [GPU 2] Sample 34/63 | tokens=512 | tau=1.40 | time=13.6s | <think> Okay, so I need to find the probability that a randomly selected number ...
  [GPU 5] Sample 36/62 | tokens=512 | tau=1.59 | time=11.6s | <think> Okay, so Steve is thinking of a polynomial with all positive integer roo...
  [GPU 7] Sample 36/62 | tokens=512 | tau=1.46 | time=12.7s | <think> Okay, so I need to figure out after how many seconds both gears will hav...
  [GPU 1] Sample 35/63 | tokens=512 | tau=1.50 | time=12.5s | <think> Okay, so I need to figure out how many dollars are equivalent to 1,000,0...
  [GPU 0] Sample 34/63 | tokens=512 | tau=1.45 | time=13.4s | <think> Okay, so I need to find the length of BH in this figure. Let me try to v...
  [GPU 3] Sample 34/63 | tokens=512 | tau=1.39 | time=14.1s | <think> Okay, so I need to find the sum of the measures of angle J and angle H i...
  [GPU 4] Sample 35/62 | tokens=512 | tau=1.49 | time=13.0s | <think> Okay, so I need to figure out for how many real values of x the expressi...
  [GPU 6] Sample 36/62 | tokens=512 | tau=1.46 | time=12.7s | <think> Okay, so I need to compute the sum over all triples (a, b, c) of positiv...
  [GPU 2] Sample 35/63 | tokens=512 | tau=1.38 | time=13.8s | <think> Okay, so I need to find the perimeter of this set S. Let me try to visua...
  [GPU 7] Sample 37/62 | tokens=512 | tau=1.51 | time=12.2s | <think> Okay, so I need to solve this equation: $ z^4 + 4z^3i - 6z^2 - 4zi - i =...
  [GPU 5] Sample 37/62 | tokens=512 | tau=1.41 | time=13.1s | <think> Okay, so I need to find all values of p that satisfy both inequalities: ...
  [GPU 1] Sample 36/63 | tokens=512 | tau=1.42 | time=13.2s | <think> Okay, so I need to find the measure of angle A in this regular pentagon ...
  [GPU 0] Sample 35/63 | tokens=512 | tau=1.63 | time=11.9s | <think> Okay, so I need to convert the repeating decimal 0.133113311331... into ...
  [GPU 4] Sample 36/62 | tokens=512 | tau=1.69 | time=11.4s | <think> Okay, so I need to solve the equation:  $$ \sin \left( \tan^{-1} (x) + \...
  [GPU 3] Sample 35/63 | tokens=512 | tau=1.42 | time=13.8s | <think> Okay, so I need to find the value of g(f(5) - 1). Let me start by recall...
  [GPU 6] Sample 37/62 | tokens=512 | tau=1.54 | time=12.0s | <think> Okay, so I need to find three consecutive positive integers where their ...
  [GPU 2] Sample 36/63 | tokens=512 | tau=1.69 | time=11.3s | <think> Okay, let me try to figure out this sequence problem. The sequence start...
  [GPU 5] Sample 38/62 | tokens=512 | tau=1.49 | time=12.2s | <think> Okay, so I need to figure out the average price of Juan's stamps from th...
  [GPU 7] Sample 38/62 | tokens=512 | tau=1.35 | time=13.6s | <think> Okay, so I need to find the area of triangle ACD in this trapezoid ABCD ...
  [GPU 1] Sample 37/63 | tokens=512 | tau=1.47 | time=12.8s | <think> Okay, so I need to find the minimum value of the expression $(a + b + c ...
  [GPU 0] Sample 36/63 | tokens=512 | tau=1.51 | time=12.8s | <think> Okay, so I need to figure out how many whole-number divisors the express...
  [GPU 4] Sample 37/62 | tokens=512 | tau=1.82 | time=10.6s | <think> Okay, so I need to find the value of $ x_{531} + x_{753} + x_{975} $ giv...
  [GPU 3] Sample 36/63 | tokens=512 | tau=1.42 | time=13.7s | <think> Okay, so I need to figure out what (4 5/8)^55 multiplied by (8/37)^55 is...
  [GPU 6] Sample 38/62 | tokens=512 | tau=1.51 | time=12.2s | <think> Okay, so I need to figure out how many digits repeat in the decimal expa...
  [GPU 2] Sample 37/63 | tokens=512 | tau=1.64 | time=11.6s | <think> Okay, so I need to find the value of r that satisfies the equation (6r² ...
  [GPU 7] Sample 39/62 | tokens=512 | tau=1.58 | time=11.7s | <think> Okay, so I need to find the value of n where the sum 1 + 12 + 123 + 1234...
  [GPU 5] Sample 39/62 | tokens=512 | tau=1.41 | time=13.1s | <think> Okay, so I need to find the least possible sum of a set of distinct posi...
  [GPU 1] Sample 38/63 | tokens=512 | tau=1.48 | time=12.7s | <think> Okay, so I need to figure out the smallest number of leaves in a book wh...
  [GPU 0] Sample 37/63 | tokens=512 | tau=1.55 | time=12.4s | <think> Okay, so I need to find the distance between two parallel lines. Let me ...
  [GPU 4] Sample 38/62 | tokens=512 | tau=1.42 | time=13.6s | <think> Okay, so I need to figure out the maximum number of points where at leas...
  [GPU 3] Sample 37/63 | tokens=512 | tau=1.48 | time=13.2s | <think> Okay, so I need to figure out how many integer coordinate points are str...
  [GPU 2] Sample 38/63 | tokens=512 | tau=1.64 | time=11.6s | <think> Okay, so I need to compute the cross product (2b - a) × (3c + a). The pr...
  [GPU 6] Sample 39/62 | tokens=512 | tau=1.37 | time=13.5s | <think> Okay, so I need to figure out the value of this operation @ between two ...
  [GPU 7] Sample 40/62 | tokens=512 | tau=1.45 | time=12.7s | <think> Okay, so I need to solve the equation |x - 4| - 10 = 2 and find the prod...
  [GPU 5] Sample 40/62 | tokens=512 | tau=1.38 | time=13.3s | <think> Okay, so I need to find the degree of the polynomial p(x) given by that ...
  [GPU 1] Sample 39/63 | tokens=512 | tau=1.45 | time=13.0s | <think> Okay, so I need to solve the equation √(2x)/√(3x - 1) = 3/2. Hmm, let me...
  [GPU 0] Sample 38/63 | tokens=512 | tau=1.45 | time=13.3s | <think> Okay, so I need to figure out which of these equations has the largest s...
  [GPU 4] Sample 39/62 | tokens=512 | tau=1.38 | time=14.0s | <think> Okay, so I need to find the surface area of one of the pieces created wh...
  [GPU 2] Sample 39/63 | tokens=512 | tau=1.55 | time=12.3s | <think> Okay, so I need to find the number of quadratic equations of the form $x...
  [GPU 3] Sample 38/63 | tokens=512 | tau=1.55 | time=12.6s | <think> Okay, so I need to figure out how many integer coordinates are strictly ...
  [GPU 6] Sample 40/62 | tokens=512 | tau=1.47 | time=12.5s | <think> Okay, so I need to combine these two fractions into a single fraction. T...
  [GPU 5] Sample 41/62 | tokens=512 | tau=1.50 | time=12.1s | <think> Okay, so I need to figure out how many cylindrical beakers it takes to f...
  [GPU 7] Sample 41/62 | tokens=512 | tau=1.38 | time=13.4s | <think> Okay, so I need to find P(5) where P(x) is a monic cubic polynomial. Let...
  [GPU 0] Sample 39/63 | tokens=512 | tau=1.61 | time=12.0s | <think> Okay, so I need to find the minimum value of the function $\frac{(x + 5)...
  [GPU 1] Sample 40/63 | tokens=512 | tau=1.43 | time=13.2s | <think> Okay, so Charlie is riding his unicycle, and I need to figure out the sp...
  [GPU 4] Sample 40/62 | tokens=512 | tau=1.54 | time=12.6s | <think> Okay, so I need to factor the quadratic expression $10x^2 - x - 24$ into...
  [GPU 2] Sample 40/63 | tokens=512 | tau=1.52 | time=12.5s | <think> Okay, so I need to figure out where the point (0,0) ends up after two re...
  [GPU 6] Sample 41/62 | tokens=512 | tau=1.49 | time=12.4s | <think> Okay, so I need to evaluate this expression: sin(arcsin 0.4 + arcsin 0.5...
  [GPU 3] Sample 39/63 | tokens=512 | tau=1.41 | time=13.9s | <think> Okay, so I need to find the range of the function y = log base 2 of the ...
  [GPU 5] Sample 42/62 | tokens=512 | tau=1.55 | time=11.8s | <think> Okay, so I need to find the value of $ b $ in the continued fraction exp...
  [GPU 7] Sample 42/62 | tokens=512 | tau=1.55 | time=11.8s | <think> Okay, so I need to find the remainder when the 100th term of the Fibonac...
  [GPU 0] Sample 40/63 | tokens=512 | tau=1.43 | time=13.5s | <think> Okay, so I need to solve the inequality 1 divided by (x minus 5) is grea...
  [GPU 1] Sample 41/63 | tokens=512 | tau=1.37 | time=13.7s | <think> Okay, so there's this robot that moves at a constant speed. It takes 2.5...
  [GPU 4] Sample 41/62 | tokens=512 | tau=1.36 | time=14.1s | <think> Okay, so I need to find the measure of angle ADC in this diagram with tw...
  [GPU 2] Sample 41/63 | tokens=512 | tau=1.51 | time=12.6s | <think> Okay, so I need to find the value of $ b $ given the functions $ f(x) = ...
  [GPU 6] Sample 42/62 | tokens=512 | tau=1.47 | time=12.6s | <think> Okay, so I need to find the value of the product abc given these three e...
  [GPU 3] Sample 40/63 | tokens=512 | tau=1.50 | time=13.0s | <think> Okay, so I need to find positive integers a, b, and 2009, where a < b < ...
  [GPU 5] Sample 43/62 | tokens=512 | tau=1.46 | time=12.6s | <think> Okay, so I need to find the smallest number that is one less than twice ...
  [GPU 7] Sample 43/62 | tokens=512 | tau=1.43 | time=12.8s | <think> Okay, so I need to figure out how many different license plates can be m...
  [GPU 0] Sample 41/63 | tokens=512 | tau=1.48 | time=13.0s | <think> Okay, so I need to find cos(angle RPS) given that sin(angle RPQ) is 7/25...
  [GPU 1] Sample 42/63 | tokens=512 | tau=1.41 | time=13.3s | <think> Okay, so I need to figure out the bicycle's speed in inches per second w...
  [GPU 4] Sample 42/62 | tokens=512 | tau=1.38 | time=13.9s | <think> Okay, so I need to find the minimum value of (x + y)(y + z) given that x...
  [GPU 2] Sample 42/63 | tokens=512 | tau=1.42 | time=13.4s | <think> Okay, so I need to figure out how many ways we can form a subcommittee o...
  [GPU 6] Sample 43/62 | tokens=512 | tau=1.42 | time=13.0s | <think> Okay, so I need to find an integer x that satisfies the inequality 1/4 <...
  [GPU 3] Sample 41/63 | tokens=512 | tau=1.43 | time=13.7s | <think> Okay, so I need to find the probability that two segments AB and CD inte...
  [GPU 7] Sample 44/62 | tokens=512 | tau=1.55 | time=11.8s | <think> Okay, so I need to simplify this product of cosines: cos(2π/15) * cos(4π...
  [GPU 5] Sample 44/62 | tokens=512 | tau=1.38 | time=13.2s | <think> Okay, so I need to figure out how many ways 8 people can be seated aroun...
  [GPU 0] Sample 42/63 | tokens=512 | tau=1.49 | time=12.8s | <think> Okay, so I need to figure out how many distinct values the function $ f(...
  [GPU 1] Sample 43/63 | tokens=512 | tau=1.45 | time=13.0s | <think> Okay, so I need to find three consecutive integers whose product is 120,...
  [GPU 6] Sample 44/62 | tokens=512 | tau=1.50 | time=12.3s | <think> Okay, so I need to find the units digit of 18 raised to the 6th power. H...
  [GPU 4] Sample 43/62 | tokens=512 | tau=1.51 | time=12.8s | <think> Okay, so I need to find the angle between vectors a and a - b. The probl...
  [GPU 2] Sample 43/63 | tokens=512 | tau=1.46 | time=12.9s | <think> Okay, so I need to figure out what 999 in base 10 is in base six. Hmm, l...
  [GPU 7] Sample 45/62 | tokens=512 | tau=1.61 | time=11.4s | <think> Okay, so I need to find the value of $ xy + yz + zx $ given these three ...
  [GPU 3] Sample 42/63 | tokens=512 | tau=1.41 | time=13.8s | <think> Okay, so I need to simplify this expression: the square root of a fracti...
  [GPU 5] Sample 45/62 | tokens=512 | tau=1.50 | time=12.2s | <think> Okay, so I need to figure out how many possible values of x there are wh...
  [GPU 0] Sample 43/63 | tokens=512 | tau=1.44 | time=13.4s | <think> Okay, so I need to find the value of 513 squared minus 487 squared. Hmm,...
  [GPU 1] Sample 44/63 | tokens=512 | tau=1.45 | time=13.1s | <think> Okay, let me try to figure out this problem. So, the question is: If t(x...
  [GPU 6] Sample 45/62 | tokens=512 | tau=1.46 | time=12.7s | <think> Okay, so I need to figure out what kind of graph the equation $\left(\fr...
  [GPU 4] Sample 44/62 | tokens=512 | tau=1.54 | time=12.5s | <think> Okay, so I need to compute the binomial coefficient $\dbinom{31}{28}$. H...
  [GPU 2] Sample 44/63 | tokens=512 | tau=1.51 | time=12.6s | <think> Okay, so I need to solve this equation: the cube root of (x squared minu...
  [GPU 7] Sample 46/62 | tokens=512 | tau=1.52 | time=12.2s | <think> Okay, so I need to find $ f^{-1}(f^{-1}(6)) $. Let me start by recalling...
  [GPU 5] Sample 46/62 | tokens=512 | tau=1.66 | time=11.1s | <think> Okay, so I need to figure out how many possible values there are for $ a...
  [GPU 3] Sample 43/63 | tokens=512 | tau=1.39 | time=14.1s | <think> Okay, so I need to figure out how to express a + b + c + d + e + f in te...
  [GPU 0] Sample 44/63 | tokens=512 | tau=1.44 | time=13.4s | <think> Okay, so I need to find the value of 'a' that makes the function f(n) co...
  [GPU 1] Sample 45/63 | tokens=512 | tau=1.35 | time=13.9s | <think> Okay, so I need to figure out how many ways I can stack my 6 different b...
  [GPU 6] Sample 46/62 | tokens=512 | tau=1.39 | time=13.3s | <think> Okay, so I need to find the modulo 7 remainder of the sum of all the odd...
  [GPU 4] Sample 45/62 | tokens=512 | tau=1.45 | time=13.3s | <think> Okay, so I need to find all real numbers x such that -4 < x⁴ + 4x² < 21....
  [GPU 2] Sample 45/63 | tokens=512 | tau=1.45 | time=13.1s | <think> Okay, so I need to find the median of 27 consecutive positive integers w...
  [GPU 7] Sample 47/62 | tokens=512 | tau=1.55 | time=11.9s | <think> Okay, so I need to find the sum of the positive divisors of 500, which i...
  [GPU 5] Sample 47/62 | tokens=512 | tau=1.56 | time=11.8s | <think> Okay, so William Sydney Porter tried to calculate (-3 + 4i) divided by (...
  [GPU 3] Sample 44/63 | tokens=512 | tau=1.61 | time=12.2s | <think> Okay, so I need to simplify this algebraic expression: 4 times (3r³ + 5r...
  [GPU 0] Sample 45/63 | tokens=512 | tau=1.40 | time=13.7s | <think> Okay, so I need to find the perimeter of triangle ABC, which is isoscele...
  [GPU 1] Sample 46/63 | tokens=512 | tau=1.51 | time=12.5s | <think> Okay, so I need to find the side length of an equilateral triangle inscr...
  [GPU 6] Sample 47/62 | tokens=512 | tau=1.48 | time=12.5s | <think> Okay, so I need to figure out the difference between the positive square...
  [GPU 7] Sample 48/62 | tokens=512 | tau=1.50 | time=12.3s | <think> Okay, so I need to solve the inequality $ x^2 - 5x - 4 \leq 10 $. Let me...
  [GPU 4] Sample 46/62 | tokens=512 | tau=1.52 | time=12.8s | <think> Okay, so I need to figure out the equation of the set of image points af...
  [GPU 2] Sample 46/63 | tokens=512 | tau=1.48 | time=12.8s | <think> Okay, so there's this problem about two candidates running for class pre...
  [GPU 5] Sample 48/62 | tokens=512 | tau=1.49 | time=12.3s | <think> Okay, so I need to find the probability that a triangle with sides of le...
  [GPU 3] Sample 45/63 | tokens=512 | tau=1.62 | time=12.0s | <think> Okay, so I need to find the minimum value of this expression:   $$ \frac...
  [GPU 0] Sample 46/63 | tokens=512 | tau=1.56 | time=12.3s | <think> Okay, so I need to find the value of b in the direction vector of the li...
  [GPU 1] Sample 47/63 | tokens=512 | tau=1.47 | time=12.8s | <think> Okay, so I need to find the area of this trapezoid. Let me recall the fo...
  [GPU 6] Sample 48/62 | tokens=512 | tau=1.51 | time=12.3s | <think> Okay, so I need to find the largest possible area of a rectangular field...
  [GPU 7] Sample 49/62 | tokens=512 | tau=1.50 | time=12.4s | <think> Okay, so I need to find the inverse function values for f(x) at 0 and 6,...
  [GPU 5] Sample 49/62 | tokens=512 | tau=1.43 | time=12.8s | <think> Okay, so I need to find sin T in triangle RST. They told me that sin R i...
  [GPU 4] Sample 47/62 | tokens=512 | tau=1.44 | time=13.4s | <think> Okay, so I need to find the measure of angle BAC in this diagram. Let me...
  [GPU 2] Sample 47/63 | tokens=512 | tau=1.39 | time=13.7s | <think> Okay, so I need to find the dot product of these two vectors: the first ...
  [GPU 3] Sample 46/63 | tokens=512 | tau=1.41 | time=13.8s | <think> Okay, so I need to solve this equation: Three plus the reciprocal of a n...
  [GPU 0] Sample 47/63 | tokens=512 | tau=1.47 | time=13.1s | <think> Okay, so I need to find the greatest possible perimeter of a triangle wh...
  [GPU 6] Sample 49/62 | tokens=512 | tau=1.61 | time=11.5s | <think> Okay, so I need to find the smallest distance between the origin and a p...
  [GPU 1] Sample 48/63 | tokens=512 | tau=1.42 | time=13.3s | <think> Okay, so I need to find the units digit of 4$, which is defined as a sup...
  [GPU 7] Sample 50/62 | tokens=512 | tau=1.38 | time=13.4s | <think> Okay, so I need to add 313.9 and 12.6 together. Let me think about how t...
  [GPU 4] Sample 48/62 | tokens=512 | tau=1.53 | time=12.6s | <think> Okay, so I need to solve the inequality $\frac{|x^2 - 81|}{x^2 - 36x} < ...
  [GPU 5] Sample 50/62 | tokens=512 | tau=1.43 | time=12.9s | <think> Okay, so I need to solve this equation: 3x + 2(1 + x) = 17, and then fin...
  [GPU 2] Sample 48/63 | tokens=512 | tau=1.49 | time=12.8s | <think> Okay, so I need to figure out how many two-digit prime numbers have digi...
  [GPU 3] Sample 47/63 | tokens=512 | tau=1.39 | time=14.0s | <think> Okay, so I need to find the largest possible value of |a| + |b| + |c| gi...
  [GPU 0] Sample 48/63 | tokens=512 | tau=1.61 | time=11.9s | <think> Okay, so I need to find the coordinates of point P on the line y = -x + ...
  [GPU 6] Sample 50/62 | tokens=512 | tau=1.59 | time=11.6s | <think> Okay, so Navin, Luka, and Ian are talking about their part-time jobs, an...
  [GPU 1] Sample 49/63 | tokens=512 | tau=1.47 | time=12.8s | <think> Okay, let's see. Kathy has $300 in the bank, and she wants to withdraw h...
  [GPU 5] Sample 51/62 | tokens=512 | tau=1.44 | time=12.6s | <think> Okay, so I need to figure out how many ways 3 people can be assigned to ...
  [GPU 7] Sample 51/62 | tokens=512 | tau=1.38 | time=13.3s | <think> Okay, so I need to find the value of the inverse function of f at 1/5, w...
  [GPU 4] Sample 49/62 | tokens=512 | tau=1.47 | time=13.1s | <think> Okay, so I need to find the smallest real number x in the domain of the ...
  [GPU 2] Sample 49/63 | tokens=512 | tau=1.48 | time=12.7s | <think> Okay, so I need to figure out how many integers satisfy the inequality |...
  [GPU 3] Sample 48/63 | tokens=512 | tau=1.49 | time=13.0s | <think> Okay, so I need to figure out for which grade the number of male bus rid...
  [GPU 6] Sample 51/62 | tokens=512 | tau=1.45 | time=12.7s | <think> Okay, so I need to find the remainder when 2004 is divided by 12. Hmm, l...
  [GPU 0] Sample 49/63 | tokens=512 | tau=1.37 | time=14.0s | <think> Okay, so I need to simplify this expression: 19x plus 1 minus 4x minus 8...
  [GPU 1] Sample 50/63 | tokens=512 | tau=1.51 | time=12.5s | <think> Okay, so I need to figure out the ratio of the acceleration of Jen's sof...
  [GPU 7] Sample 52/62 | tokens=512 | tau=1.51 | time=12.2s | <think> Okay, so I need to find the remainder when $129^{34} + 96^{38}$ is divid...
  [GPU 5] Sample 52/62 | tokens=512 | tau=1.38 | time=13.3s | <think> Okay, so I need to simplify this expression: (10r³)(4r⁶) divided by 8r⁴....
  [GPU 4] Sample 50/62 | tokens=512 | tau=1.46 | time=13.1s | <think> Okay, so I need to find the area of the gray piece in this tangram puzzl...
  [GPU 2] Sample 50/63 | tokens=512 | tau=1.48 | time=12.8s | <think> Okay, so I need to figure out the value of x that Archimedes should choo...
  [GPU 3] Sample 49/63 | tokens=512 | tau=1.43 | time=13.7s | <think> Okay, so I need to find the value of f(-2) for the function f(x) = 5x² +...
  [GPU 6] Sample 52/62 | tokens=512 | tau=1.45 | time=12.7s | <think> Okay, so I need to solve this equation: (3)5² - 4(5 - a)² ÷ 3 = 63. Hmm,...
  [GPU 0] Sample 50/63 | tokens=512 | tau=1.49 | time=13.0s | <think> Okay, so I need to find the distance from point P to the sixth vertex of...
  [GPU 1] Sample 51/63 | tokens=512 | tau=1.41 | time=13.3s | <think> Okay, so I need to find the maximum value of the expression |1 + z| + |1...
  [GPU 7] Sample 53/62 | tokens=512 | tau=1.52 | time=12.2s | <think> Okay, so I need to find the largest integer less than 2010 that satisfie...
  [GPU 5] Sample 53/62 | tokens=512 | tau=1.50 | time=12.3s | <think> Okay, so I need to solve this equation: arccos x + arccos 2x + arccos 3x...
  [GPU 4] Sample 51/62 | tokens=512 | tau=1.43 | time=13.5s | <think> Okay, so Roslyn has ten boxes total. Let me try to figure out how many b...
  [GPU 2] Sample 51/63 | tokens=512 | tau=1.36 | time=14.0s | <think> Okay, so I need to figure out what happens when I rotate the complex num...
  [GPU 6] Sample 53/62 | tokens=512 | tau=1.65 | time=11.2s | <think> Okay, so I need to find the unordered set containing the three expressio...
  [GPU 3] Sample 50/63 | tokens=512 | tau=1.40 | time=13.9s | <think> Okay, so I need to find the value of this expression: (16 times the cube...
  [GPU 1] Sample 52/63 | tokens=512 | tau=1.57 | time=12.0s | <think> Okay, so I need to find the distance between the foci of a hyperbola. Th...
  [GPU 0] Sample 51/63 | tokens=512 | tau=1.48 | time=13.0s | <think> Okay, so I need to find the radius of the smaller semicircle in this cir...
  [GPU 7] Sample 54/62 | tokens=512 | tau=1.59 | time=11.6s | <think> Okay, so I need to find the range of the function $ f(x) = (\arccos x)^2...
  [GPU 5] Sample 54/62 | tokens=512 | tau=1.64 | time=11.2s | <think> Okay, so I need to find the minimum value of $ a^4 + b^8 $ given that $ ...
  [GPU 2] Sample 52/63 | tokens=512 | tau=1.59 | time=12.1s | <think> Okay, so I need to figure out the units digit N of the number 21420N suc...
  [GPU 4] Sample 52/62 | tokens=512 | tau=1.51 | time=12.8s | <think> Okay, so I need to find P(16) where P(x) is a quadratic polynomial that'...
  [GPU 6] Sample 54/62 | tokens=512 | tau=1.39 | time=13.3s | <think> Okay, so I need to figure out what 9 divided by 2 is as a decimal. Hmm, ...
  [GPU 3] Sample 51/63 | tokens=512 | tau=1.46 | time=13.4s | <think> Okay, so I need to figure out how many of the same digits are found in t...
  [GPU 1] Sample 53/63 | tokens=512 | tau=1.48 | time=12.8s | <think> Okay, so I need to find the sum of the coefficients of the polynomial g(...
  [GPU 0] Sample 52/63 | tokens=512 | tau=1.55 | time=12.4s | <think> Okay, so I need to figure out where the reflection takes the vector $\be...
  [GPU 7] Sample 55/62 | tokens=512 | tau=1.44 | time=12.8s | <think> Okay, so I need to find the quotient when x^9 + 1 is divided by x - 1. H...
  [GPU 5] Sample 55/62 | tokens=512 | tau=1.43 | time=12.8s | <think> Okay, so I need to figure out the value of the square symbol, which is r...
  [GPU 2] Sample 53/63 | tokens=512 | tau=1.50 | time=12.7s | <think> Okay, so I need to find the shortest distance from the point (6, 0) to t...
  [GPU 4] Sample 53/62 | tokens=512 | tau=1.46 | time=13.2s | <think> Okay, so I need to find the projection of vector a onto vector b. The pr...
  [GPU 6] Sample 55/62 | tokens=512 | tau=1.52 | time=12.2s | <think> Okay, so I need to find the last nonzero digit to the right of the decim...
  [GPU 3] Sample 52/63 | tokens=512 | tau=1.43 | time=13.7s | <think> Okay, so there's this problem about six witches and ten sorcerers at an ...
  [GPU 7] Sample 56/62 | tokens=512 | tau=1.49 | time=12.4s | <think> Okay, so there's this problem about thirty-five students attending a mat...
  [GPU 1] Sample 54/63 | tokens=512 | tau=1.37 | time=13.9s | <think> Okay, so I need to find an expression for AF² + BF² + CF² in terms of th...
  [GPU 5] Sample 56/62 | tokens=512 | tau=1.45 | time=12.6s | <think> Okay, so I need to find the area of the quadrilateral formed by the four...
  [GPU 0] Sample 53/63 | tokens=512 | tau=1.33 | time=14.5s | <think> Okay, so I need to compute the value of sin³18° + sin²18°. Hmm, let me t...
  [GPU 2] Sample 54/63 | tokens=512 | tau=1.44 | time=13.2s | <think> Okay, so I need to find the length of the diagonal of a square when it h...
  [GPU 4] Sample 54/62 | tokens=512 | tau=1.48 | time=13.0s | <think> Okay, so I need to find the minimum value of the expression $\frac{1}{a}...
  [GPU 6] Sample 56/62 | tokens=512 | tau=1.52 | time=12.1s | <think> Okay, so I need to find the value of n such that the sum of the first n ...
  [GPU 3] Sample 53/63 | tokens=512 | tau=1.60 | time=12.2s | <think> Okay, so I need to find a vector v such that when I take the cross produ...
  [GPU 5] Sample 57/62 | tokens=512 | tau=1.50 | time=12.2s | <think> Okay, so I need to figure out how many representatives the 8th grade sho...
  [GPU 7] Sample 57/62 | tokens=512 | tau=1.38 | time=13.4s | <think> Okay, so I need to figure out how many ways 5 students can be selected f...
  [GPU 1] Sample 55/63 | tokens=512 | tau=1.34 | time=14.3s | <think> Okay, so I need to convert the fraction 57/160 into a terminating decima...
  [GPU 0] Sample 54/63 | tokens=512 | tau=1.39 | time=13.9s | <think> Okay, so I need to solve this problem where y varies inversely as the sq...
  [GPU 2] Sample 55/63 | tokens=512 | tau=1.44 | time=13.3s | <think> Okay, so I need to find the area of an isosceles right triangle where th...
  [GPU 4] Sample 55/62 | tokens=512 | tau=1.38 | time=14.1s | <think> Okay, so I need to find the number of dice, n, such that when you roll n...
  [GPU 6] Sample 57/62 | tokens=512 | tau=1.57 | time=11.8s | <think> Okay, so I need to find the image of the line y = 2x + 1 under the matri...
  [GPU 3] Sample 54/63 | tokens=512 | tau=1.65 | time=11.9s | <think> Okay, so I need to figure out the cost of a pencil in cents. The problem...
  [GPU 5] Sample 58/62 | tokens=512 | tau=1.46 | time=12.5s | <think> Okay, so I need to find the value of this function f(n) at three differe...
  [GPU 7] Sample 58/62 | tokens=512 | tau=1.48 | time=12.4s | <think> Okay, so I need to figure out for how many values of x the expression (x...
  [GPU 1] Sample 56/63 | tokens=512 | tau=1.64 | time=11.5s | <think> Okay, so Karla drove her vehicle 12,000 miles last year. The question is...
  [GPU 0] Sample 55/63 | tokens=512 | tau=1.48 | time=12.9s | <think> Okay, so I need to solve this recurrence relation problem. Let me first ...
  [GPU 2] Sample 56/63 | tokens=512 | tau=1.49 | time=12.7s | <think> Okay, so I need to find the square root of f(f(f(f(1)))) where f(x) is 2...
  [GPU 6] Sample 58/62 | tokens=512 | tau=1.68 | time=11.0s | <think> Okay, so Linda, Sherry, June, and Connie sold cookies and earned differe...
  [GPU 4] Sample 56/62 | tokens=512 | tau=1.40 | time=13.9s | <think> Okay, so I need to find the probability that a randomly chosen point ins...
  [GPU 3] Sample 55/63 | tokens=512 | tau=1.46 | time=13.3s | <think> Okay, so I need to find the domain of the function f(x) = (2x - 7)/√(x² ...
  [GPU 5] Sample 59/62 | tokens=512 | tau=1.50 | time=12.2s | <think> Okay, so I need to evaluate the ceiling of the square root of 20, and th...
  [GPU 7] Sample 59/62 | tokens=512 | tau=1.55 | time=12.0s | <think> Okay, so I need to find the class average for this test. Let me think. T...
  [GPU 1] Sample 57/63 | tokens=512 | tau=1.42 | time=13.4s | <think> Okay, so I need to figure out the value of 5 star 1, where the operation...
  [GPU 0] Sample 56/63 | tokens=512 | tau=1.49 | time=12.9s | <think> Okay, so I need to simplify this expression: (u + 4)(u - 1) minus (u - 3...
  [GPU 2] Sample 57/63 | tokens=512 | tau=1.43 | time=13.3s | <think> Okay, so I need to find the average of the two smallest positive integer...
  [GPU 6] Sample 59/62 | tokens=512 | tau=1.42 | time=13.0s | <think> Okay, so I need to find the maximum value of the expression $ ab^2 c^3 d...
  [GPU 4] Sample 57/62 | tokens=512 | tau=1.56 | time=12.4s | <think> Okay, so I need to solve this problem about a two-digit number. Let me r...
  [GPU 3] Sample 56/63 | tokens=512 | tau=1.43 | time=13.7s | <think> Okay, so I need to find the integer value of x in the arithmetic sequenc...
  [GPU 5] Sample 60/62 | tokens=512 | tau=1.49 | time=12.3s | <think> Okay, so I need to figure out how many distinct possible values there ar...
  [GPU 7] Sample 60/62 | tokens=512 | tau=1.46 | time=12.6s | <think> Okay, so I need to figure out for which prime numbers p the congruence 8...
  [GPU 1] Sample 58/63 | tokens=512 | tau=1.42 | time=13.4s | <think> Okay, so I need to figure out the remainder when 54 is divided by 6. Let...
  [GPU 0] Sample 57/63 | tokens=512 | tau=1.37 | time=14.1s | <think> Okay, so I need to find the inverse of 17 modulo 83. That means I need t...
  [GPU 6] Sample 60/62 | tokens=512 | tau=1.62 | time=11.4s | <think> Okay, so I need to find the sum of all complex solutions to this equatio...
  [GPU 2] Sample 58/63 | tokens=512 | tau=1.41 | time=13.5s | <think> Okay, let me try to figure out this problem. So, the question is about h...
  [GPU 4] Sample 58/62 | tokens=512 | tau=1.50 | time=13.0s | <think> Okay, so I need to find the measure of angle STR in this diagram. Let me...
  [GPU 5] Sample 61/62 | tokens=512 | tau=1.50 | time=12.3s | <think> Okay, so I need to figure out the shortest distance you can travel if yo...
  [GPU 3] Sample 57/63 | tokens=512 | tau=1.44 | time=13.6s | <think> Okay, so I need to figure out how many inches on the map correspond to 5...
  [GPU 7] Sample 61/62 | tokens=512 | tau=1.40 | time=13.3s | <think> Okay, so I need to figure out the remainder when the sum of numbers from...
  [GPU 1] Sample 59/63 | tokens=512 | tau=1.48 | time=12.9s | <think> Okay, so I need to figure out the fifth number in the list of positive i...
  [GPU 0] Sample 58/63 | tokens=512 | tau=1.50 | time=12.8s | <think> Okay, so I need to find all the integer roots of the polynomial equation...
  [GPU 2] Sample 59/63 | tokens=512 | tau=1.58 | time=12.2s | <think> Okay, so I need to find the sum of all possible values of θ where re^{iθ...
  [GPU 6] Sample 61/62 | tokens=512 | tau=1.41 | time=13.1s | <think> Okay, so I need to figure out the volume of a cube from which a steel sp...
  [GPU 4] Sample 59/62 | tokens=512 | tau=1.42 | time=13.7s | <think> Okay, so I need to figure out how many integer values of t satisfy the c...
  [GPU 5] Sample 62/62 | tokens=512 | tau=1.60 | time=11.5s | <think> Okay, so I need to figure out the value of $(\sqrt{2} + \sqrt{3})^3$ and...
  [GPU 7] Sample 62/62 | tokens=512 | tau=1.52 | time=12.1s | <think> Okay, so I need to find the domain of the function f(x) = (2 - x) / log(...
  [GPU 3] Sample 58/63 | tokens=512 | tau=1.57 | time=12.4s | <think> Okay, so I need to figure out the cost of a 3-inch cube made of fake gol...
  [GPU 1] Sample 60/63 | tokens=512 | tau=1.48 | time=12.8s | <think> Okay, so I need to figure out the value of n in this magic square. Let m...
  [GPU 6] Sample 62/62 | tokens=512 | tau=1.56 | time=11.8s | <think> Okay, so I need to find the area of the set S, which consists of points ...
  [GPU 0] Sample 59/63 | tokens=512 | tau=1.45 | time=13.3s | <think> Okay, so I need to solve this system of logarithmic equations:  First eq...
  [GPU 2] Sample 60/63 | tokens=512 | tau=1.45 | time=13.0s | <think> Okay, so I need to find the value of this product of logarithms: log bas...
  [GPU 4] Sample 60/62 | tokens=512 | tau=1.46 | time=13.2s | <think> Okay, so Jim and Martha are at the corner of a rectangular field. The fi...
  [GPU 3] Sample 59/63 | tokens=512 | tau=1.53 | time=12.7s | <think> Okay, so I need to find the area of the shaded triangle in the diagram. ...
  [GPU 1] Sample 61/63 | tokens=512 | tau=1.63 | time=11.6s | <think> Okay, so I need to simplify this big fraction where the numerator is the...
  [GPU 0] Sample 60/63 | tokens=512 | tau=1.45 | time=13.2s | <think> Okay, so I need to figure out how far a car would travel if it's going 5...
  [GPU 2] Sample 61/63 | tokens=512 | tau=1.42 | time=13.3s | <think> Okay, so I need to find the probability that the reciprocal of a randoml...
  [GPU 4] Sample 61/62 | tokens=512 | tau=1.52 | time=12.6s | <think> Okay, so I need to solve this equation: √(x + √(3x + 6)) + √(x - √(3x + ...
  [GPU 3] Sample 60/63 | tokens=512 | tau=1.49 | time=13.0s | <think> Okay, so I need to solve this problem about an unfair six-sided die. Let...
  [GPU 1] Sample 62/63 | tokens=512 | tau=1.45 | time=12.9s | <think> Okay, so I need to find the minimum value of the function f(x) = |x - p|...
  [GPU 0] Sample 61/63 | tokens=512 | tau=1.43 | time=13.3s | <think> Okay, so I need to find all possible values of the expression $\frac{1}{...
  [GPU 2] Sample 62/63 | tokens=512 | tau=1.46 | time=12.8s | <think> Okay, so I need to find the least possible value of |a_{n-1}| for a poly...
  [GPU 4] Sample 62/62 | tokens=512 | tau=1.44 | time=13.3s | <think> Okay, so I need to find the equation of a line that consists of all vect...
  [GPU 3] Sample 61/63 | tokens=512 | tau=1.61 | time=12.0s | <think> Okay, so I need to find tan A for triangle ABC, given that the area of t...
  [GPU 1] Sample 63/63 | tokens=512 | tau=1.36 | time=13.9s | <think> Okay, so I need to find the area of an equiangular octagon that has four...
  [GPU 2] Sample 63/63 | tokens=512 | tau=1.60 | time=11.8s | <think> Okay, so I need to solve this problem where there's a sequence defined b...
  [GPU 0] Sample 62/63 | tokens=512 | tau=1.53 | time=12.5s | <think> Okay, so I need to figure out the original price of the shirt when the s...
  [GPU 3] Sample 62/63 | tokens=512 | tau=1.47 | time=13.2s | <think> Okay, so Tom has this Mr. Potato Head, and he wants to figure out how ma...
  [GPU 0] Sample 63/63 | tokens=512 | tau=1.51 | time=12.6s | <think> Okay, so I need to find the modulus of this complex number w, which is g...
  [GPU 3] Sample 63/63 | tokens=512 | tau=1.33 | time=15.1s | <think> Okay, so I need to find the measure of angle AHB in triangle ABC where A...

