on-policy-self-distillation
gpt-5.6-sol
on-policy-self-distillation — graded by the task's verifier against a measured baseline.
- backend
- modal
- variant
- codex azure_ai/gpt-5.6-sol
- metric
- AIME24 avg@12 accuracy
- actions
- 428
- duration
- 9h 21m
- recorded
- 2026-08-02
run idopsd-aime24-4gpus__eNDoWrD
Everything gpt-5.6-sol did on this task, in order.
download JSON ↗codexgpt-5.6-sol444 turns16 narration428 reasoning428 action428 observation1 final
#26
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolwait
args
{
"cell_id": "20",
"yield_time_ms": 30000,
"max_tokens": 5000
}wait result
Script completed
Wall time 2.7 seconds
Output:
/workspace/repo/opsd_trainer.py:63: TRLExperimentalWarning: You are importing from 'trl.experimental'. APIs here are unstable and may change or be removed without notice. Silence this warning by setting environment variable TRL_EXPERIMENTAL_SILENCE=1.
from trl.experimental.gold.gold_config import GOLDConfig
None 0.8359822034835815 0.2020130306482315
0.05 0.04999999701976776 0.014745842665433884
total 2
drwxr-xr-x 1 root root 32 Aug 2 17:15 .
drwxr-xr-x 1 root root 120 Aug 2 18:27 ..
-rw-r--r-- 1 root root 624 Aug 2 17:15 recipe.env
# OPSD method recipe — whitelisted hyper-parameter overrides (KEY=VALUE per line).
# Empty/all-commented == the OPSD baseline recipe on top of your /workspace/repo
# code changes. The scorer re-trains with THIS file + your repo for 100 steps.
# Budget knobs (max_steps, epochs, batch, gradient_accumulation, num_processes,
# model) are FIXED by the scorer and ignored here.
#
# learning_rate=5e-6
# lora_r=64
# lora_alpha=128
# beta=0
# jsd_token_clip=0.05
# temperature=1.1
# lmbda=1
# max_completion_length=1024 # <= 4096
# fixed_teacher=true
# use_ema_teacher=false
# reason_first=false
# teacher_thinking=false
21310
#27
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolexec
args
{
"input": "const r = await tools.exec_command({cmd:\"SEED=42 OUT_DIR=/workspace/runs/klclip PORT=12951 bash /workspace/train_capped.sh\",\"workdir\":\"/workspace\",\"yield_time_ms\":1000,\"max_output_tokens\":3000});\ntext(r.output); if (r.session_id) text(`SESSION_ID=${r.session_id}`);"
}exec result
Script completed
Wall time 1.2 seconds
Output:
SESSION_ID=80474#28
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolexec
args
{
"input": "const r = await tools.write_stdin({session_id:80474,chars:\"\",yield_time_ms:30000,max_output_tokens:5000});\ntext(r.output);"
}exec result
Script running with cell ID 22
Wall time 11.0 seconds
Output:
#29
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolwait
args
{
"cell_id": "22",
"yield_time_ms": 30000,
"max_tokens": 5000
}wait result
Script completed
Wall time 11.9 seconds
Output:
df: /root/.triton/autotune: No such file or directory
<string>:24: FutureWarning: `torch_dtype` is deprecated and will be removed in version 0.27.0, please use `dtype` instead.
================================================================================
RUN CONFIGURATION
================================================================================
WandB Run Name: capped_seed42_lr5e-6_bs32
Output Directory: /workspace/runs/klclip/capped_seed42
================================================================================
================================================================================
Loading model with dtype: torch.bfloat16
Using attention implementation: flash_attention_2
================================================================================
<string>:24: FutureWarning: `torch_dtype` is deprecated and will be removed in version 0.27.0, please use `dtype` instead.
