[dynamo] use cache size to detect recompilation

[anijain2305]

Stack from ghstack (oldest at bottom):

• [dynamo] Readability - Rename name to get_frame_name #106880
• -> [dynamo] use cache size to detect recompilation #106878

cc @voznesenskym @penguinwu @EikanWang @jgong5 @Guobing-Chen @XiaobingSuper @zhuhaozhe @blzheng @Xia-Weiwen @wenzhe-nrv @jiayisunx @ipiszy @chenyang78 @aakhundov

[pytorch-bot]

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🧪 See artifacts and rendered test results at hud.pytorch.org/pr/106878

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❌ 6 New Failures

As of commit 3d71287:

NEW FAILURES - The following jobs have failed:

• cuda11.8-py3.10-gcc7-sm86 / test (inductor_timm_dynamic, 1, 2, linux.g5.4xlarge.nvidia.gpu) (gh)
• cuda11.8-py3.10-gcc7-sm86 / test (inductor_torchbench_dynamic, 1, 1, linux.g5.4xlarge.nvidia.gpu) (gh)
• cuda11.8-py3.10-gcc7-sm86 / test (inductor_torchbench, 1, 1, linux.g5.4xlarge.nvidia.gpu) (gh)
• cuda12.1-py3.10-gcc9-sm86-periodic-dynamo-benchmarks / test (aot_eager_torchbench, 1, 1, linux.g5.4xlarge.nvidia.gpu) (gh)
• cuda12.1-py3.10-gcc9-sm86-periodic-dynamo-benchmarks / test (dynamic_aot_eager_torchbench, 1, 1, linux.g5.4xlarge.nvidia.gpu) (gh)
• cuda12.1-py3.10-gcc9-sm86-periodic-dynamo-benchmarks / test (dynamo_eager_torchbench, 1, 1, linux.g5.4xlarge.nvidia.gpu) (gh)

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