============================================================
RESULTS SUMMARY
============================================================
  Denoise steps:              2
  GPUs used:                  8
  Samples evaluated:          500
  Total blocks:               173732
  Total generated tokens:     256000
  Total GPU-time:             6414.28s
  Wall-clock time (approx):   15.07s
  ---
  Avg acceptance length (tau): 1.47
  Median acceptance length:    1.0
  Per-sample avg tau:          ['1.38', '1.42', '1.43', '1.62', '1.36', '1.44', '1.41', '1.48', '1.43', '1.49', '1.52', '1.38', '1.65', '1.60', '1.46', '1.38', '1.34', '1.51', '1.41', '1.36', '1.51', '1.45', '1.36', '1.51', '1.43', '1.47', '1.49', '1.43', '1.60', '1.45', '1.45', '1.57', '1.49', '1.45', '1.63', '1.51', '1.55', '1.45', '1.61', '1.43', '1.48', '1.49', '1.44', '1.44', '1.40', '1.56', '1.47', '1.61', '1.37', '1.49', '1.48', '1.55', '1.33', '1.39', '1.48', '1.49', '1.37', '1.50', '1.45', '1.45', '1.43', '1.53', '1.51', '1.51', '1.46', '1.45', '1.54', '1.43', '1.31', '1.52', '1.43', '1.38', '1.43', '1.54', '1.71', '1.42', '1.67', '1.51', '1.37', '1.46', '1.48', '1.47', '1.46', '1.45', '1.39', '1.53', '1.39', '1.45', '1.40', '1.76', '1.49', '1.54', '1.43', '1.40', '1.42', '1.48', '1.60', '1.50', '1.42', '1.47', '1.48', '1.45', '1.43', '1.37', '1.41', '1.45', '1.45', '1.35', '1.51', '1.47', '1.42', '1.47', '1.51', '1.41', '1.57', '1.48', '1.37', '1.34', '1.64', '1.42', '1.42', '1.48', '1.48', '1.63', '1.45', '1.36', '1.56', '1.44', '1.44', '1.33', '1.55', '1.42', '1.43', '1.69', '1.52', '1.60', '1.58', '1.28', '1.42', '1.49', '1.58', '1.58', '1.38', '1.44', '1.30', '1.48', '1.49', '1.50', '1.51', '1.45', '1.41', '1.35', '1.47', '1.39', '1.48', '1.55', '1.39', '1.43', '1.45', '1.40', '1.38', '1.69', '1.64', '1.64', '1.55', '1.52', '1.51', '1.42', '1.46', '1.51', '1.45', '1.48', '1.39', '1.49', '1.48', '1.48', '1.36', '1.59', '1.50', '1.44', '1.44', '1.49', '1.43', '1.41', '1.58', '1.45', '1.42', '1.46', '1.60', '1.43', '1.42', '1.42', '1.44', '1.58', '1.69', '1.44', '1.50', '1.47', '1.45', '1.35', '1.46', '1.50', '1.63', '1.48', '1.40', '1.48', '1.54', '1.38', '1.47', '1.53', '1.39', '1.51', '1.53', '1.51', '1.65', '1.40', '1.51', '1.35', '1.56', '1.44', '1.52', '1.42', '1.39', '1.42', '1.42', '1.48', '1.55', '1.41', '1.50', '1.43', '1.41', '1.39', '1.61', '1.62', '1.41', '1.39', '1.49', '1.43', '1.40', '1.46', '1.43', '1.60', '1.65', '1.46', '1.43', '1.44', '1.57', '1.53', '1.49', '1.61', '1.47', '1.33', '1.54', '1.58', '1.40', '1.43', '1.75', '1.51', '1.51', '1.52', '1.48', '1.41', '1.66', '1.42', '1.32', '1.50', '1.44', '1.50', '1.51', '1.47', '1.41', '1.53', '1.38', '1.54', '1.46', '1.78', '1.42', '1.43', '1.50', '1.51', '1.76', '1.48', '1.51', '1.50', '1.51', '1.46', '1.49', '1.69', '1.82', '1.42', '1.38', '1.54', '1.36', '1.38', '1.51', '1.54', '1.45', '1.52', '1.44', '1.53', '1.47', '1.46', '1.43', '1.51', '1.46', '1.48', '1.38', '1.40', '1.56', '1.50', '1.42', '1.46', '1.52', '1.44', '1.45', '1.38', '1.50', '1.48', '1.38', '1.40', '1.41', '1.58', '1.60', '1.40', '1.49', '1.52', '1.52', '1.69', '1.41', '1.59', '1.44', '1.43', '1.59', '1.51', '1.58', '1.48', '1.50', '1.51', '1.50', '1.40', '1.80', '1.48', '1.40', '1.45', '1.45', '1.38', '1.38', '1.49', '1.39', '1.59', '1.41', '1.49', '1.41', '1.38', '1.50', '1.55', '1.46', '1.38', '1.50', '1.66', '1.56', '1.49', '1.43', '1.43', '1.44', '1.38', '1.50', '1.64', '1.43', '1.45', '1.50', '1.46', '1.50', '1.49', '1.50', '1.60', '1.49', '1.38', '1.48', '1.40', '1.43', '1.41', '1.33', '1.48', '1.44', '1.61', '1.36', '1.45', '1.38', '1.57', '1.50', '1.43', '1.48', '1.43', '1.49', '1.41', '1.46', '1.45', '1.47', '1.59', '1.35', '1.54', '1.49', '1.45', '1.43', '1.64', '1.53', '1.43', '1.58', '1.42', '1.49', '1.46', '1.54', '1.51', '1.37', '1.47', '1.49', '1.47', '1.42', '1.50', '1.46', '1.39', '1.48', '1.51', '1.61', '1.59', '1.45', '1.45', '1.65', '1.39', '1.52', '1.52', '1.57', '1.68', '1.42', '1.62', '1.41', '1.56', '1.44', '1.50', '1.51', '1.39', '1.50', '1.45', '1.45', '1.47', '1.48', '1.39', '1.52', '1.53', '1.43', '1.48', '1.43', '1.48', '1.34', '1.55', '1.56', '1.44', '1.36', '1.66', '1.52', '1.45', '1.43', '1.41', '1.44', '1.61', '1.48', '1.48', '1.55', '1.50', '1.50', '1.53', '1.50', '1.46', '1.51', '1.35', '1.58', '1.45', '1.38', '1.55', '1.43', '1.55', '1.61', '1.52', '1.55', '1.50', '1.50', '1.38', '1.38', '1.51', '1.52', '1.59', '1.44', '1.49', '1.38', '1.48', '1.55', '1.46', '1.40', '1.52']
  Min per-sample tau:          1.28
  Max per-sample tau:          1.82
============================================================