================================================================================
RUN CONFIGURATION
================================================================================
WandB Run Name: capped_seed42_lr5e-6_bs32
Output Directory: /workspace/runs/klclip/capped_seed42
================================================================================
================================================================================
Loading model with dtype: torch.bfloat16
Using attention implementation: flash_attention_2
================================================================================
<string>:24: FutureWarning: `torch_dtype` is deprecated and will be removed in version 0.27.0, please use `dtype` instead.
================================================================================
RUN CONFIGURATION
================================================================================
WandB Run Name: capped_seed42_lr5e-6_bs32
Output Directory: /workspace/runs/klclip/capped_seed42
================================================================================
================================================================================
Loading model with dtype: torch.bfloat16
Using attention implementation: flash_attention_2
================================================================================
<string>:24: FutureWarning: `torch_dtype` is deprecated and will be removed in version 0.27.0, please use `dtype` instead.
================================================================================
RUN CONFIGURATION
================================================================================
WandB Run Name: capped_seed42_lr5e-6_bs32
Output Directory: /workspace/runs/klclip/capped_seed42
================================================================================
================================================================================
Loading model with dtype: torch.bfloat16
Using attention implementation: flash_attention_2
================================================================================
Using the latest cached version of the dataset since siyanzhao/Openthoughts_math_30k_opsd couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /opt/hf_cache/datasets/siyanzhao___openthoughts_math_30k_opsd/default/0.0.0/1f33e9dc2e8a1c639ca74f8024ad4a9f1f5eae62 (last modified on Sun Aug 2 17:14:36 2026).
Using the latest cached version of the dataset since siyanzhao/Openthoughts_math_30k_opsd couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /opt/hf_cache/datasets/siyanzhao___openthoughts_math_30k_opsd/default/0.0.0/1f33e9dc2e8a1c639ca74f8024ad4a9f1f5eae62 (last modified on Sun Aug 2 17:14:36 2026).
Using the latest cached version of the dataset since siyanzhao/Openthoughts_math_30k_opsd couldn't be found on the Hugging Face Hub (offline mode is enabled).
Using the latest cached version of the dataset since siyanzhao/Openthoughts_math_30k_opsd couldn't be found on the Hugging Face Hub (offline mode is enabled).
Found the latest cached dataset configuration 'default' at /opt/hf_cache/datasets/siyanzhao___openthoughts_math_30k_opsd/default/0.0.0/1f33e9dc2e8a1c639ca74f8024ad4a9f1f5eae62 (last modified on Sun Aug 2 17:14:36 2026).
Found the latest cached dataset configuration 'default' at /opt/hf_cache/datasets/siyanzhao___openthoughts_math_30k_opsd/default/0.0.0/1f33e9dc2e8a1c639ca74f8024ad4a9f1f5eae62 (last modified on Sun Aug 2 17:14:36 2026).
[DataCollator] Original padding_side: left
[DataCollator] Set padding_side to: right
[DataCollator] Reason first mode: False
`torch_dtype` is deprecated! Use `dtype` instead!
[DataCollator] Original padding_side: left
[DataCollator] Set padding_side to: right
[DataCollator] Reason first mode: False
[DataCollator] Original padding_side: left
[DataCollator] Set padding_side to: right
[DataCollator] Reason first mode: False
`torch_dtype` is deprecated! Use `dtype` instead!
`torch_dtype` is deprecated! Use `dtype` instead!
[DataCollator] Original padding_side: left
[DataCollator] Set padding_side to: right
[DataCollator] Reason first mode: False
`torch_dtype` is deprecated! Use `dtype` instead!
