{"model": "reduced-order HBM bandwidth roofline -- DRAM efficiency, latency, LLM token gating (educational)", "inputs": {"num_stacks": 6, "bus_width_bits": 1024, "data_rate_gbps": 6.4, "row_hit_rate": 60.0, "read_pct": 70.0, "banks": 16, "access_bytes": 256.0, "model_params_b": 70.0, "precision_bits": 16.0, "batch": 1}, "outputs": {"peak_bandwidth_gbs": 4915.2, "effective_bandwidth_gbs": 3610.9, "dram_efficiency_percent": 73.5, "row_efficiency_percent": 81.7, "rw_efficiency_percent": 92.7, "refresh_efficiency_percent": 97.0, "channels": 96, "per_channel_gbs": 51.2, "page_hit_latency_ns": 19.0, "random_latency_ns": 47.0, "model_size_gb": 140.0, "arithmetic_intensity": 1.0, "time_per_token_ms": 38.772, "decode_tokens_per_s": 25.8, "power_w": 112.7, "gbs_per_watt": 32.1, "verdict": "moderate DRAM efficiency (page management and read/write turnaround leave bandwidth on the table -- larger, more sequential accesses recover it)"}, "profile": {"bw_vs_access": [[32.0, 342.1], [35.5, 395.9], [39.3, 461.5], [43.6, 542.5], [48.4, 644.5], [53.6, 776.1], [59.5, 951.4], [65.9, 1194.6], [73.1, 1552.8], [81.0, 2128.2], [89.8, 2697.8], [99.6, 2805.0], [110.4, 2909.2], [122.5, 3010.1], [135.8, 3107.3], [150.5, 3200.6], [166.9, 3289.6], [185.1, 3374.2], [205.2, 3454.3], [227.5, 3530.0], [252.3, 3601.1], [279.7, 3667.7], [310.1, 3729.9], [343.8, 3787.9], [381.2, 3841.8], [422.7, 3891.7], [468.6, 3937.8], [519.6, 3980.4], [576.1, 4019.6], [638.8, 4055.6], [708.2, 4088.6], [785.3, 4118.9], [870.7, 4146.6], [965.3, 4171.9], [1070.3, 4194.9], [1186.7, 4216.0], [1315.8, 4235.1], [1458.9, 4252.5], [1617.5, 4268.4], [1793.4, 4282.8], [1988.5, 4295.8], [2204.7, 4307.7], [2444.5, 4318.4], [2710.3, 4328.1], [3005.1, 4336.9], [3331.9, 4344.9], [3694.2, 4352.1], [4096.0, 4358.7]], "bw_vs_hit": [[0.0, 2833.1], [0.0213, 2854.9], [0.0426, 2877.1], [0.0638, 2899.6], [0.0851, 2922.4], [0.1064, 2945.6], [0.1277, 2969.2], [0.1489, 2993.2], [0.1702, 3017.5], [0.1915, 3042.3], [0.2128, 3067.4], [0.234, 3093.0], [0.2553, 3119.0], [0.2766, 3145.5], [0.2979, 3172.4], [0.3191, 3199.7], [0.3404, 3227.6], [0.3617, 3255.9], [0.383, 3284.7], [0.4043, 3314.1], [0.4255, 3343.9], [0.4468, 3374.4], [0.4681, 3405.3], [0.4894, 3436.9], [0.5106, 3469.0], [0.5319, 3501.8], [0.5532, 3535.2], [0.5745, 3569.2], [0.5957, 3603.8], [0.617, 3639.2], [0.6383, 3675.3], [0.6596, 3712.0], [0.6809, 3749.6], [0.7021, 3787.8], [0.7234, 3826.9], [0.7447, 3866.8], [0.766, 3907.6], [0.7872, 3949.2], [0.8085, 3991.7], [0.8298, 4035.1], [0.8511, 4079.4], [0.8723, 4124.8], [0.8936, 4171.2], [0.9149, 4218.6], [0.9362, 4267.2], [0.9574, 4316.8], [0.9787, 4367.7], [1.0, 4419.7]], "peak_bw": 4915.2, "eff_bw": 3610.9, "op_access": 256.0, "row_eff": 0.817, "rw_eff": 0.927, "refresh_eff": 0.97, "dram_eff": 0.7346, "row_hit": 0.6, "banks": 16, "read_pct": 70.0}, "steps": 96, "node": "ip-172-26-4-148", "compute_ms": 0.2}