Results saved to /workspace/hanrui/idea1/results/dflash_eval/math500_steps2.json

============================================
  Running DFlash eval: denoise_steps=3
  GPUs: 8, Samples: 500
============================================
W0407 19:39:37.680000 6186 site-packages/torch/distributed/run.py:803] 
W0407 19:39:37.680000 6186 site-packages/torch/distributed/run.py:803] *****************************************
W0407 19:39:37.680000 6186 site-packages/torch/distributed/run.py:803] Setting OMP_NUM_THREADS environment variable for each process to be 1 in default, to avoid your system being overloaded, please further tune the variable for optimal performance in your application as needed. 
W0407 19:39:37.680000 6186 site-packages/torch/distributed/run.py:803] *****************************************
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
Set TORCH_CUDA_ARCH_LIST to 9.0
Set TORCH_CUDA_ARCH_LIST to 9.0
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
Set TORCH_CUDA_ARCH_LIST to 9.0
Set TORCH_CUDA_ARCH_LIST to 9.0
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
/workspace/hanrui/idea1/specforge/modeling/draft/llama3_eagle.py:29: UserWarning: flash_attn is not found, falling back to flex_attention. Please install flash_attn if you want to use the flash attention backend.
  warnings.warn(
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
`torch_dtype` is deprecated! Use `dtype` instead!

Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 156.76it/s]
`torch_dtype` is deprecated! Use `dtype` instead!

Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 154.88it/s]
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.cudart module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.runtime module instead.
<frozen importlib._bootstrap_external>:1241: FutureWarning: The cuda.nvrtc module is deprecated and will be removed in a future release, please switch to use the cuda.bindings.nvrtc module instead.
============================================================
DFlash Evaluation (Multi-GPU Data Parallel)
============================================================
  Target model:       /workspace/models/Qwen3-8B
  Draft model:        /workspace/models/Qwen3-8B-DFlash-b16
  Dataset:            math500
  Max samples:        500
  Max new tokens:     512
  Denoise steps:      3
  Temperature:        0.0
  GPUs:               8
  Dtype:              bfloat16
============================================================

[1/4] Loading tokenizer...
`torch_dtype` is deprecated! Use `dtype` instead!

Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 158.37it/s]
`torch_dtype` is deprecated! Use `dtype` instead!
[2/4] Loading target model on 8 GPUs...
`torch_dtype` is deprecated! Use `dtype` instead!
`torch_dtype` is deprecated! Use `dtype` instead!
`torch_dtype` is deprecated! Use `dtype` instead!
`torch_dtype` is deprecated! Use `dtype` instead!

Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 130.51it/s]

Loading checkpoint shards:   0%|          | 0/5 [00:00<?, ?it/s]
Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 130.65it/s]

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 157.59it/s]

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 157.57it/s]

Loading checkpoint shards: 100%|██████████| 5/5 [00:00<00:00, 156.97it/s]
[3/4] Loading draft model on 8 GPUs...
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
  Draft layers:       5
  Draft block_size:   16
  Draft mask_token:   151669
  Draft layer_ids:    [1, 9, 17, 25, 33]
[4/4] Loading evaluation data...
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
  Total prompts: 500, ~63 per GPU