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Tokenizing train dataset: 3%|▎ | 785/29434 [00:05<03:05, 154.85 examples/s]#30
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolexec
args
{
"input": "const r = await tools.write_stdin({session_id:80474,chars:\"\",yield_time_ms:30000,max_output_tokens:1000});\ntext(r.output);"
}exec result
Script running with cell ID 23
Wall time 11.0 seconds
Output:
#31
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolwait
args
{
"cell_id": "23",
"yield_time_ms": 30000,
"max_tokens": 1000
}wait result
Script completed
Wall time 11.3 seconds
Output:
Warning: truncated output (original token count: 1027)
Total output lines: 4
Warning: truncated output (original token count: 6744)
Total output lines: 1
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Tokenizing train dataset: 23%|██▎ | 6703/29434 [00:43<02:11, 172.60 examples/s]#32
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolexec
args
{
"input": "const r = await tools.write_stdin({session_id:80474,chars:\"\",yield_time_ms:30000,max_output_tokens:1500});\ntext(r.output);"
}exec result
Script running with cell ID 24
Wall time 11.0 seconds
Output:
#33
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolwait
args
{
"cell_id": "24",
"yield_time_ms": 30000,
"max_tokens": 1500
}wait result
Script completed
Wall time 12.9 seconds
Output:
Warning: truncated output (original token count: 1527)
Total output lines: 4
Warning: truncated output (original token count: 6683)
Total output lines: 1
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Tokenizing train dataset: 25%|██▌…27 tokens truncated…%|████ | 12074/29434 [01:15<02:15, 127.96 examples/s]
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Tokenizing train dataset: 43%|████▎ | 12686/29434 [01:19<01:34, 177.23 examples/s]#34
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolexec
args
{
"input": "const r = await tools.write_stdin({session_id:80474,chars:\"\",yield_time_ms:60000,max_output_tokens:1000});\ntext(r.output);"
}exec result
Script running with cell ID 25
Wall time 11.0 seconds
Output:
#35
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolwait
args
{
"cell_id": "25",
"yield_time_ms": 50000,
"max_tokens": 1000
}wait result
Script completed
Wall time 42.6 seconds
Output:
Warning: truncated output (original token count: 1027)
Total output lines: 4
Warning: truncated output (original token count: 13177)
Total output lines: 1
Tokenizing train dataset: 43%|████▎ | 12706/29434 [01:19<01:33, 179.32 examples/s]
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Tokenizing train dataset: 45%|████▍ | 13137…27 tokens truncated…ain dataset: 85%|████████▍ | 25000/29434 [02:23<00:30, 144.47 examples/s]
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Tokenizing train dataset: 87%|████████▋ | 25498/29434 [02:25<00:14, 271.08 examples/s]
Tokenizing train dataset: 87%|████████▋ | 25530/29434 [02:25<00:15, 248.58 examples/s]#36
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolexec
args
{
"input": "const r = await tools.write_stdin({session_id:80474,chars:\"\",yield_time_ms:60000,max_output_tokens:1500});\ntext(r.output);"
}exec result
Script running with cell ID 26
Wall time 11.0 seconds
Output:
#37
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolwait
args
{
"cell_id": "26",
"yield_time_ms": 50000,
"max_tokens": 1500
}wait result
Script completed
Wall time 41.9 seconds
Output:
Warning: truncated output (original token count: 1527)
Total output lines: 44
Warning: truncated output (original token count: 5746)
Total output lines: 63
Tokenizing train dataset: 87%|████████▋ | 25559/29434 [02:25<00:15, 258.07 examples/s]
Tokenizing train dataset: 87%|████████▋ | 25595/29434 [02:25<00:15, 243.60 examples/s]
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Tokenizing train dataset: 89%|████████▉ | 26208/29434 [02:28<00:13, 236.22 examples/s]
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Tokenizing train dataset: 89%|████████▉ | 26263/29434 [02:28<00:12, 248.41 examples/s]
Tokenizing train dataset: 89%|████████▉ | 26300/29434 [02:28<00:12, 242.43 examples/s]
Tokenizing train dataset: 89%|████████▉ | 26325/29434 [02:29<00:12, 241.24 examples/s]
Tokenizing train dataset: 90%|████████▉…27 tokens truncated…==============================================================
================================================================================
FIXED TEACHER MODE ENABLED
Teacher will use the initial policy (base model without LoRA adapters)
Student will update with LoRA adapters
================================================================================
`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!