============================================================
Running evaluation...
============================================================
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
WARNING:datasets.load:Using the latest cached version of the dataset since HuggingFaceH4/MATH-500 couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
WARNING:datasets.packaged_modules.cache.cache:Found the latest cached dataset configuration 'default' at /workspace/hanrui/datasets/HuggingFaceH4___math-500/default/0.0.0/6e4ed1a2a79af7d8630a6b768ec859cb5af4d3be (last modified on Tue Mar 17 13:17:15 2026).
  [GPU 7] Sample 1/62 | tokens=512 | tau=1.46 | time=14.8s | <think> Okay, so I need to find the angle between two lines given by these equat...
  [GPU 3] Sample 1/63 | tokens=512 | tau=1.43 | time=15.1s | <think> Okay, so I need to figure out how many positive whole-number divisors 19...
  [GPU 4] Sample 1/62 | tokens=512 | tau=1.56 | time=13.6s | <think> Okay, so I need to figure out which student has the greatest average spe...
  [GPU 2] Sample 1/63 | tokens=512 | tau=1.59 | time=13.9s | <think> Okay, so I need to find the value of f(-2) + f(-1) + f(0) where the func...
  [GPU 6] Sample 1/62 | tokens=512 | tau=1.48 | time=14.4s | <think> Okay, so I need to find the smallest positive perfect cube that can be w...
  [GPU 1] Sample 1/63 | tokens=512 | tau=1.51 | time=14.7s | <think> Okay, so I need to find a way to express the double sum $\sum_{j = 1}^\i...
  [GPU 0] Sample 1/63 | tokens=512 | tau=1.40 | time=15.7s | <think> Okay, so I need to convert the rectangular coordinates (0, 3) to polar c...
  [GPU 5] Sample 1/62 | tokens=512 | tau=1.44 | time=15.3s | <think> Okay, so I need to figure out the perimeter of a regular hexagon when I ...
  [GPU 7] Sample 2/62 | tokens=512 | tau=1.48 | time=13.8s | <think> Okay, so I need to find the complex number w, which is the result of rot...
  [GPU 3] Sample 2/63 | tokens=512 | tau=1.41 | time=14.7s | <think> Okay, so I need to find p(8) where p(x) is a degree 5 polynomial that sa...
  [GPU 4] Sample 2/62 | tokens=512 | tau=1.58 | time=13.0s | <think> Okay, so I need to find the sum of the proper divisors of the sum of the...
  [GPU 2] Sample 2/63 | tokens=512 | tau=1.45 | time=14.7s | <think> Okay, so I need to find the least positive integer multiple of 30 that c...
  [GPU 1] Sample 2/63 | tokens=512 | tau=1.48 | time=14.4s | <think> Okay, so I need to figure out how many different values can be obtained ...
  [GPU 6] Sample 2/62 | tokens=512 | tau=1.36 | time=15.1s | <think> Okay, so I need to find the length of DE in this diagram. Let me try to ...
  [GPU 0] Sample 2/63 | tokens=512 | tau=1.40 | time=15.0s | <think> Okay, so I need to find the distance between the two points (2, -6) and ...
  [GPU 5] Sample 2/62 | tokens=512 | tau=1.38 | time=15.4s | <think> Okay, so I need to find the height of a cylinder when the volume is give...
  [GPU 7] Sample 3/62 | tokens=512 | tau=1.54 | time=13.3s | <think> Okay, so I need to solve the equation $ x = \sqrt{11 - 2x} + 4 $. Hmm, l...
  [GPU 3] Sample 3/63 | tokens=512 | tau=1.41 | time=14.6s | <think> Okay, so I need to find the smallest possible value of a positive real n...
  [GPU 4] Sample 3/62 | tokens=512 | tau=1.42 | time=14.4s | <think> Okay, so I need to evaluate the expression (1 + 2i) multiplied by 6, and...
  [GPU 6] Sample 3/62 | tokens=512 | tau=1.50 | time=13.7s | <think> Okay, let me try to figure out this problem. So, Denali and Nate are dog...
  [GPU 1] Sample 3/63 | tokens=512 | tau=1.45 | time=14.7s | <think> Okay, so I need to find the smallest possible value of c for the functio...
  [GPU 2] Sample 3/63 | tokens=512 | tau=1.42 | time=15.0s | <think> Okay, let me try to figure out this geometry problem. So, we have a diag...
  [GPU 5] Sample 3/62 | tokens=512 | tau=1.51 | time=14.1s | <think> Okay, so I need to find the greatest integer less than $(\sqrt{7} + \sqr...
  [GPU 0] Sample 3/63 | tokens=512 | tau=1.44 | time=14.6s | <think> Okay, so I need to compute this series: 1 - 2 + 3 - 4 + 5 - ... + 99 - 1...
  [GPU 7] Sample 4/62 | tokens=512 | tau=1.41 | time=14.6s | <think> Okay, so I need to simplify the square root of 242. Hmm, let me think. I...
  [GPU 3] Sample 4/63 | tokens=512 | tau=1.46 | time=14.2s | <think> Okay, let's see. The math club is having a bake sale to raise money for ...
  [GPU 4] Sample 4/62 | tokens=512 | tau=1.45 | time=14.2s | <think> Okay, so I need to figure out what happens when I rotate the complex num...
  [GPU 1] Sample 4/63 | tokens=512 | tau=1.61 | time=13.4s | <think> Okay, so I need to solve this functional equation problem. The function ...
  [GPU 6] Sample 4/62 | tokens=512 | tau=1.41 | time=14.6s | <think> Okay, so I need to find the product of 6 base 8 and 7 base 8, and then e...
  [GPU 0] Sample 4/63 | tokens=512 | tau=1.65 | time=12.8s | <think> Okay, so there's this worker who gets $20,000 every year and deposits it...
  [GPU 5] Sample 4/62 | tokens=512 | tau=1.49 | time=14.3s | <think> Okay, so I need to figure out how many different battalions can be sent ...
  [GPU 2] Sample 4/63 | tokens=512 | tau=1.32 | time=16.3s | <think> Okay, so I need to figure out how many ways 7 people can sit around a ro...
  [GPU 7] Sample 5/62 | tokens=512 | tau=1.51 | time=13.6s | <think> Okay, so I need to find the greatest common factor (GCF) of 6432 and 132...
  [GPU 4] Sample 5/62 | tokens=512 | tau=1.77 | time=11.6s | <think> Okay, so I need to find the roots of the equation $(x - 3)^3 + (x - 7)^3...
  [GPU 3] Sample 5/63 | tokens=512 | tau=1.60 | time=12.9s | <think> Okay, so I need to find the remainder when (n + 2)(n + 4)(n + 6) is divi...
  [GPU 6] Sample 5/62 | tokens=512 | tau=1.45 | time=14.2s | <think> Okay, so I need to figure out how many calories make up a person's daily...
  [GPU 1] Sample 5/63 | tokens=512 | tau=1.42 | time=15.1s | <think> Okay, so I need to find the eighth term of this geometric sequence: 125/...
  [GPU 0] Sample 5/63 | tokens=512 | tau=1.36 | time=15.6s | <think> Okay, so I need to figure out how many ways 8 people can sit around a ro...
  [GPU 2] Sample 5/63 | tokens=512 | tau=1.60 | time=14.2s | <think> Okay, so I need to find the constant term in the expansion of $\left(10x...
  [GPU 5] Sample 5/62 | tokens=512 | tau=1.37 | time=15.5s | <think> Okay, so I need to figure out the minimum number of degrees a regular pe...
  [GPU 4] Sample 6/62 | tokens=512 | tau=1.54 | time=13.3s | <think> Okay, so Bill is walking in different directions, and I need to figure o...
  [GPU 3] Sample 6/63 | tokens=512 | tau=1.68 | time=12.3s | <think> Okay, so I need to find the minimum value of this expression:  $$ \sqrt{...
  [GPU 7] Sample 6/62 | tokens=512 | tau=1.47 | time=14.0s | <think> Okay, so I need to find the vertical asymptotes and the horizontal asymp...
  [GPU 6] Sample 6/62 | tokens=512 | tau=1.43 | time=14.4s | <think> Okay, so I need to find the smallest positive integer n such that all th...
  [GPU 0] Sample 6/63 | tokens=512 | tau=1.45 | time=14.6s | <think> Okay, so I need to find the side length of a regular octagon that has th...
  [GPU 1] Sample 6/63 | tokens=512 | tau=1.31 | time=16.4s | <think> Okay, so I need to find the coordinates (x, y) of the fourth vertex of a...
  [GPU 2] Sample 6/63 | tokens=512 | tau=1.44 | time=15.5s | <think> Okay, so I need to solve this inequality: -4 < 2(x - 1) < 8. And then ex...
  [GPU 5] Sample 6/62 | tokens=512 | tau=1.40 | time=15.2s | <think> Okay, so I need to find tan A in this right triangle ABC where angle B i...
  [GPU 4] Sample 7/62 | tokens=512 | tau=1.54 | time=13.3s | <think> Okay, so I need to simplify this expression: the square root of (2.5 squ...
  [GPU 3] Sample 7/63 | tokens=512 | tau=1.48 | time=14.0s | <think> Okay, so I need to find the quotient when x⁶ - 3 is divided by x + 1. Hm...
  [GPU 7] Sample 7/62 | tokens=512 | tau=1.45 | time=14.2s | <think> Okay, so I need to figure out the degree of the polynomial f. The proble...
  [GPU 6] Sample 7/62 | tokens=512 | tau=1.33 | time=15.4s | <think> Okay, so I need to convert the fraction 3/20 into a decimal. Hmm, let me...
  [GPU 1] Sample 7/63 | tokens=512 | tau=1.55 | time=13.7s | <think> Okay, so I need to solve this equation: Half the value of 3x minus 9 is ...
  [GPU 0] Sample 7/63 | tokens=512 | tau=1.41 | time=14.9s | <think> Okay, so I need to figure out what power of 4 equals 8. Hmm, let me thin...
  [GPU 2] Sample 7/63 | tokens=512 | tau=1.46 | time=15.3s | <think> Okay, let me try to figure out this problem. So, there are seven bags of...
  [GPU 5] Sample 7/62 | tokens=512 | tau=1.41 | time=14.9s | <think> Okay, so I need to compute the arcsin of -1/2. Hmm, let me recall what a...
  [GPU 4] Sample 8/62 | tokens=512 | tau=1.56 | time=13.1s | <think> Okay, so I need to figure out the ordered triple (p, q, r) such that the...
  [GPU 3] Sample 8/63 | tokens=512 | tau=1.50 | time=13.7s | <think> Okay, so there's this problem about a class of 50 students. Some partici...
  [GPU 7] Sample 8/62 | tokens=512 | tau=1.47 | time=13.9s | <think> Okay, so I need to factor the polynomial $ x^8 + 3x^4 - 4 $ into monic p...
  [GPU 6] Sample 8/62 | tokens=512 | tau=1.50 | time=13.8s | <think> Okay, so I need to find the smallest positive real number C such that th...
  [GPU 0] Sample 8/63 | tokens=512 | tau=1.52 | time=13.8s | <think> Okay, so I need to find the value of N where the sum of the first N posi...
  [GPU 1] Sample 8/63 | tokens=512 | tau=1.45 | time=14.7s | <think> Okay, so Ringo is trying to calculate the modulus of (1 - i) raised to t...
  [GPU 2] Sample 8/63 | tokens=512 | tau=1.71 | time=13.2s | <think> Okay, so I need to compute 99 squared plus 99 plus 1. Let me think about...
  [GPU 5] Sample 8/62 | tokens=512 | tau=1.61 | time=13.2s | <think> Okay, so I need to find the value of $ a $ given that the cubic equation...
  [GPU 4] Sample 9/62 | tokens=512 | tau=1.48 | time=13.9s | <think> Okay, so I need to solve this equation: tan 53° tan 81° tan x° = tan 53°...
  [GPU 3] Sample 9/63 | tokens=512 | tau=1.49 | time=13.8s | <think> Okay, so I need to figure out by what percentage the area of a square de...
  [GPU 7] Sample 9/62 | tokens=512 | tau=1.51 | time=13.6s | <think> Okay, so I need to convert the binary number 10101001110₂ to octal. Hmm,...
  [GPU 6] Sample 9/62 | tokens=512 | tau=1.45 | time=14.2s | <think> Okay, so I need to subtract two numbers in base 9: 58 base 9 minus 18 ba...
  [GPU 5] Sample 9/62 | tokens=512 | tau=1.62 | time=13.1s | <think> Okay, so I need to compute the value of $ z + \frac{1}{z} + z^2 + \frac{...
  [GPU 0] Sample 9/63 | tokens=512 | tau=1.42 | time=14.8s | <think> Okay, so I need to find the constant $ d $ such that the equation $ (\si...
  [GPU 1] Sample 9/63 | tokens=512 | tau=1.38 | time=15.5s | <think> Okay, so I need to figure out what 1 raised to the power of 2 raised to ...
  [GPU 2] Sample 9/63 | tokens=512 | tau=1.52 | time=14.9s | <think> Okay, so I need to expand and simplify this algebraic expression: x time...
  [GPU 4] Sample 10/62 | tokens=512 | tau=1.43 | time=14.2s | <think> Okay, so I need to figure out the domain of the function log(x²) and the...
  [GPU 3] Sample 10/63 | tokens=512 | tau=1.47 | time=14.0s | <think> Okay, so I need to find the probability that when I throw two fair 6-sid...
  [GPU 7] Sample 10/62 | tokens=512 | tau=1.40 | time=14.7s | <think> Okay, so I need to find the value of x that makes the equation 2³ times ...
  [GPU 6] Sample 10/62 | tokens=512 | tau=1.62 | time=12.7s | <think> Okay, so I need to find real numbers a (which isn't zero) and b such tha...
  [GPU 0] Sample 10/63 | tokens=512 | tau=1.47 | time=14.2s | <think> Okay, so I need to find the radius of a sphere where the volume and surf...
  [GPU 5] Sample 10/62 | tokens=512 | tau=1.42 | time=14.9s | <think> Okay, so I need to solve the equation $2^8 = 4^x$ and find the value of ...
  [GPU 4] Sample 11/62 | tokens=512 | tau=1.68 | time=12.0s | <think> Okay, so I need to find the values of 'a' and 'b' such that when I multi...
  [GPU 2] Sample 10/63 | tokens=512 | tau=1.57 | time=14.4s | <think> Okay, so I need to simplify this expression: $\frac{\sec x}{\sin x} - \f...
  [GPU 1] Sample 10/63 | tokens=512 | tau=1.42 | time=14.9s | <think> Okay, so I need to figure out the value of 9 & 2 using this operation th...
  [GPU 7] Sample 11/62 | tokens=512 | tau=1.55 | time=13.2s | <think> Okay, so I need to solve the equation |5x - 1| = x + 3 and find the larg...
  [GPU 3] Sample 11/63 | tokens=512 | tau=1.35 | time=15.2s | <think> Okay, so I need to solve the equation $3^{2x} + 19 = 10^x$. Hmm, let me ...
  [GPU 6] Sample 11/62 | tokens=512 | tau=1.38 | time=14.9s | <think> Okay, so I need to figure out how many different outfits I can make with...
  [GPU 0] Sample 11/63 | tokens=512 | tau=1.54 | time=13.7s | <think> Okay, so I need to find the number of integer values of k in the interva...
  [GPU 5] Sample 11/62 | tokens=512 | tau=1.49 | time=14.2s | <think> Okay, so I need to find the radius of a right cylindrical tank. The prob...
  [GPU 4] Sample 12/62 | tokens=512 | tau=1.45 | time=14.1s | <think> Okay, so I need to figure out the probability that exactly 4 out of 7 is...
  [GPU 1] Sample 11/63 | tokens=512 | tau=1.53 | time=13.9s | <think> Okay, let me try to figure out this problem. So, we have three different...
  [GPU 2] Sample 11/63 | tokens=512 | tau=1.62 | time=14.1s | <think> Okay, so I need to find the greatest possible value of the slope of the ...
  [GPU 7] Sample 12/62 | tokens=512 | tau=1.57 | time=13.0s | <think> Okay, so I need to find the value of y such that the projection of the v...
  [GPU 3] Sample 12/63 | tokens=512 | tau=1.47 | time=14.1s | <think> Okay, so I need to find the smallest integer value of x for which the fu...
  [GPU 6] Sample 12/62 | tokens=512 | tau=1.46 | time=14.0s | <think> Okay, so I need to find the measure of angle AFD in quadrilateral ABCD. ...
  [GPU 1] Sample 12/63 | tokens=512 | tau=1.76 | time=12.2s | <think> Okay, so I need to find the greatest common divisor (GCD) of three numbe...
  [GPU 5] Sample 12/62 | tokens=512 | tau=1.55 | time=13.8s | <think> Okay, so I need to find the value of $ c $ such that the circle given by...
  [GPU 0] Sample 12/63 | tokens=512 | tau=1.36 | time=15.5s | <think> Okay, so I need to find the largest value of 'a' such that the graph of ...
  [GPU 4] Sample 13/62 | tokens=512 | tau=1.32 | time=15.4s | <think> Okay, so I need to find the measure of angle α in this hexagon inscribed...
  [GPU 7] Sample 13/62 | tokens=512 | tau=1.44 | time=14.3s | <think> Okay, so I need to find the values of λ between 0 and 4 such that there'...
  [GPU 3] Sample 13/63 | tokens=512 | tau=1.51 | time=13.8s | <think> Okay, so I need to find a vector v such that when I take the dot product...
  [GPU 2] Sample 12/63 | tokens=512 | tau=1.29 | time=17.6s | <think> Okay, so Remmy wants to divide 10 by 2/3, but he's confused about how to...
  [GPU 6] Sample 13/62 | tokens=512 | tau=1.39 | time=14.9s | <think> Okay, so I need to factor the expression ab + 5b + 2a + 10. Hmm, factori...
  [GPU 0] Sample 13/63 | tokens=512 | tau=1.71 | time=12.3s | <think> Okay, so I need to solve this equation:  $$\frac{( x+ 1)(x - 3)}{5(x + 2...
  [GPU 5] Sample 13/62 | tokens=512 | tau=1.52 | time=14.0s | <think> Okay, so I need to solve this equation: $x^{10} + (13x - 1)^{10} = 0$. T...
  [GPU 1] Sample 13/63 | tokens=512 | tau=1.44 | time=14.9s | <think> Okay, so there's this figure skater who starts facing north, and she beg...
  [GPU 4] Sample 14/62 | tokens=512 | tau=1.51 | time=13.6s | <think> Okay, so I need to find the value of k for the ellipse given by the equa...
  [GPU 7] Sample 14/62 | tokens=512 | tau=1.53 | time=13.4s | <think> Okay, so Mr. Brennan has 7 boys and 4 girls in his statistics class, and...
  [GPU 3] Sample 14/63 | tokens=512 | tau=1.70 | time=12.3s | <think> Okay, so I need to figure out how many elements are in the intersection ...
  [GPU 2] Sample 13/63 | tokens=512 | tau=1.43 | time=15.8s | <think> Okay, so I need to simplify this expression: (-k + 4) + (-2 + 3k). Let m...
  [GPU 6] Sample 14/62 | tokens=512 | tau=1.60 | time=12.9s | <think> Okay, so I need to find the value of $ a_1 $ in a strictly increasing se...
  [GPU 0] Sample 14/63 | tokens=512 | tau=1.63 | time=12.9s | <think> Okay, so I need to find the sum of the distances from the four intersect...
  [GPU 5] Sample 14/62 | tokens=512 | tau=1.68 | time=12.7s | <think> Okay, so I need to find the degree measure of the least positive angle θ...
  [GPU 1] Sample 14/63 | tokens=512 | tau=1.70 | time=12.6s | <think> Okay, so I need to find the median number of students in 2005 for these ...
  [GPU 4] Sample 15/62 | tokens=512 | tau=1.46 | time=14.0s | <think> Okay, so I need to solve the equation $2^{2x} = 256^{\frac{1}{2}}$. Hmm,...
  [GPU 3] Sample 15/63 | tokens=512 | tau=1.49 | time=13.9s | <think> Okay, so I need to figure out how many ways there are to arrange the let...
  [GPU 7] Sample 15/62 | tokens=512 | tau=1.45 | time=14.2s | <think> Okay, so I need to figure out the minimum possible value of the expressi...
  [GPU 2] Sample 14/63 | tokens=512 | tau=1.49 | time=15.1s | <think> Okay, so I need to find the horizontal asymptote of the function y = (4x...
  [GPU 6] Sample 15/62 | tokens=512 | tau=1.50 | time=13.6s | <think> Okay, so I need to find the number of ordered pairs (a, b) of integers s...
  [GPU 0] Sample 15/63 | tokens=512 | tau=1.46 | time=14.4s | <think> Okay, so I need to simplify the expression (1 + √2)/(2 + √3). The proble...
  [GPU 1] Sample 15/63 | tokens=512 | tau=1.52 | time=14.0s | <think> Okay, so I need to figure out the value of this expression: (26² - 24² -...
  [GPU 5] Sample 15/62 | tokens=512 | tau=1.42 | time=15.0s | <think> Okay, so I need to solve the equation √(3x - 5) = 2. Hmm, let me think. ...
  [GPU 4] Sample 16/62 | tokens=512 | tau=1.53 | time=13.3s | <think> Okay, so I need to solve the equation |x + 5| - |3x - 6| = 0. Hmm, absol...
  [GPU 7] Sample 16/62 | tokens=512 | tau=1.48 | time=13.8s | <think> Okay, so I need to convert the decimal number 555 into base 5. Hmm, let ...
  [GPU 3] Sample 16/63 | tokens=512 | tau=1.43 | time=14.4s | <think> Okay, so I need to find the area of quadrilateral DBEF. Let me first try...
  [GPU 2] Sample 15/63 | tokens=512 | tau=1.58 | time=14.3s | <think> Okay, so I need to find the product CD where C and D are integers that s...
  [GPU 6] Sample 16/62 | tokens=512 | tau=1.45 | time=14.0s | <think> Okay, so I need to find z_{2002} where each term is defined by iterating...
  [GPU 5] Sample 16/62 | tokens=512 | tau=1.60 | time=13.4s | <think> Okay, so I need to evaluate this expression: the ceiling of (3.6 squared...
  [GPU 0] Sample 16/63 | tokens=512 | tau=1.37 | time=15.4s | <think> Okay, so I need to figure out whether the composition of these functions...
  [GPU 1] Sample 16/63 | tokens=512 | tau=1.41 | time=15.3s | <think> Okay, so I need to solve the equation (x/2) + (x/3) = 5. Hmm, let me thi...
  [GPU 4] Sample 17/62 | tokens=512 | tau=1.49 | time=13.9s | <think> Okay, so Rick is thinking of a positive factor of 14, and Steve is think...
  [GPU 3] Sample 17/63 | tokens=512 | tau=1.49 | time=13.9s | <think> Okay, so I need to find the value of f(3) given that f(-3) = 2 for the f...
  [GPU 7] Sample 17/62 | tokens=512 | tau=1.35 | time=15.2s | <think> Okay, so I need to figure out how many zeros are at the end of 42 factor...
  [GPU 2] Sample 16/63 | tokens=512 | tau=1.58 | time=14.4s | <think> Okay, so Daniel says that the popularity of a television, which is measu...
  [GPU 6] Sample 17/62 | tokens=512 | tau=1.49 | time=13.7s | <think> Okay, so I need to find the equation of a hyperbola given two foci, F₁ =...
  [GPU 5] Sample 17/62 | tokens=512 | tau=1.45 | time=14.6s | <think> Okay, so I need to figure out the measure of the largest angle in this c...
  [GPU 4] Sample 18/62 | tokens=512 | tau=1.50 | time=13.7s | <think> Okay, so I need to find the greatest possible value of the greatest comm...
  [GPU 1] Sample 17/63 | tokens=512 | tau=1.47 | time=14.6s | <think> Okay, so I need to find the area of triangle ACD in triangle ABC where A...
  [GPU 0] Sample 17/63 | tokens=512 | tau=1.36 | time=15.5s | <think> Okay, so Suzanne walks four miles every third day. The question is askin...
  [GPU 3] Sample 18/63 | tokens=512 | tau=1.57 | time=13.2s | <think> Okay, so I need to find the maximum value of the function $ f(x, y) = x ...
  [GPU 7] Sample 18/62 | tokens=512 | tau=1.55 | time=13.3s | <think> Okay, so I need to find the area of triangle OAB, given the vectors OA a...
  [GPU 6] Sample 18/62 | tokens=512 | tau=1.43 | time=14.4s | <think> Okay, so I need to figure out how many ways the Senate committee can sit...
  [GPU 2] Sample 17/63 | tokens=512 | tau=1.38 | time=16.5s | <think> Okay, so I need to find an integer n between 0 and 17 (since 0 ≤ n < 18)...
  [GPU 5] Sample 18/62 | tokens=512 | tau=1.45 | time=14.6s | <think> Okay, so Zach has three bags and a bunch of pencils. He needs to place t...
  [GPU 1] Sample 18/63 | tokens=512 | tau=1.49 | time=14.3s | <think> Okay, so I need to divide 413 base 5 by 2 base 5 and give the answer in ...
  [GPU 0] Sample 18/63 | tokens=512 | tau=1.55 | time=13.6s | <think> Okay, so I need to find the sum of all possible values of n for a sequen...
  [GPU 4] Sample 19/62 | tokens=512 | tau=1.40 | time=14.7s | <think> Okay, so I need to solve the equation 2/3 equals 4 divided by (x minus 5...
  [GPU 7] Sample 19/62 | tokens=512 | tau=1.56 | time=13.2s | <think> Okay, so I need to find the square of the determinant of a 3x3 matrix wi...
  [GPU 3] Sample 19/63 | tokens=512 | tau=1.38 | time=15.0s | <think> Okay, so I need to find the minimum value of the expression $ x^4 + 4y^2...
  [GPU 6] Sample 19/62 | tokens=512 | tau=1.53 | time=13.5s | <think> Okay, so I need to figure out what f(2015, 2) is based on this recursive...
  [GPU 2] Sample 18/63 | tokens=512 | tau=1.44 | time=15.8s | <think> Okay, so Bob and Alice each have a bag with balls of five different colo...
  [GPU 5] Sample 19/62 | tokens=512 | tau=1.61 | time=13.2s | <think> Okay, let's try to figure out Rosa's age. The problem says that when her...
  [GPU 4] Sample 20/62 | tokens=512 | tau=1.50 | time=13.7s | <think> Okay, so there's this problem about two runners, A and B, starting from ...
  [GPU 1] Sample 19/63 | tokens=512 | tau=1.48 | time=14.4s | <think> Okay, so I need to find $ z^{85} + \frac{1}{z^{85}} $ given that $ z + \...
  [GPU 0] Sample 19/63 | tokens=512 | tau=1.43 | time=14.8s | <think> Okay, so I need to find the point on the curve that's given by the param...
  [GPU 7] Sample 20/62 | tokens=512 | tau=1.45 | time=14.1s | <think> Okay, so I need to rewrite the quadratic equation $x^2 + 2.6x + 3.6$ in ...
  [GPU 3] Sample 20/63 | tokens=512 | tau=1.52 | time=13.6s | <think> Okay, so I need to find the probability that a randomly selected point (...
  [GPU 6] Sample 20/62 | tokens=512 | tau=1.43 | time=14.4s | <think> Okay, so I need to find the sum of all multiples of 7 between 100 and 20...
  [GPU 5] Sample 20/62 | tokens=512 | tau=1.56 | time=13.7s | <think> Okay, so I need to find the value of a + b + c, where a, b, and c are th...
  [GPU 4] Sample 21/62 | tokens=512 | tau=1.39 | time=14.8s | <think> Okay, so I need to simplify the expression tan 100° + 4 sin 100°. Hmm, l...
  [GPU 2] Sample 19/63 | tokens=512 | tau=1.31 | time=17.2s | <think> Okay, so I need to simplify the fraction 3 over the square root of 27. L...
  [GPU 1] Sample 20/63 | tokens=512 | tau=1.47 | time=14.6s | <think> Okay, so I need to find the probability that three randomly chosen point...
  [GPU 3] Sample 21/63 | tokens=512 | tau=1.53 | time=13.6s | <think> Okay, so I need to find the greatest possible value of the expression $\...
  [GPU 0] Sample 20/63 | tokens=512 | tau=1.36 | time=15.4s | <think> Okay, so I need to find the area of triangle ENG in triangle ABC, where ...
  [GPU 7] Sample 21/62 | tokens=512 | tau=1.35 | time=15.2s | <think> Okay, so I need to find the volume of a cone. The formula given is V equ...
  [GPU 6] Sample 21/62 | tokens=512 | tau=1.45 | time=14.2s | <think> Okay, so I need to find the measure of angle BAC, where there's a square...
  [GPU 5] Sample 21/62 | tokens=512 | tau=1.62 | time=13.2s | <think> Okay, let me try to figure out this problem. So, there's a bookcase with...
  [GPU 4] Sample 22/62 | tokens=512 | tau=1.55 | time=13.3s | <think> Okay, so I need to find the sixth term of an arithmetic sequence where t...
  [GPU 7] Sample 22/62 | tokens=512 | tau=1.65 | time=12.5s | <think> Okay, so I need to find the smallest possible value of |m - n| where m a...
  [GPU 1] Sample 21/63 | tokens=512 | tau=1.47 | time=14.6s | <think> Okay, so I need to evaluate log base 2 of 64. Hmm, let me think. Logarit...
  [GPU 3] Sample 22/63 | tokens=512 | tau=1.41 | time=14.7s | <think> Okay, so Louis and Jack are sharing a pie, and I need to figure out how ...
  [GPU 2] Sample 20/63 | tokens=512 | tau=1.49 | time=15.0s | <think> Okay, so there's this gecko in a room, and it needs to get to a fly. The...
  [GPU 0] Sample 21/63 | tokens=512 | tau=1.52 | time=13.8s | <think> Okay, so I need to find two consecutive positive even integers whose pro...
  [GPU 6] Sample 22/62 | tokens=512 | tau=1.45 | time=14.2s | <think> Okay, so I need to figure out how many y-intercepts the graph of the par...
  [GPU 5] Sample 22/62 | tokens=512 | tau=1.48 | time=14.4s | <think> Okay, so I need to find the smallest positive integer value of 'a' such ...
  [GPU 4] Sample 23/62 | tokens=512 | tau=1.47 | time=14.0s | <think> Okay, so I need to figure out how many positive two-digit integers are f...
  [GPU 7] Sample 23/62 | tokens=512 | tau=1.51 | time=13.5s | <think> Okay, so I need to figure out how to write the expression √2 + 1/√2 + √3...
  [GPU 3] Sample 23/63 | tokens=512 | tau=1.51 | time=13.7s | <think> Okay, so I need to find the equation of the plane that contains the thre...
  [GPU 0] Sample 22/63 | tokens=512 | tau=1.43 | time=14.6s | <think> Okay, so I need to figure out the value of n for a 3×n grid of points wh...
  [GPU 2] Sample 21/63 | tokens=512 | tau=1.51 | time=14.9s | <think> Okay, so I need to find the probability that a randomly selected integer...
  [GPU 1] Sample 22/63 | tokens=512 | tau=1.41 | time=15.2s | <think> Okay, so I need to find the area of a triangle with sides 5, 5, and 6 un...
  [GPU 6] Sample 23/62 | tokens=512 | tau=1.48 | time=14.0s | <think> Okay, so I need to figure out how many students are at Baker Middle Scho...
  [GPU 4] Sample 24/62 | tokens=512 | tau=1.81 | time=11.2s | <think> Okay, so I need to find the largest x-value where the graphs of f(x) and...
  [GPU 5] Sample 23/62 | tokens=512 | tau=1.52 | time=13.8s | <think> Okay, so I need to simplify this expression: the square root of the cube...
  [GPU 7] Sample 24/62 | tokens=512 | tau=1.44 | time=14.2s | <think> Okay, so I need to find the value of b when the point (a, b) is on the l...
  [GPU 3] Sample 24/63 | tokens=512 | tau=1.53 | time=13.4s | <think> Okay, so Hillary has eleven coins, and they're all either dimes or nicke...
  [GPU 1] Sample 23/63 | tokens=512 | tau=1.55 | time=13.7s | <think> Okay, so I need to find the degree measure of the smallest angle in tria...
  [GPU 2] Sample 22/63 | tokens=512 | tau=1.50 | time=14.8s | <think> Okay, so I need to find the product of the y-coordinates of all the dist...
  [GPU 0] Sample 23/63 | tokens=512 | tau=1.38 | time=15.0s | <think> Okay, so I need to convert the fraction 21 divided by (2 squared times 5...
  [GPU 6] Sample 24/62 | tokens=512 | tau=1.60 | time=13.0s | <think> Okay, so Paul and Jesse each pick a number at random from the first six ...
  [GPU 4] Sample 25/62 | tokens=512 | tau=1.43 | time=14.4s | <think> Okay, so I need to solve this equation: 441 plus 2 times 21 times 19 plu...
  [GPU 5] Sample 24/62 | tokens=512 | tau=1.51 | time=14.0s | <think> Okay, so I need to figure out the greatest length of rope that can be sa...
  [GPU 3] Sample 25/63 | tokens=512 | tau=1.51 | time=13.7s | <think> Okay, so I need to find p(0) + p(4) where p(x) is a monic polynomial of ...
  [GPU 7] Sample 25/62 | tokens=512 | tau=1.43 | time=14.4s | <think> Okay, so I need to find the value of x such that the arithmetic mean of ...
  [GPU 0] Sample 24/63 | tokens=512 | tau=1.51 | time=13.9s | <think> Okay, so I need to find all possible values of the expression $\frac{c}{...
  [GPU 1] Sample 24/63 | tokens=512 | tau=1.39 | time=15.5s | <think> Okay, so I need to find the value of k such that (3^k)^6 equals 3^6. Let...
  [GPU 2] Sample 23/63 | tokens=512 | tau=1.53 | time=14.6s | <think> Okay, so I need to find the positive square root of the product 10 times...
  [GPU 6] Sample 25/62 | tokens=512 | tau=1.36 | time=15.2s | <think> Okay, so I need to figure out how many ways 6 girls and 2 boys can sit i...
  [GPU 4] Sample 26/62 | tokens=512 | tau=1.45 | time=14.3s | <think> Okay, so I need to find the maximum value of the product |(a + b)(a + c)...
  [GPU 5] Sample 25/62 | tokens=512 | tau=1.53 | time=13.9s | <think> Okay, so I need to figure out how many possible integer values of x ther...
  [GPU 3] Sample 26/63 | tokens=512 | tau=1.65 | time=12.6s | <think> Okay, so I need to find the remainder when this big polynomial is divide...
  [GPU 7] Sample 26/62 | tokens=512 | tau=1.40 | time=14.7s | <think> Okay, so Mikka wants to order a pizza with two different toppings, and h...
  [GPU 0] Sample 25/63 | tokens=512 | tau=1.43 | time=14.6s | <think> Okay, so I need to find the length of the median QM in triangle PQR wher...
  [GPU 1] Sample 25/63 | tokens=512 | tau=1.45 | time=14.8s | <think> Okay, so I need to find the number of different possible rational roots ...
  [GPU 2] Sample 24/63 | tokens=512 | tau=1.47 | time=15.3s | <think> Okay, so I need to figure out for how many positive integers n > 1 it's ...
  [GPU 6] Sample 26/62 | tokens=512 | tau=1.53 | time=13.4s | <think> Okay, so I need to find the equation of a line given its parametric equa...
  [GPU 4] Sample 27/62 | tokens=512 | tau=1.52 | time=13.5s | <think> Okay, let's see. Frank took a 100-question test. Each correct answer giv...
  [GPU 5] Sample 26/62 | tokens=512 | tau=1.40 | time=15.2s | <think> Okay, so I need to find the matrix A multiplied by the vector (-13, 3, 4...
  [GPU 3] Sample 27/63 | tokens=512 | tau=1.40 | time=14.8s | <think> Okay, so I need to figure out how to compute this expression: 5^5 divide...
  [GPU 7] Sample 27/62 | tokens=512 | tau=1.43 | time=14.4s | <think> Okay, so I need to find the value of $ x^3 - 2x + 1 $ given that $ x^2 -...
  [GPU 0] Sample 26/63 | tokens=512 | tau=1.49 | time=13.9s | <think> Okay, so I need to figure out how many daps equal 42 baps. Let me start ...
  [GPU 1] Sample 26/63 | tokens=512 | tau=1.41 | time=15.1s | <think> Okay, so there's this problem about a group of N students, and N is less...
  [GPU 2] Sample 25/63 | tokens=512 | tau=1.42 | time=15.9s | <think> Okay, so I need to find the maximum value of the expression $\frac{x - y...
  [GPU 6] Sample 27/62 | tokens=512 | tau=1.50 | time=13.7s | <think> Okay, let's try to figure out how many students take physics. There are ...
  [GPU 5] Sample 27/62 | tokens=512 | tau=1.87 | time=11.5s | <think> Okay, so I need to compute the infinite sum $\sum_{n = 1}^\infty \frac{F...
  [GPU 4] Sample 28/62 | tokens=512 | tau=1.53 | time=13.5s | <think> Okay, so Sam is carrying a 2-gallon bucket of milk, and he needs to walk...
  [GPU 3] Sample 28/63 | tokens=512 | tau=1.53 | time=13.4s | <think> Okay, so I need to figure out the probability that when I spin this whee...
  [GPU 7] Sample 28/62 | tokens=512 | tau=1.62 | time=12.8s | <think> Okay, so I need to find the sum of the digits in the terminating decimal...
  [GPU 1] Sample 27/63 | tokens=512 | tau=1.81 | time=11.8s | <think> Okay, so I need to find a two-digit integer AB such that when it's cubed...
  [GPU 0] Sample 27/63 | tokens=512 | tau=1.52 | time=13.7s | <think> Okay, so I need to figure out how many numbers from 1 to 100 are divisib...
  [GPU 4] Sample 29/62 | tokens=512 | tau=1.77 | time=11.6s | <think> Okay, so I need to find the region of the volume enclosed by the set S, ...
  [GPU 6] Sample 28/62 | tokens=512 | tau=1.45 | time=14.1s | <think> Okay, so I need to find the area of triangle CDE given that the area of ...
  [GPU 2] Sample 26/63 | tokens=512 | tau=1.34 | time=16.8s | <think> Okay, so Alice and Bob are playing this game where they take turns flipp...
  [GPU 5] Sample 28/62 | tokens=512 | tau=1.49 | time=14.2s | <think> Okay, so I need to find the smallest positive integer k such that when I...
  [GPU 3] Sample 29/63 | tokens=512 | tau=1.38 | time=15.0s | <think> Okay, so I need to figure out what shape the equation z = c represents i...
  [GPU 7] Sample 29/62 | tokens=512 | tau=1.50 | time=13.7s | <think> Okay, let's try to figure out how old Chris is now. The problem says tha...
  [GPU 1] Sample 28/63 | tokens=512 | tau=1.51 | time=14.2s | <think> Okay, so I need to find the smallest positive multiple of 450 where all ...
  [GPU 0] Sample 28/63 | tokens=512 | tau=1.45 | time=14.3s | <think> Okay, so I need to figure out how much 56 Drinkets is worth in Trinkets....
  [GPU 4] Sample 30/62 | tokens=512 | tau=1.51 | time=13.6s | <think> Okay, so I need to compute the value of this expression: 1 over cos squa...
  [GPU 6] Sample 29/62 | tokens=512 | tau=1.42 | time=14.3s | <think> Okay, so I need to find the maximum value of e given these two equations...
  [GPU 5] Sample 29/62 | tokens=512 | tau=1.43 | time=14.9s | <think> Okay, so Yann and Camille are going to a restaurant, and there are 10 it...
  [GPU 2] Sample 27/63 | tokens=512 | tau=1.47 | time=15.3s | <think> Okay, so I need to find the total area of the shaded region in this figu...
  [GPU 3] Sample 30/63 | tokens=512 | tau=1.55 | time=13.6s | <think> Okay, so I need to compute this expression: 0.7 repeating minus 0.4 repe...
  [GPU 7] Sample 30/62 | tokens=512 | tau=1.49 | time=13.7s | <think> Okay, so I need to solve this problem about parallelograms bounded by li...
  [GPU 0] Sample 29/63 | tokens=512 | tau=1.63 | time=12.7s | <think> Okay, so I need to find the value of the product sin20° sin40° sin60° si...
  [GPU 1] Sample 29/63 | tokens=512 | tau=1.55 | time=13.8s | <think> Okay, so I need to find the value of this expression when x is 4. The ex...
  [GPU 4] Sample 31/62 | tokens=512 | tau=1.53 | time=13.5s | <think> Okay, so I need to figure out how many sides a convex polygon has if the...
  [GPU 6] Sample 30/62 | tokens=512 | tau=1.64 | time=12.6s | <think> Okay, so I need to figure out the real values of x that are not in the d...
  [GPU 5] Sample 30/62 | tokens=512 | tau=1.45 | time=14.7s | <think> Okay, so I need to find the value of x + y + z given that xy = 24, xz = ...
  [GPU 2] Sample 28/63 | tokens=512 | tau=1.42 | time=15.8s | <think> Okay, so I need to find the midpoint between two points, (-5, 5) and (3,...
  [GPU 7] Sample 31/62 | tokens=512 | tau=1.53 | time=13.4s | <think> Okay, so I need to find the value of p(3)/p(4) where p(x) is a quadratic...
  [GPU 3] Sample 31/63 | tokens=512 | tau=1.46 | time=14.4s | <think> Okay, so I need to figure out the length of the third side of a triangle...
  [GPU 0] Sample 30/63 | tokens=512 | tau=1.46 | time=14.3s | <think> Okay, so I need to evaluate the sum S = 1/(1 + ω) + 1/(1 + ω²) + ... + 1...
  [GPU 1] Sample 30/63 | tokens=512 | tau=1.43 | time=14.9s | <think> Okay, so I need to find the smallest possible angle between vectors a an...
  [GPU 4] Sample 32/62 | tokens=512 | tau=1.53 | time=13.5s | <think> Okay, so I need to find the maximum value of the function $ 4(x + 7)(2 -...
  [GPU 6] Sample 31/62 | tokens=512 | tau=1.53 | time=13.6s | <think> Okay, so there's this problem about twelve friends who went to dinner, a...
  [GPU 5] Sample 31/62 | tokens=512 | tau=1.47 | time=14.6s | <think> Okay, so I need to find the remainder when this big polynomial f(x) is d...
  [GPU 7] Sample 32/62 | tokens=512 | tau=1.50 | time=13.8s | <think> Okay, so I need to figure out what kind of curve is defined by the equat...
  [GPU 3] Sample 32/63 | tokens=512 | tau=1.53 | time=13.7s | <think> Okay, so there's this problem about six cars pulling up to a red light o...
  [GPU 2] Sample 29/63 | tokens=512 | tau=1.49 | time=15.1s | <think> Okay, so I need to figure out how many ways there are to put 5 indisting...
  [GPU 0] Sample 31/63 | tokens=512 | tau=1.46 | time=14.2s | <think> Okay, so I need to find the measure of angle PQR in this diagram. Let me...