[Gloo] Rank 0 is connected to 3 peer ranks. Expected number of connected peer ranks is : 3
[Gloo] Rank 3 is connected to 3 peer ranks. Expected number of connected peer ranks is : 3
[Gloo] Rank 1 is connected to 3 peer ranks. Expected number of connected peer ranks is : 3
[Gloo] Rank 2 is connected to 3 peer ranks. Expected number of connected peer ranks is : 3
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
[Gloo] Rank 0 is connected to 0 peer ranks. Expected number of connected peer ranks is : 0
Loading safetensors checkpoint shards: 0% Completed | 0/2 [00:00<?, ?it/s]
Loading safetensors checkpoint shards: 100% Completed | 2/2 [00:00<00:00, 2.20it/s]
Loading safetensors checkpoint shards: 100% Completed | 2/2 [00:00<00:00, 2.20it/s]
#38
narration
The corrected objective is stable in a gradient sanity check: the clipped loss is positive and retains nonzero gradients. The first exact capped run is now training; once it finishes I’ll use a cheap partial evaluation only as a screening signal, not as the final decision metric.
#39
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolexec
args
{
"input": "const r = await tools.write_stdin({session_id:80474,chars:\"\",yield_time_ms:60000,max_output_tokens:2000});\ntext(r.output);"
}exec result
Script running with cell ID 27
Wall time 11.0 seconds
Output:
#40
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolwait
args
{
"cell_id": "27",
"yield_time_ms": 50000,
"max_tokens": 2000
}wait result
Script completed
Wall time 46.2 seconds
Output:
Capturing CUDA graphs (mixed prefill-decode, PIECEWISE): 0%| | 0/5 [00:00<?, ?it/s]
Capturing CUDA graphs (mixed prefill-decode, PIECEWISE): 40%|████ | 2/5 [00:00<00:00, 18.16it/s]
Capturing CUDA graphs (mixed prefill-decode, PIECEWISE): 100%|██████████| 5/5 [00:00<00:00, 24.79it/s]
Capturing CUDA graphs (mixed prefill-decode, PIECEWISE): 100%|██████████| 5/5 [00:00<00:00, 23.72it/s]
Capturing CUDA graphs (decode, FULL): 0%| | 0/4 [00:00<?, ?it/s]
Capturing CUDA graphs (decode, FULL): 100%|██████████| 4/4 [00:00<00:00, 39.46it/s]
Capturing CUDA graphs (decode, FULL): 100%|██████████| 4/4 [00:00<00:00, 39.34it/s]
The tokenizer has new PAD/BOS/EOS tokens that differ from the model config and generation config. The model config and generation config were aligned accordingly, being updated with the tokenizer's values. Updated tokens: {'bos_token_id': None, 'pad_token_id': 151643}.
The tokenizer has new PAD/BOS/EOS tokens that differ from the model config and generation config. The model config and generation config were aligned accordingly, being updated with the tokenizer's values. Updated tokens: {'bos_token_id': None, 'pad_token_id': 151643}.
The tokenizer has new PAD/BOS/EOS tokens that differ from the model config and generation config. The model config and generation config were aligned accordingly, being updated with the tokenizer's values. Updated tokens: {'bos_token_id': None, 'pad_token_id': 151643}.
The tokenizer has new PAD/BOS/EOS tokens that differ from the model config and generation config. The model config and generation config were aligned accordingly, being updated with the tokenizer's values. Updated tokens: {'bos_token_id': None, 'pad_token_id': 151643}.
[rank3]:W0802 18:37:08.089000 1112 torch/utils/cpp_extension.py:2425] TORCH_CUDA_ARCH_LIST is not set, all archs for visible cards are included for compilation.
[rank3]:W0802 18:37:08.089000 1112 torch/utils/cpp_extension.py:2425] If this is not desired, please set os.environ['TORCH_CUDA_ARCH_LIST'] to specific architectures.