  [GPU 1] Sample 31/63 | tokens=512 | tau=1.42 | time=15.1s | <think> Okay, so I need to find the smallest distance between the origin (0,0) a...
  [GPU 4] Sample 33/62 | tokens=512 | tau=1.53 | time=13.4s | <think> Okay, so I need to find the angle ABC, which is the angle at point B for...
  [GPU 6] Sample 32/62 | tokens=512 | tau=1.43 | time=14.3s | <think> Okay, so Pat wants to select six cookies from a tray that has chocolate ...
  [GPU 7] Sample 33/62 | tokens=512 | tau=1.52 | time=13.5s | <think> Okay, so I need to figure out how many sides a regular polygon has if it...
  [GPU 5] Sample 32/62 | tokens=512 | tau=1.38 | time=15.5s | <think> Okay, so I need to figure out what fraction of 2 feet is 3 inches. Hmm, ...
  [GPU 2] Sample 30/63 | tokens=512 | tau=1.60 | time=14.1s | <think> Okay, so I need to find the sum of the roots of the function g(x), which...
  [GPU 3] Sample 33/63 | tokens=512 | tau=1.42 | time=14.8s | <think> Okay, so I need to compute the product of the number 5 plus the square r...
  [GPU 0] Sample 32/63 | tokens=512 | tau=1.58 | time=13.2s | <think> Okay, so I need to compute A^27 + A^31 + A^40 where A is the matrix [[3,...
  [GPU 4] Sample 34/62 | tokens=512 | tau=1.49 | time=13.8s | <think> Okay, so I need to find the remainder when the sum of numbers from 1 to ...
  [GPU 1] Sample 32/63 | tokens=512 | tau=1.42 | time=15.0s | <think> Okay, so I need to find an odd integer t between 0 and 23 such that t + ...
  [GPU 6] Sample 33/62 | tokens=512 | tau=1.61 | time=12.8s | <think> Okay, so I need to solve the equation $10^x - 10 = 9990$. Let me think a...
  [GPU 7] Sample 34/62 | tokens=512 | tau=1.58 | time=13.1s | <think> Okay, so I need to find the inverse of 997 modulo 1000. That means I nee...
  [GPU 5] Sample 33/62 | tokens=512 | tau=1.39 | time=15.3s | <think> Okay, so I need to find the measure of angle B in triangle ABC, where an...
  [GPU 3] Sample 34/63 | tokens=512 | tau=1.39 | time=15.0s | <think> Okay, so I need to find the sum of the measures of angle J and angle H i...
  [GPU 0] Sample 33/63 | tokens=512 | tau=1.52 | time=13.7s | <think> Okay, so I need to simplify this expression: (1/5) multiplied by (8/7) d...
  [GPU 2] Sample 31/63 | tokens=512 | tau=1.41 | time=15.9s | <think> Okay, so I need to figure out how much money will be in the investment a...
  [GPU 4] Sample 35/62 | tokens=512 | tau=1.49 | time=13.8s | <think> Okay, so I need to figure out for how many real values of x the expressi...
  [GPU 1] Sample 33/63 | tokens=512 | tau=1.51 | time=14.1s | <think> Okay, so I need to find the total surface area of a cube that has a volu...
  [GPU 6] Sample 34/62 | tokens=512 | tau=1.44 | time=14.2s | <think> Okay, so I need to figure out how many more dollars Pam pays than Susan ...
  [GPU 7] Sample 35/62 | tokens=512 | tau=1.51 | time=13.6s | <think> Okay, so I need to figure out the difference between the area of the reg...
  [GPU 5] Sample 34/62 | tokens=512 | tau=1.50 | time=14.2s | <think> Okay, so I need to figure out how many distinct arrangements there are f...
  [GPU 3] Sample 35/63 | tokens=512 | tau=1.46 | time=14.3s | <think> Okay, so I need to find the value of g(f(5) - 1). Let me start by recall...
  [GPU 0] Sample 34/63 | tokens=512 | tau=1.47 | time=14.1s | <think> Okay, so I need to find the length of BH in this figure. Let me try to v...
  [GPU 4] Sample 36/62 | tokens=512 | tau=1.69 | time=12.2s | <think> Okay, so I need to solve the equation:  $$ \sin \left( \tan^{-1} (x) + \...
  [GPU 2] Sample 32/63 | tokens=512 | tau=1.43 | time=15.8s | <think> Okay, so I need to find the x-intercept (a), the y-intercept (b), and th...
  [GPU 1] Sample 34/63 | tokens=512 | tau=1.61 | time=13.3s | <think> Okay, so I need to find the 2003rd term of the sequence of odd numbers: ...
  [GPU 6] Sample 35/62 | tokens=512 | tau=1.49 | time=13.8s | <think> Okay, so I need to figure out the largest eight-digit number in base 2, ...
  [GPU 7] Sample 36/62 | tokens=512 | tau=1.47 | time=14.0s | <think> Okay, so I need to figure out after how many seconds both gears will hav...
  [GPU 4] Sample 37/62 | tokens=512 | tau=1.86 | time=11.0s | <think> Okay, so I need to find the value of $ x_{531} + x_{753} + x_{975} $ giv...
  [GPU 0] Sample 35/63 | tokens=512 | tau=1.64 | time=12.7s | <think> Okay, so I need to convert the repeating decimal 0.133113311331... into ...
  [GPU 5] Sample 35/62 | tokens=512 | tau=1.41 | time=15.1s | <think> Okay, so I need to figure out what the square root of 53 is in its simpl...
  [GPU 3] Sample 36/63 | tokens=512 | tau=1.43 | time=14.5s | <think> Okay, so I need to figure out what (4 5/8)^55 multiplied by (8/37)^55 is...
  [GPU 2] Sample 33/63 | tokens=512 | tau=1.46 | time=15.3s | <think> Okay, so I need to figure out how many blue marbles were in the bag orig...
  [GPU 1] Sample 35/63 | tokens=512 | tau=1.50 | time=14.2s | <think> Okay, so I need to figure out how many dollars are equivalent to 1,000,0...
  [GPU 6] Sample 36/62 | tokens=512 | tau=1.47 | time=14.0s | <think> Okay, so I need to compute the sum over all triples (a, b, c) of positiv...
  [GPU 7] Sample 37/62 | tokens=512 | tau=1.53 | time=13.5s | <think> Okay, so I need to solve this equation: $ z^4 + 4z^3i - 6z^2 - 4zi - i =...
  [GPU 0] Sample 36/63 | tokens=512 | tau=1.53 | time=13.7s | <think> Okay, so I need to figure out how many whole-number divisors the express...
  [GPU 4] Sample 38/62 | tokens=512 | tau=1.43 | time=14.4s | <think> Okay, so I need to figure out the maximum number of points where at leas...
  [GPU 5] Sample 36/62 | tokens=512 | tau=1.60 | time=13.3s | <think> Okay, so Steve is thinking of a polynomial with all positive integer roo...
  [GPU 3] Sample 37/63 | tokens=512 | tau=1.49 | time=14.0s | <think> Okay, so I need to figure out how many integer coordinate points are str...
  [GPU 6] Sample 37/62 | tokens=512 | tau=1.53 | time=13.4s | <think> Okay, so I need to find three consecutive positive integers where their ...
  [GPU 1] Sample 36/63 | tokens=512 | tau=1.42 | time=14.9s | <think> Okay, so I need to find the measure of angle A in this regular pentagon ...
  [GPU 2] Sample 34/63 | tokens=512 | tau=1.39 | time=16.2s | <think> Okay, so I need to find the probability that a randomly selected number ...
  [GPU 7] Sample 38/62 | tokens=512 | tau=1.36 | time=15.1s | <think> Okay, so I need to find the area of triangle ACD in this trapezoid ABCD ...
  [GPU 0] Sample 37/63 | tokens=512 | tau=1.58 | time=13.1s | <think> Okay, so I need to find the distance between two parallel lines. Let me ...
  [GPU 4] Sample 39/62 | tokens=512 | tau=1.40 | time=14.7s | <think> Okay, so I need to find the surface area of one of the pieces created wh...
  [GPU 3] Sample 38/63 | tokens=512 | tau=1.55 | time=13.4s | <think> Okay, so I need to figure out how many integer coordinates are strictly ...
  [GPU 5] Sample 37/62 | tokens=512 | tau=1.43 | time=14.8s | <think> Okay, so I need to find all values of p that satisfy both inequalities: ...
  [GPU 6] Sample 38/62 | tokens=512 | tau=1.51 | time=13.5s | <think> Okay, so I need to figure out how many digits repeat in the decimal expa...
  [GPU 1] Sample 37/63 | tokens=512 | tau=1.45 | time=14.6s | <think> Okay, so I need to find the minimum value of the expression $(a + b + c ...
  [GPU 2] Sample 35/63 | tokens=512 | tau=1.38 | time=16.2s | <think> Okay, so I need to find the perimeter of this set S. Let me try to visua...
  [GPU 7] Sample 39/62 | tokens=512 | tau=1.60 | time=12.8s | <think> Okay, so I need to find the value of n where the sum 1 + 12 + 123 + 1234...
  [GPU 0] Sample 38/63 | tokens=512 | tau=1.48 | time=14.0s | <think> Okay, so I need to figure out which of these equations has the largest s...
  [GPU 4] Sample 40/62 | tokens=512 | tau=1.55 | time=13.1s | <think> Okay, so I need to factor the quadratic expression $10x^2 - x - 24$ into...
  [GPU 5] Sample 38/62 | tokens=512 | tau=1.50 | time=14.1s | <think> Okay, so I need to figure out the average price of Juan's stamps from th...
  [GPU 3] Sample 39/63 | tokens=512 | tau=1.39 | time=15.0s | <think> Okay, so I need to find the range of the function y = log base 2 of the ...
  [GPU 6] Sample 39/62 | tokens=512 | tau=1.37 | time=15.0s | <think> Okay, so I need to figure out the value of this operation @ between two ...
  [GPU 1] Sample 38/63 | tokens=512 | tau=1.49 | time=14.2s | <think> Okay, so I need to figure out the smallest number of leaves in a book wh...
  [GPU 2] Sample 36/63 | tokens=512 | tau=1.74 | time=12.9s | <think> Okay, let me try to figure out this sequence problem. The sequence start...
  [GPU 7] Sample 40/62 | tokens=512 | tau=1.46 | time=14.0s | <think> Okay, so I need to solve the equation |x - 4| - 10 = 2 and find the prod...
  [GPU 0] Sample 39/63 | tokens=512 | tau=1.65 | time=12.7s | <think> Okay, so I need to find the minimum value of the function $\frac{(x + 5)...
  [GPU 4] Sample 41/62 | tokens=512 | tau=1.39 | time=14.7s | <think> Okay, so I need to find the measure of angle ADC in this diagram with tw...
  [GPU 3] Sample 40/63 | tokens=512 | tau=1.51 | time=13.9s | <think> Okay, so I need to find positive integers a, b, and 2009, where a < b < ...
  [GPU 5] Sample 39/62 | tokens=512 | tau=1.40 | time=15.2s | <think> Okay, so I need to find the least possible sum of a set of distinct posi...
  [GPU 6] Sample 40/62 | tokens=512 | tau=1.46 | time=14.1s | <think> Okay, so I need to combine these two fractions into a single fraction. T...
  [GPU 1] Sample 39/63 | tokens=512 | tau=1.51 | time=14.2s | <think> Okay, so I need to solve the equation √(2x)/√(3x - 1) = 3/2. Hmm, let me...
  [GPU 2] Sample 37/63 | tokens=512 | tau=1.64 | time=13.8s | <think> Okay, so I need to find the value of r that satisfies the equation (6r² ...
  [GPU 7] Sample 41/62 | tokens=512 | tau=1.38 | time=15.0s | <think> Okay, so I need to find P(5) where P(x) is a monic cubic polynomial. Let...
  [GPU 0] Sample 40/63 | tokens=512 | tau=1.45 | time=14.5s | <think> Okay, so I need to solve the inequality 1 divided by (x minus 5) is grea...
  [GPU 4] Sample 42/62 | tokens=512 | tau=1.37 | time=15.0s | <think> Okay, so I need to find the minimum value of (x + y)(y + z) given that x...
  [GPU 3] Sample 41/63 | tokens=512 | tau=1.41 | time=14.8s | <think> Okay, so I need to find the probability that two segments AB and CD inte...
  [GPU 5] Sample 40/62 | tokens=512 | tau=1.41 | time=15.0s | <think> Okay, so I need to find the degree of the polynomial p(x) given by that ...
  [GPU 6] Sample 41/62 | tokens=512 | tau=1.50 | time=13.6s | <think> Okay, so I need to evaluate this expression: sin(arcsin 0.4 + arcsin 0.5...
  [GPU 2] Sample 38/63 | tokens=512 | tau=1.67 | time=13.5s | <think> Okay, so I need to compute the cross product (2b - a) × (3c + a). The pr...
  [GPU 1] Sample 40/63 | tokens=512 | tau=1.42 | time=15.0s | <think> Okay, so Charlie is riding his unicycle, and I need to figure out the sp...
  [GPU 7] Sample 42/62 | tokens=512 | tau=1.57 | time=13.1s | <think> Okay, so I need to find the remainder when the 100th term of the Fibonac...
  [GPU 0] Sample 41/63 | tokens=512 | tau=1.49 | time=14.1s | <think> Okay, so I need to find cos(angle RPS) given that sin(angle RPQ) is 7/25...
  [GPU 4] Sample 43/62 | tokens=512 | tau=1.53 | time=13.5s | <think> Okay, so I need to find the angle between vectors a and a - b. The probl...
  [GPU 3] Sample 42/63 | tokens=512 | tau=1.42 | time=14.8s | <think> Okay, so I need to simplify this expression: the square root of a fracti...
  [GPU 5] Sample 41/62 | tokens=512 | tau=1.52 | time=14.0s | <think> Okay, so I need to figure out how many cylindrical beakers it takes to f...
  [GPU 6] Sample 42/62 | tokens=512 | tau=1.48 | time=13.8s | <think> Okay, so I need to find the value of the product abc given these three e...
  [GPU 2] Sample 39/63 | tokens=512 | tau=1.52 | time=14.8s | <think> Okay, so I need to find the number of quadratic equations of the form $x...
  [GPU 1] Sample 41/63 | tokens=512 | tau=1.37 | time=15.6s | <think> Okay, so there's this robot that moves at a constant speed. It takes 2.5...
  [GPU 7] Sample 43/62 | tokens=512 | tau=1.45 | time=14.2s | <think> Okay, so I need to figure out how many different license plates can be m...
  [GPU 0] Sample 42/63 | tokens=512 | tau=1.49 | time=14.1s | <think> Okay, so I need to figure out how many distinct values the function $ f(...
  [GPU 4] Sample 44/62 | tokens=512 | tau=1.54 | time=13.4s | <think> Okay, so I need to compute the binomial coefficient $\dbinom{31}{28}$. H...
  [GPU 5] Sample 42/62 | tokens=512 | tau=1.57 | time=13.6s | <think> Okay, so I need to find the value of $ b $ in the continued fraction exp...
  [GPU 3] Sample 43/63 | tokens=512 | tau=1.37 | time=15.2s | <think> Okay, so I need to figure out how to express a + b + c + d + e + f in te...
  [GPU 6] Sample 43/62 | tokens=512 | tau=1.43 | time=14.4s | <think> Okay, so I need to find an integer x that satisfies the inequality 1/4 <...
  [GPU 2] Sample 40/63 | tokens=512 | tau=1.54 | time=14.7s | <think> Okay, so I need to figure out where the point (0,0) ends up after two re...
  [GPU 7] Sample 44/62 | tokens=512 | tau=1.55 | time=13.2s | <think> Okay, so I need to simplify this product of cosines: cos(2π/15) * cos(4π...
  [GPU 1] Sample 42/63 | tokens=512 | tau=1.41 | time=15.1s | <think> Okay, so I need to figure out the bicycle's speed in inches per second w...
  [GPU 0] Sample 43/63 | tokens=512 | tau=1.43 | time=14.8s | <think> Okay, so I need to find the value of 513 squared minus 487 squared. Hmm,...
  [GPU 4] Sample 45/62 | tokens=512 | tau=1.46 | time=14.1s | <think> Okay, so I need to find all real numbers x such that -4 < x⁴ + 4x² < 21....
  [GPU 3] Sample 44/63 | tokens=512 | tau=1.62 | time=12.9s | <think> Okay, so I need to simplify this algebraic expression: 4 times (3r³ + 5r...
  [GPU 5] Sample 43/62 | tokens=512 | tau=1.48 | time=14.4s | <think> Okay, so I need to find the smallest number that is one less than twice ...
  [GPU 6] Sample 44/62 | tokens=512 | tau=1.49 | time=13.8s | <think> Okay, so I need to find the units digit of 18 raised to the 6th power. H...
  [GPU 7] Sample 45/62 | tokens=512 | tau=1.62 | time=12.8s | <think> Okay, so I need to find the value of $ xy + yz + zx $ given these three ...
  [GPU 2] Sample 41/63 | tokens=512 | tau=1.50 | time=15.0s | <think> Okay, so I need to find the value of $ b $ given the functions $ f(x) = ...
  [GPU 1] Sample 43/63 | tokens=512 | tau=1.45 | time=14.8s | <think> Okay, so I need to find three consecutive integers whose product is 120,...
  [GPU 0] Sample 44/63 | tokens=512 | tau=1.45 | time=14.5s | <think> Okay, so I need to find the value of 'a' that makes the function f(n) co...
  [GPU 4] Sample 46/62 | tokens=512 | tau=1.54 | time=13.4s | <think> Okay, so I need to figure out the equation of the set of image points af...
  [GPU 3] Sample 45/63 | tokens=512 | tau=1.64 | time=12.7s | <think> Okay, so I need to find the minimum value of this expression:   $$ \frac...
  [GPU 6] Sample 45/62 | tokens=512 | tau=1.49 | time=13.8s | <think> Okay, so I need to figure out what kind of graph the equation $\left(\fr...
  [GPU 5] Sample 44/62 | tokens=512 | tau=1.38 | time=15.3s | <think> Okay, so I need to figure out how many ways 8 people can be seated aroun...
  [GPU 7] Sample 46/62 | tokens=512 | tau=1.51 | time=13.6s | <think> Okay, so I need to find $ f^{-1}(f^{-1}(6)) $. Let me start by recalling...
  [GPU 2] Sample 42/63 | tokens=512 | tau=1.42 | time=15.7s | <think> Okay, so I need to figure out how many ways we can form a subcommittee o...
  [GPU 1] Sample 44/63 | tokens=512 | tau=1.47 | time=14.5s | <think> Okay, let me try to figure out this problem. So, the question is: If t(x...
  [GPU 4] Sample 47/62 | tokens=512 | tau=1.44 | time=14.2s | <think> Okay, so I need to find the measure of angle BAC in this diagram. Let me...
  [GPU 0] Sample 45/63 | tokens=512 | tau=1.40 | time=15.1s | <think> Okay, so I need to find the perimeter of triangle ABC, which is isoscele...
  [GPU 3] Sample 46/63 | tokens=512 | tau=1.43 | time=14.6s | <think> Okay, so I need to solve this equation: Three plus the reciprocal of a n...
  [GPU 5] Sample 45/62 | tokens=512 | tau=1.51 | time=14.1s | <think> Okay, so I need to figure out how many possible values of x there are wh...
  [GPU 6] Sample 46/62 | tokens=512 | tau=1.40 | time=14.8s | <think> Okay, so I need to find the modulo 7 remainder of the sum of all the odd...
  [GPU 7] Sample 47/62 | tokens=512 | tau=1.57 | time=13.1s | <think> Okay, so I need to find the sum of the positive divisors of 500, which i...
  [GPU 2] Sample 43/63 | tokens=512 | tau=1.48 | time=15.2s | <think> Okay, so I need to figure out what 999 in base 10 is in base six. Hmm, l...
  [GPU 1] Sample 45/63 | tokens=512 | tau=1.37 | time=15.5s | <think> Okay, so I need to figure out how many ways I can stack my 6 different b...
  [GPU 4] Sample 48/62 | tokens=512 | tau=1.52 | time=13.5s | <think> Okay, so I need to solve the inequality $\frac{|x^2 - 81|}{x^2 - 36x} < ...
  [GPU 0] Sample 46/63 | tokens=512 | tau=1.57 | time=13.3s | <think> Okay, so I need to find the value of b in the direction vector of the li...
  [GPU 3] Sample 47/63 | tokens=512 | tau=1.41 | time=14.8s | <think> Okay, so I need to find the largest possible value of |a| + |b| + |c| gi...
  [GPU 5] Sample 46/62 | tokens=512 | tau=1.67 | time=12.8s | <think> Okay, so I need to figure out how many possible values there are for $ a...
  [GPU 6] Sample 47/62 | tokens=512 | tau=1.48 | time=13.8s | <think> Okay, so I need to figure out the difference between the positive square...
  [GPU 7] Sample 48/62 | tokens=512 | tau=1.52 | time=13.5s | <think> Okay, so I need to solve the inequality $ x^2 - 5x - 4 \leq 10 $. Let me...
  [GPU 2] Sample 44/63 | tokens=512 | tau=1.50 | time=15.1s | <think> Okay, so I need to solve this equation: the cube root of (x squared minu...
  [GPU 1] Sample 46/63 | tokens=512 | tau=1.52 | time=14.1s | <think> Okay, so I need to find the side length of an equilateral triangle inscr...
  [GPU 4] Sample 49/62 | tokens=512 | tau=1.47 | time=14.0s | <think> Okay, so I need to find the smallest real number x in the domain of the ...
  [GPU 0] Sample 47/63 | tokens=512 | tau=1.47 | time=14.4s | <think> Okay, so I need to find the greatest possible perimeter of a triangle wh...