0%| | 0/100 [00:00<?, ?it/s]vLLM generation done - elapsed time: 3.19s, prompts: 4, total tokens: 2052, avg length: 513.0, speed: 643.4 tok/s
vLLM generation done - elapsed time: 3.39s, prompts: 4, total tokens: 3421, avg length: 855.2, speed: 1007.8 tok/s
vLLM generation done - elapsed time: 3.41s, prompts: 4, total tokens: 3588, avg length: 897.0, speed: 1050.8 tok/s
vLLM generation done - elapsed time: 3.40s, prompts: 4, total tokens: 3468, avg length: 867.0, speed: 1019.5 tok/s
/usr/local/lib/python3.10/dist-packages/torch/utils/checkpoint.py:85: UserWarning: None of the inputs have requires_grad=True. Gradients will be None
warnings.warn(
/usr/local/lib/python3.10/dist-packages/torch/utils/checkpoint.py:85: UserWarning: None of the inputs have requires_grad=True. Gradients will be None
warnings.warn(
/usr/local/lib/python3.10/dist-packages/torch/utils/checkpoint.py:85: UserWarning: None of the inputs have requires_grad=True. Gradients will be None
warnings.warn(
/usr/local/lib/python3.10/dist-packages/torch/utils/checkpoint.py:85: UserWarning: None of the inputs have requires_grad=True. Gradients will be None
warnings.warn(
Could not estimate the number of tokens of the input, floating-point operations will not be computed
Could not estimate the number of tokens of the input, floating-point operations will not be computed
Could not estimate the number of tokens of the input, floating-point operations will not be computed
Could not estimate the number of tokens of the input, floating-point operations will not be computed
vLLM generation done - elapsed time: 3.32s, prompts: 4, total tokens: 2828, avg length: 707.0, speed: 852.9 tok/s
vLLM generation done - elapsed time: 3.37s, prompts: 4, total tokens: 3335, avg length: 833.8, speed: 990.6 tok/s
vLLM generation done - elapsed time: 3.39s, prompts: 4, total tokens: 3686, avg length: 921.5, speed: 1085.8 tok/s
vLLM generation done - elapsed time: 3.40s, prompts: 4, total tokens: 3861, avg length: 965.2, speed: 1134.3 tok/s
1%| | 1/100 [00:08<13:47, 8.36s/it]vLLM generation done - elapsed time: 3.05s, prompts: 4, total tokens: 2383, avg length: 595.8, speed: 781.3 tok/s
vLLM generation done - elapsed time: 3.05s, prompts: 4, total tokens: 3304, avg length: 826.0, speed: 1081.5 tok/s
vLLM generation done - elapsed time: 3.25s, prompts: 4, total tokens: 2284, avg length: 571.0, speed: 702.2 tok/s
vLLM generation done - elapsed time: 3.42s, prompts: 4, total tokens: 4096, avg length: 1024.0, speed: 1198.4 tok/s
vLLM generation done - elapsed time: 3.31s, prompts: 4, total tokens: 2627, avg length: 656.8, speed: 794.6 tok/s
vLLM generation done - elapsed time: 3.36s, prompts: 4, total tokens: 3423, avg length: 855.8, speed: 1019.4 tok/s
vLLM generation done - elapsed time: 3.38s, prompts: 4, total tokens: 3235, avg length: 808.8, speed: 958.0 tok/s
vLLM generation done - elapsed time: 3.38s, prompts: 4, total tokens: 3703, avg length: 925.8, speed: 1094.2 tok/s
2%|▏ | 2/100 [00:16<13:29, 8.26s/it]
{'loss': 0.0159, 'grad_norm': 0.17466895282268524, 'learning_rate': 5e-06, 'on_policy_loss': 0.0159, 'epoch': 0.0}
2%|▏ | 2/100 [00:16<13:29, 8.26s/it]vLLM generation done - elapsed time: 3.27s, prompts: 4, total tokens: 2992, avg length: 748.0, speed: 914.5 tok/s
vLLM generation done - elapsed time: 3.30s, prompts: 4, total tokens: 2512, avg length: 628.0, speed: 761.6 tok/s
vLLM generation done - elapsed time: 3.37s, prompts: 4, total tokens: 3411, avg length: 852.8, speed: 1011.0 tok/s
vLLM generation done - elapsed time: 3.40s, prompts: 4, total tokens: 4096, avg length: 1024.0, speed: 1204.3 tok/s
#41
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolexec
args
{
"input": "const r = await tools.write_stdin({session_id:80474,chars:\"\",yield_time_ms:60000,max_output_tokens:500});\ntext(r.output);"
}exec result
Script running with cell ID 28
Wall time 11.0 seconds
Output:
#42
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolwait
args
{
"cell_id": "28",
"yield_time_ms": 50000,
"max_tokens": 500
}wait result
Script completed
Wall time 46.2 seconds
Output:
Warning: truncated output (original token count: 527)
Total output lines: 63
Warning: truncated output (original token count: 4004)
Total output lines: 357
vLLM generation done - elapsed time: 3.24s, prompts: 4, total tokens: 2742, avg length: 685.5, speed: 846.7 tok/s
vLLM generation done - elapsed time: 3.31s, prompts: 4, total tokens: 2865, avg length: 716.2, speed: 865.5 tok/s
vLLM generation done - elapsed time: 3.34s, prompts: 4, total tokens: 3156, avg length: 789.0, speed: 945.9 tok/s
vLLM generation done - elapsed time: 3.38s, prompts: 4, total tokens: 3705, avg length: 926.2, speed: 1096.2 tok/s
3%|▎ | 3/100 [00:24<13:15, 8.20s/it]vLLM generation done - elapsed time: 3.34s, prompts: 4, total tokens: 3292, avg length: 823.0, speed: 984.9 tok/s
vLLM generation done - elapsed time: 3.37s, prompts: 4, total tokens: 3594, avg length: 898.5, speed: 1066.1 tok/s
vLLM generation done - elapsed time: 3.39s, prompts: 4, total tokens: 3813, avg length: 953.2, speed: 1124.6 tok/s
vLLM generation done - elapsed time: 3.40s, prompts: 4, total tokens:…27 tokens truncated…### Step 4: Expand and simplify
$$
\frac{n(n + 1)}{n + 3} = \frac{n^2 + n}{n + 3}
$$
We can divide this expression as a polynomial:
Divide $n^2 + n$ by $n + 3$:
$$
\frac{n^2 + n}{n + 3} = \frac{n(n + 1)}{n + 3} = n - \frac{3n}{n + 3}
$$
So:
$$
\frac{n^2 + n}{n + 3} - n = \left(n - \frac{3n}{n + 3}\right) - n = -\frac{3n}{n + 3}
$$
---
### Step 5: Take the limit
Now take the limit as $n \to \infty$:
$$
\lim_{n \to \infty} -\frac{3n}{n + 3}
$$
Divide numerator and denominator by $n$:
$$
-\frac{3}{1 + \frac{3}{n}} \to -3
$$
---
### ✅ Final Answer:
$$
\boxed{-3}
$$<|im_end|>
================================================================================
================================================================================
Saved 40 generation outputs to:
/workspace/runs/klclip/capped_seed42/generations/generations_step_10.json
================================================================================
11%|█ | 11/100 [01:29<12:00, 8.10s/it]#43
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolexec
args
{
"input": "const r = await tools.write_stdin({session_id:80474,chars:\"\",yield_time_ms:60000,max_output_tokens:300});\ntext(r.output);"
}exec result
Script running with cell ID 29
Wall time 11.0 seconds
Output:
#44
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolwait
args
{
"cell_id": "29",
"yield_time_ms": 50000,
"max_tokens": 300
}wait result
Script completed
Wall time 46.5 seconds
Output:
Warning: truncated output (original token count: 327)
Total output lines: 13
Warning: truncated output (original token count: 2338)