  [GPU 3] Sample 48/63 | tokens=512 | tau=1.49 | time=14.0s | <think> Okay, so I need to figure out for which grade the number of male bus rid...
  [GPU 5] Sample 47/62 | tokens=512 | tau=1.57 | time=13.7s | <think> Okay, so William Sydney Porter tried to calculate (-3 + 4i) divided by (...
  [GPU 6] Sample 48/62 | tokens=512 | tau=1.53 | time=13.5s | <think> Okay, so I need to find the largest possible area of a rectangular field...
  [GPU 7] Sample 49/62 | tokens=512 | tau=1.50 | time=13.7s | <think> Okay, so I need to find the inverse function values for f(x) at 0 and 6,...
  [GPU 0] Sample 48/63 | tokens=512 | tau=1.64 | time=12.9s | <think> Okay, so I need to find the coordinates of point P on the line y = -x + ...
  [GPU 4] Sample 50/62 | tokens=512 | tau=1.49 | time=13.7s | <think> Okay, so I need to find the area of the gray piece in this tangram puzzl...
  [GPU 1] Sample 47/63 | tokens=512 | tau=1.49 | time=14.3s | <think> Okay, so I need to find the area of this trapezoid. Let me recall the fo...
  [GPU 2] Sample 45/63 | tokens=512 | tau=1.47 | time=15.4s | <think> Okay, so I need to find the median of 27 consecutive positive integers w...
  [GPU 5] Sample 48/62 | tokens=512 | tau=1.49 | time=14.2s | <think> Okay, so I need to find the probability that a triangle with sides of le...
  [GPU 6] Sample 49/62 | tokens=512 | tau=1.60 | time=12.9s | <think> Okay, so I need to find the smallest distance between the origin and a p...
  [GPU 3] Sample 49/63 | tokens=512 | tau=1.43 | time=14.7s | <think> Okay, so I need to find the value of f(-2) for the function f(x) = 5x² +...
  [GPU 7] Sample 50/62 | tokens=512 | tau=1.39 | time=14.8s | <think> Okay, so I need to add 313.9 and 12.6 together. Let me think about how t...
  [GPU 4] Sample 51/62 | tokens=512 | tau=1.43 | time=14.3s | <think> Okay, so Roslyn has ten boxes total. Let me try to figure out how many b...
  [GPU 0] Sample 49/63 | tokens=512 | tau=1.37 | time=15.3s | <think> Okay, so I need to simplify this expression: 19x plus 1 minus 4x minus 8...
  [GPU 1] Sample 48/63 | tokens=512 | tau=1.42 | time=15.0s | <think> Okay, so I need to find the units digit of 4$, which is defined as a sup...
  [GPU 2] Sample 46/63 | tokens=512 | tau=1.49 | time=15.1s | <think> Okay, so there's this problem about two candidates running for class pre...
  [GPU 6] Sample 50/62 | tokens=512 | tau=1.61 | time=12.7s | <think> Okay, so Navin, Luka, and Ian are talking about their part-time jobs, an...
  [GPU 5] Sample 49/62 | tokens=512 | tau=1.44 | time=14.8s | <think> Okay, so I need to find sin T in triangle RST. They told me that sin R i...
  [GPU 3] Sample 50/63 | tokens=512 | tau=1.40 | time=14.9s | <think> Okay, so I need to find the value of this expression: (16 times the cube...
  [GPU 7] Sample 51/62 | tokens=512 | tau=1.39 | time=14.7s | <think> Okay, so I need to find the value of the inverse function of f at 1/5, w...
  [GPU 4] Sample 52/62 | tokens=512 | tau=1.51 | time=13.5s | <think> Okay, so I need to find P(16) where P(x) is a quadratic polynomial that'...
  [GPU 0] Sample 50/63 | tokens=512 | tau=1.49 | time=14.0s | <think> Okay, so I need to find the distance from point P to the sixth vertex of...
  [GPU 1] Sample 49/63 | tokens=512 | tau=1.50 | time=14.2s | <think> Okay, let's see. Kathy has $300 in the bank, and she wants to withdraw h...
  [GPU 6] Sample 51/62 | tokens=512 | tau=1.45 | time=14.1s | <think> Okay, so I need to find the remainder when 2004 is divided by 12. Hmm, l...
  [GPU 2] Sample 47/63 | tokens=512 | tau=1.40 | time=15.9s | <think> Okay, so I need to find the dot product of these two vectors: the first ...
  [GPU 3] Sample 51/63 | tokens=512 | tau=1.49 | time=13.9s | <think> Okay, so I need to figure out how many of the same digits are found in t...
  [GPU 5] Sample 50/62 | tokens=512 | tau=1.45 | time=14.6s | <think> Okay, so I need to solve this equation: 3x + 2(1 + x) = 17, and then fin...
  [GPU 7] Sample 52/62 | tokens=512 | tau=1.51 | time=13.6s | <think> Okay, so I need to find the remainder when $129^{34} + 96^{38}$ is divid...
  [GPU 4] Sample 53/62 | tokens=512 | tau=1.49 | time=13.8s | <think> Okay, so I need to find the projection of vector a onto vector b. The pr...
  [GPU 0] Sample 51/63 | tokens=512 | tau=1.47 | time=14.3s | <think> Okay, so I need to find the radius of the smaller semicircle in this cir...
  [GPU 1] Sample 50/63 | tokens=512 | tau=1.52 | time=13.9s | <think> Okay, so I need to figure out the ratio of the acceleration of Jen's sof...
  [GPU 6] Sample 52/62 | tokens=512 | tau=1.49 | time=13.7s | <think> Okay, so I need to solve this equation: (3)5² - 4(5 - a)² ÷ 3 = 63. Hmm,...
  [GPU 2] Sample 48/63 | tokens=512 | tau=1.51 | time=14.7s | <think> Okay, so I need to figure out how many two-digit prime numbers have digi...
  [GPU 3] Sample 52/63 | tokens=512 | tau=1.44 | time=14.5s | <think> Okay, so there's this problem about six witches and ten sorcerers at an ...
  [GPU 5] Sample 51/62 | tokens=512 | tau=1.44 | time=14.6s | <think> Okay, so I need to figure out how many ways 3 people can be assigned to ...
  [GPU 7] Sample 53/62 | tokens=512 | tau=1.51 | time=13.7s | <think> Okay, so I need to find the largest integer less than 2010 that satisfie...
  [GPU 4] Sample 54/62 | tokens=512 | tau=1.49 | time=13.7s | <think> Okay, so I need to find the minimum value of the expression $\frac{1}{a}...
  [GPU 0] Sample 52/63 | tokens=512 | tau=1.60 | time=13.3s | <think> Okay, so I need to figure out where the reflection takes the vector $\be...
  [GPU 6] Sample 53/62 | tokens=512 | tau=1.66 | time=12.4s | <think> Okay, so I need to find the unordered set containing the three expressio...
  [GPU 1] Sample 51/63 | tokens=512 | tau=1.41 | time=15.1s | <think> Okay, so I need to find the maximum value of the expression |1 + z| + |1...
  [GPU 3] Sample 53/63 | tokens=512 | tau=1.62 | time=13.0s | <think> Okay, so I need to find a vector v such that when I take the cross produ...
  [GPU 2] Sample 49/63 | tokens=512 | tau=1.50 | time=14.9s | <think> Okay, so I need to figure out how many integers satisfy the inequality |...
  [GPU 7] Sample 54/62 | tokens=512 | tau=1.61 | time=12.8s | <think> Okay, so I need to find the range of the function $ f(x) = (\arccos x)^2...
  [GPU 5] Sample 52/62 | tokens=512 | tau=1.38 | time=15.4s | <think> Okay, so I need to simplify this expression: (10r³)(4r⁶) divided by 8r⁴....
  [GPU 4] Sample 55/62 | tokens=512 | tau=1.41 | time=14.6s | <think> Okay, so I need to find the number of dice, n, such that when you roll n...
  [GPU 6] Sample 54/62 | tokens=512 | tau=1.40 | time=14.6s | <think> Okay, so I need to figure out what 9 divided by 2 is as a decimal. Hmm, ...
  [GPU 1] Sample 52/63 | tokens=512 | tau=1.59 | time=13.4s | <think> Okay, so I need to find the distance between the foci of a hyperbola. Th...
  [GPU 0] Sample 53/63 | tokens=512 | tau=1.31 | time=16.1s | <think> Okay, so I need to compute the value of sin³18° + sin²18°. Hmm, let me t...
  [GPU 3] Sample 54/63 | tokens=512 | tau=1.64 | time=12.8s | <think> Okay, so I need to figure out the cost of a pencil in cents. The problem...
  [GPU 7] Sample 55/62 | tokens=512 | tau=1.45 | time=14.3s | <think> Okay, so I need to find the quotient when x^9 + 1 is divided by x - 1. H...
  [GPU 2] Sample 50/63 | tokens=512 | tau=1.47 | time=15.2s | <think> Okay, so I need to figure out the value of x that Archimedes should choo...
  [GPU 5] Sample 53/62 | tokens=512 | tau=1.51 | time=14.1s | <think> Okay, so I need to solve this equation: arccos x + arccos 2x + arccos 3x...
  [GPU 4] Sample 56/62 | tokens=512 | tau=1.41 | time=14.7s | <think> Okay, so I need to find the probability that a randomly chosen point ins...
  [GPU 6] Sample 55/62 | tokens=512 | tau=1.53 | time=13.5s | <think> Okay, so I need to find the last nonzero digit to the right of the decim...
  [GPU 1] Sample 53/63 | tokens=512 | tau=1.48 | time=14.4s | <think> Okay, so I need to find the sum of the coefficients of the polynomial g(...
  [GPU 0] Sample 54/63 | tokens=512 | tau=1.41 | time=15.0s | <think> Okay, so I need to solve this problem where y varies inversely as the sq...
  [GPU 3] Sample 55/63 | tokens=512 | tau=1.47 | time=14.3s | <think> Okay, so I need to find the domain of the function f(x) = (2x - 7)/√(x² ...
  [GPU 7] Sample 56/62 | tokens=512 | tau=1.51 | time=13.6s | <think> Okay, so there's this problem about thirty-five students attending a mat...
  [GPU 5] Sample 54/62 | tokens=512 | tau=1.64 | time=13.1s | <think> Okay, so I need to find the minimum value of $ a^4 + b^8 $ given that $ ...
  [GPU 2] Sample 51/63 | tokens=512 | tau=1.36 | time=16.6s | <think> Okay, so I need to figure out what happens when I rotate the complex num...
  [GPU 4] Sample 57/62 | tokens=512 | tau=1.56 | time=13.2s | <think> Okay, so I need to solve this problem about a two-digit number. Let me r...
  [GPU 6] Sample 56/62 | tokens=512 | tau=1.51 | time=13.6s | <think> Okay, so I need to find the value of n such that the sum of the first n ...
  [GPU 0] Sample 55/63 | tokens=512 | tau=1.49 | time=14.2s | <think> Okay, so I need to solve this recurrence relation problem. Let me first ...
  [GPU 1] Sample 54/63 | tokens=512 | tau=1.37 | time=15.5s | <think> Okay, so I need to find an expression for AF² + BF² + CF² in terms of th...
  [GPU 3] Sample 56/63 | tokens=512 | tau=1.44 | time=14.5s | <think> Okay, so I need to find the integer value of x in the arithmetic sequenc...
  [GPU 7] Sample 57/62 | tokens=512 | tau=1.40 | time=14.7s | <think> Okay, so I need to figure out how many ways 5 students can be selected f...
  [GPU 5] Sample 55/62 | tokens=512 | tau=1.45 | time=14.7s | <think> Okay, so I need to figure out the value of the square symbol, which is r...
  [GPU 2] Sample 52/63 | tokens=512 | tau=1.61 | time=14.0s | <think> Okay, so I need to figure out the units digit N of the number 21420N suc...
  [GPU 4] Sample 58/62 | tokens=512 | tau=1.54 | time=13.3s | <think> Okay, so I need to find the measure of angle STR in this diagram. Let me...
  [GPU 6] Sample 57/62 | tokens=512 | tau=1.61 | time=12.8s | <think> Okay, so I need to find the image of the line y = 2x + 1 under the matri...
  [GPU 0] Sample 56/63 | tokens=512 | tau=1.50 | time=14.0s | <think> Okay, so I need to simplify this expression: (u + 4)(u - 1) minus (u - 3...
  [GPU 3] Sample 57/63 | tokens=512 | tau=1.45 | time=14.4s | <think> Okay, so I need to figure out how many inches on the map correspond to 5...
  [GPU 1] Sample 55/63 | tokens=512 | tau=1.37 | time=15.5s | <think> Okay, so I need to convert the fraction 57/160 into a terminating decima...
  [GPU 7] Sample 58/62 | tokens=512 | tau=1.50 | time=13.7s | <think> Okay, so I need to figure out for how many values of x the expression (x...
  [GPU 5] Sample 56/62 | tokens=512 | tau=1.49 | time=14.2s | <think> Okay, so I need to find the area of the quadrilateral formed by the four...
  [GPU 2] Sample 53/63 | tokens=512 | tau=1.52 | time=14.8s | <think> Okay, so I need to find the shortest distance from the point (6, 0) to t...
  [GPU 6] Sample 58/62 | tokens=512 | tau=1.69 | time=12.3s | <think> Okay, so Linda, Sherry, June, and Connie sold cookies and earned differe...
  [GPU 4] Sample 59/62 | tokens=512 | tau=1.43 | time=14.4s | <think> Okay, so I need to figure out how many integer values of t satisfy the c...
  [GPU 3] Sample 58/63 | tokens=512 | tau=1.60 | time=13.1s | <think> Okay, so I need to figure out the cost of a 3-inch cube made of fake gol...
  [GPU 1] Sample 56/63 | tokens=512 | tau=1.66 | time=12.7s | <think> Okay, so Karla drove her vehicle 12,000 miles last year. The question is...
  [GPU 0] Sample 57/63 | tokens=512 | tau=1.38 | time=15.3s | <think> Okay, so I need to find the inverse of 17 modulo 83. That means I need t...
  [GPU 7] Sample 59/62 | tokens=512 | tau=1.55 | time=13.3s | <think> Okay, so I need to find the class average for this test. Let me think. T...
  [GPU 5] Sample 57/62 | tokens=512 | tau=1.52 | time=14.1s | <think> Okay, so I need to figure out how many representatives the 8th grade sho...
  [GPU 2] Sample 54/63 | tokens=512 | tau=1.47 | time=15.4s | <think> Okay, so I need to find the length of the diagonal of a square when it h...
  [GPU 6] Sample 59/62 | tokens=512 | tau=1.43 | time=14.4s | <think> Okay, so I need to find the maximum value of the expression $ ab^2 c^3 d...
  [GPU 4] Sample 60/62 | tokens=512 | tau=1.46 | time=14.1s | <think> Okay, so Jim and Martha are at the corner of a rectangular field. The fi...
  [GPU 3] Sample 59/63 | tokens=512 | tau=1.56 | time=13.4s | <think> Okay, so I need to find the area of the shaded triangle in the diagram. ...
  [GPU 0] Sample 58/63 | tokens=512 | tau=1.55 | time=13.6s | <think> Okay, so I need to find all the integer roots of the polynomial equation...
  [GPU 1] Sample 57/63 | tokens=512 | tau=1.44 | time=14.8s | <think> Okay, so I need to figure out the value of 5 star 1, where the operation...
  [GPU 7] Sample 60/62 | tokens=512 | tau=1.49 | time=13.9s | <think> Okay, so I need to figure out for which prime numbers p the congruence 8...
  [GPU 5] Sample 58/62 | tokens=512 | tau=1.47 | time=14.5s | <think> Okay, so I need to find the value of this function f(n) at three differe...
  [GPU 6] Sample 60/62 | tokens=512 | tau=1.65 | time=12.5s | <think> Okay, so I need to find the sum of all complex solutions to this equatio...
  [GPU 4] Sample 61/62 | tokens=512 | tau=1.53 | time=13.5s | <think> Okay, so I need to solve this equation: √(x + √(3x + 6)) + √(x - √(3x + ...
  [GPU 2] Sample 55/63 | tokens=512 | tau=1.44 | time=15.6s | <think> Okay, so I need to find the area of an isosceles right triangle where th...
  [GPU 3] Sample 60/63 | tokens=512 | tau=1.49 | time=14.1s | <think> Okay, so I need to solve this problem about an unfair six-sided die. Let...
  [GPU 0] Sample 59/63 | tokens=512 | tau=1.45 | time=14.6s | <think> Okay, so I need to solve this system of logarithmic equations:  First eq...
  [GPU 7] Sample 61/62 | tokens=512 | tau=1.42 | time=14.5s | <think> Okay, so I need to figure out the remainder when the sum of numbers from...
  [GPU 1] Sample 58/63 | tokens=512 | tau=1.40 | time=15.3s | <think> Okay, so I need to figure out the remainder when 54 is divided by 6. Let...
  [GPU 5] Sample 59/62 | tokens=512 | tau=1.52 | time=14.1s | <think> Okay, so I need to evaluate the ceiling of the square root of 20, and th...
  [GPU 6] Sample 61/62 | tokens=512 | tau=1.43 | time=14.4s | <think> Okay, so I need to figure out the volume of a cube from which a steel sp...
  [GPU 4] Sample 62/62 | tokens=512 | tau=1.47 | time=14.0s | <think> Okay, so I need to find the equation of a line that consists of all vect...
  [GPU 2] Sample 56/63 | tokens=512 | tau=1.48 | time=15.3s | <think> Okay, so I need to find the square root of f(f(f(f(1)))) where f(x) is 2...
  [GPU 3] Sample 61/63 | tokens=512 | tau=1.57 | time=13.3s | <think> Okay, so I need to find tan A for triangle ABC, given that the area of t...
  [GPU 7] Sample 62/62 | tokens=512 | tau=1.53 | time=13.4s | <think> Okay, so I need to find the domain of the function f(x) = (2 - x) / log(...
  [GPU 0] Sample 60/63 | tokens=512 | tau=1.46 | time=14.4s | <think> Okay, so I need to figure out how far a car would travel if it's going 5...
  [GPU 1] Sample 59/63 | tokens=512 | tau=1.48 | time=14.3s | <think> Okay, so I need to figure out the fifth number in the list of positive i...
  [GPU 5] Sample 60/62 | tokens=512 | tau=1.48 | time=14.3s | <think> Okay, so I need to figure out how many distinct possible values there ar...
  [GPU 6] Sample 62/62 | tokens=512 | tau=1.56 | time=13.1s | <think> Okay, so I need to find the area of the set S, which consists of points ...
  [GPU 2] Sample 57/63 | tokens=512 | tau=1.45 | time=15.3s | <think> Okay, so I need to find the average of the two smallest positive integer...
  [GPU 3] Sample 62/63 | tokens=512 | tau=1.48 | time=14.1s | <think> Okay, so Tom has this Mr. Potato Head, and he wants to figure out how ma...
  [GPU 0] Sample 61/63 | tokens=512 | tau=1.45 | time=14.4s | <think> Okay, so I need to find all possible values of the expression $\frac{1}{...
  [GPU 1] Sample 60/63 | tokens=512 | tau=1.48 | time=14.2s | <think> Okay, so I need to figure out the value of n in this magic square. Let m...
  [GPU 5] Sample 61/62 | tokens=512 | tau=1.49 | time=14.2s | <think> Okay, so I need to figure out the shortest distance you can travel if yo...
  [GPU 2] Sample 58/63 | tokens=512 | tau=1.40 | time=15.9s | <think> Okay, let me try to figure out this problem. So, the question is about h...
  [GPU 3] Sample 63/63 | tokens=512 | tau=1.33 | time=15.6s | <think> Okay, so I need to find the measure of angle AHB in triangle ABC where A...
  [GPU 1] Sample 61/63 | tokens=512 | tau=1.66 | time=12.6s | <think> Okay, so I need to simplify this big fraction where the numerator is the...
  [GPU 0] Sample 62/63 | tokens=512 | tau=1.50 | time=13.9s | <think> Okay, so I need to figure out the original price of the shirt when the s...
  [GPU 5] Sample 62/62 | tokens=512 | tau=1.66 | time=12.7s | <think> Okay, so I need to figure out the value of $(\sqrt{2} + \sqrt{3})^3$ and...
  [GPU 2] Sample 59/63 | tokens=512 | tau=1.57 | time=14.1s | <think> Okay, so I need to find the sum of all possible values of θ where re^{iθ...
  [GPU 0] Sample 63/63 | tokens=512 | tau=1.52 | time=13.8s | <think> Okay, so I need to find the modulus of this complex number w, which is g...
  [GPU 1] Sample 62/63 | tokens=512 | tau=1.45 | time=14.6s | <think> Okay, so I need to find the minimum value of the function f(x) = |x - p|...
  [GPU 2] Sample 60/63 | tokens=512 | tau=1.47 | time=16.0s | <think> Okay, so I need to find the value of this product of logarithms: log bas...
  [GPU 1] Sample 63/63 | tokens=512 | tau=1.37 | time=16.1s | <think> Okay, so I need to find the area of an equiangular octagon that has four...
  [GPU 2] Sample 61/63 | tokens=512 | tau=1.42 | time=17.0s | <think> Okay, so I need to find the probability that the reciprocal of a randoml...
  [GPU 2] Sample 62/63 | tokens=512 | tau=1.46 | time=16.5s | <think> Okay, so I need to find the least possible value of |a_{n-1}| for a poly...
  [GPU 2] Sample 63/63 | tokens=512 | tau=1.60 | time=15.0s | <think> Okay, so I need to solve this problem where there's a sequence defined b...

============================================================
RESULTS SUMMARY
============================================================
  Denoise steps:              3
  GPUs used:                  8
  Samples evaluated:          500
  Total blocks:               172488
  Total generated tokens:     256000
  Total GPU-time:             7097.21s
  Wall-clock time (approx):   17.62s
  ---
  Avg acceptance length (tau): 1.49
  Median acceptance length:    1.0
  Per-sample avg tau:          ['1.40', '1.40', '1.44', '1.65', '1.36', '1.45', '1.41', '1.52', '1.42', '1.47', '1.54', '1.36', '1.71', '1.63', '1.46', '1.37', '1.36', '1.55', '1.43', '1.36', '1.52', '1.43', '1.38', '1.51', '1.43', '1.49', '1.52', '1.45', '1.63', '1.46', '1.46', '1.58', '1.52', '1.47', '1.64', '1.53', '1.58', '1.48', '1.65', '1.45', '1.49', '1.49', '1.43', '1.45', '1.40', '1.57', '1.47', '1.64', '1.37', '1.49', '1.47', '1.60', '1.31', '1.41', '1.49', '1.50', '1.38', '1.55', '1.45', '1.46', '1.45', '1.50', '1.52', '1.51', '1.48', '1.45', '1.61', '1.42', '1.31', '1.55', '1.45', '1.38', '1.42', '1.53', '1.76', '1.44', '1.70', '1.52', '1.41', '1.47', '1.49', '1.48', '1.47', '1.47', '1.41', '1.55', '1.39', '1.45', '1.41', '1.81', '1.51', '1.55', '1.43', '1.42', '1.42', '1.51', '1.61', '1.50', '1.42', '1.45', '1.49', '1.51', '1.42', '1.37', '1.41', '1.45', '1.47', '1.37', '1.52', '1.49', '1.42', '1.50', '1.52', '1.41', '1.59', '1.48', '1.37', '1.37', '1.66', '1.44', '1.40', '1.48', '1.48', '1.66', '1.45', '1.37', '1.59', '1.45', '1.42', '1.32', '1.60', '1.44', '1.46', '1.71', '1.52', '1.57', '1.62', '1.29', '1.43', '1.49', '1.58', '1.58', '1.38', '1.44', '1.31', '1.49', '1.51', '1.50', '1.53', '1.47', '1.42', '1.34', '1.47', '1.42', '1.49', '1.60', '1.41', '1.43', '1.46', '1.39', '1.38', '1.74', '1.64', '1.67', '1.52', '1.54', '1.50', '1.42', '1.48', '1.50', '1.47', '1.49', '1.40', '1.51', '1.50', '1.47', '1.36', '1.61', '1.52', '1.47', '1.44', '1.48', '1.45', '1.40', '1.57', '1.47', '1.42', '1.46', '1.60', '1.43', '1.41', '1.41', '1.46', '1.60', '1.68', '1.48', '1.50', '1.49', '1.47', '1.35', '1.47', '1.51', '1.70', '1.49', '1.43', '1.49', '1.57', '1.38', '1.52', '1.53', '1.41', '1.51', '1.53', '1.51', '1.65', '1.40', '1.53', '1.38', '1.55', '1.46', '1.53', '1.42', '1.39', '1.46', '1.43', '1.49', '1.55', '1.39', '1.51', '1.41', '1.42', '1.37', '1.62', '1.64', '1.43', '1.41', '1.49', '1.43', '1.40', '1.49', '1.44', '1.62', '1.64', '1.47', '1.44', '1.45', '1.60', '1.56', '1.49', '1.57', '1.48', '1.33', '1.56', '1.58', '1.42', '1.45', '1.77', '1.54', '1.54', '1.56', '1.48', '1.43', '1.68', '1.45', '1.32', '1.51', '1.46', '1.53', '1.49', '1.50', '1.40', '1.50', '1.39', '1.55', '1.47', '1.81', '1.43', '1.45', '1.52', '1.53', '1.77', '1.51', '1.53', '1.53', '1.53', '1.49', '1.49', '1.69', '1.86', '1.43', '1.40', '1.55', '1.39', '1.37', '1.53', '1.54', '1.46', '1.54', '1.44', '1.52', '1.47', '1.49', '1.43', '1.51', '1.49', '1.49', '1.41', '1.41', '1.56', '1.54', '1.43', '1.46', '1.53', '1.47', '1.44', '1.38', '1.51', '1.49', '1.37', '1.40', '1.41', '1.61', '1.62', '1.42', '1.49', '1.55', '1.52', '1.68', '1.42', '1.60', '1.45', '1.45', '1.61', '1.56', '1.62', '1.48', '1.52', '1.51', '1.53', '1.40', '1.87', '1.49', '1.43', '1.45', '1.47', '1.38', '1.39', '1.50', '1.41', '1.60', '1.43', '1.50', '1.40', '1.41', '1.52', '1.57', '1.48', '1.38', '1.51', '1.67', '1.57', '1.49', '1.44', '1.45', '1.44', '1.38', '1.51', '1.64', '1.45', '1.49', '1.52', '1.47', '1.52', '1.48', '1.49', '1.66', '1.48', '1.36', '1.50', '1.41', '1.45', '1.43', '1.33', '1.50', '1.45', '1.62', '1.38', '1.46', '1.39', '1.60', '1.50', '1.45', '1.49', '1.43', '1.53', '1.43', '1.45', '1.45', '1.48', '1.60', '1.36', '1.53', '1.50', '1.45', '1.42', '1.64', '1.53', '1.43', '1.61', '1.44', '1.49', '1.47', '1.53', '1.51', '1.37', '1.46', '1.50', '1.48', '1.43', '1.49', '1.49', '1.40', '1.48', '1.53', '1.60', '1.61', '1.45', '1.49', '1.66', '1.40', '1.53', '1.51', '1.61', '1.69', '1.43', '1.65', '1.43', '1.56', '1.46', '1.48', '1.54', '1.41', '1.51', '1.47', '1.45', '1.47', '1.51', '1.40', '1.55', '1.57', '1.44', '1.53', '1.45', '1.48', '1.35', '1.55', '1.56', '1.45', '1.35', '1.65', '1.51', '1.44', '1.43', '1.40', '1.43', '1.62', '1.50', '1.49', '1.53', '1.50', '1.52', '1.58', '1.51', '1.47', '1.53', '1.36', '1.60', '1.46', '1.38', '1.57', '1.45', '1.55', '1.62', '1.51', '1.57', '1.52', '1.50', '1.39', '1.39', '1.51', '1.51', '1.61', '1.45', '1.51', '1.40', '1.50', '1.55', '1.49', '1.42', '1.53']
  Min per-sample tau:          1.29
  Max per-sample tau:          1.87
============================================================

Results saved to /workspace/hanrui/idea1/results/dflash_eval/math500_steps3.json

============================================
  All evaluations complete!
  Results in: /workspace/hanrui/idea1/results/dflash_eval/
============================================

Quick comparison:
  steps=1  avg_tau=1.55
  steps=2  avg_tau=1.47
  steps=3  avg_tau=1.49