Total output lines: 78
vLLM generation done - elapsed time: 3.23s, prompts: 4, total tokens: 2567, avg length: 641.8, speed: 795.6 tok/s
vLLM generation done - elapsed time: 3.27s, prompts: 4, total tokens: 2508, avg length: 627.0, speed: 767.4 tok/s
vLLM generation done - elapsed time: 3.33s, prompts: 4, total tokens: 2837, avg length: 709.2, speed: 851.7 tok/s
vLLM generation done - elapsed time: 3.34s, prompts: 4, total tokens: 3403, avg length: 850.8, speed: 1017.4 tok/s
vLLM generation done - elapsed time: 3.31s, prompts: 4, total to…27 tokens truncated…ed time: 3.40s, prompts: 4, total tokens: 4096, avg length: 1024.0, speed: 1203.4 tok/s
19%|█▉ | 19/100 [02:34<10:56, 8.11s/it]vLLM generation done - elapsed time: 3.33s, prompts: 4, total tokens: 3100, avg length: 775.0, speed: 931.9 tok/s
vLLM generation done - elapsed time: 3.33s, prompts: 4, total tokens: 3137, avg length: 784.2, speed: 942.9 tok/s
vLLM generation done - elapsed time: 3.34s, prompts: 4, total tokens: 3391, avg length: 847.8, speed: 1015.3 tok/s
vLLM generation done - elapsed time: 3.42s, prompts: 4, total tokens: 4096, avg length: 1024.0, speed: 1199.1 tok/s
#45
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolexec
args
{
"input": "let out=\"\";\nfor (let i=0;i<3;i++){\n const r=await tools.write_stdin({session_id:80474,chars:\"\",yield_time_ms:60000,max_output_tokens:100});\n out += r.output.slice(-300)+\"\\n\";\n if(r.exit_code!==undefined) break;\n notify(`training continues (${i+1}/3 polling interval)`);\n}\ntext(out);"
}exec result
Script running with cell ID 30
Wall time 11.0 seconds
Output:
#46
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolwait
args
{
"cell_id": "30",
"yield_time_ms": 60000,
"max_tokens": 500
}wait result
Script running with cell ID 30
Wall time 61.0 seconds
Output:
#47
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolexec
args
{}exec result
training continues (1/3 polling interval)#48
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolwait
args
{
"cell_id": "30",
"yield_time_ms": 60000,
"max_tokens": 500
}wait result
Script running with cell ID 30
Wall time 61.0 seconds
Output:
#49
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolexec
args
{}exec result
training continues (2/3 polling interval)#50
reasoning (redacted)
encrypted chain-of-thought — recorded, not exposed
toolwait
args
{
"cell_id": "30",
"yield_time_ms": 60000,
"max_tokens": 500
}wait result
Script completed
Wall time 26.8 seconds
Output:
ration done - elapsed time: 3.33s, prompts: 4, total tokens: 3012, avg length…2796 tokens truncated…d time: 3.37s, prompts: 4, total tokens: 3351, avg length: 837.8, speed: 995.0 tok/s
vLLM generation done - elapsed time: 3.38s, prompts: 4, total tokens: 3787, avg length: 946.8, speed: 1120.0 tok/s
LLM generation done - elapsed time: 3.32s, prompts: 4, total tokens: 3020, avg length…2024 tokens truncated…: 733.8, speed: 884.2 tok/s
vLLM generation done - elapsed time: 3.38s, prompts: 4, total tokens: 3889, avg length: 972.2, speed: 1149.2 tok/s
35%|███▌ | 35/100 [04:43<08:47, 8.11s/it]
ration done - elapsed time: 3.31s, prompts: 4, total tokens: 2725, avg length…2078 tokens truncated…time: 3.39s, prompts: 4, total tokens: 3953, avg length: 988.2, speed: 1167.1 tok/s
vLLM generation done - elapsed time: 3.39s, prompts: 4, total tokens: 4096, avg length: 1024.0, speed: 1206.8 tok/s