Homebrew `brew install` Bottleneck Detection: Network, Dependency, or Compile?

The goal is to isolate which phase of a Homebrew installation consumes the most time when a formula with many dependencies is installed on macOS. The constraints are that only Homebrew’s built‑in verbose and log mechanisms may be used, and the analysis must be reproducible across runs.

Running brew install --verbose <formula> prints each step—download, dependency resolution, bottle pour, and compilation—along with timestamps. The log files under ~/Library/Logs/Homebrew/<formula>/ capture the full output of build tools, which can be examined for additional timing clues.

However, the verbose output is not automatically summarized, so a clear method to parse and quantify each phase remains uncertain. Additionally, the relative cost of network latency versus CPU‑bound compilation can vary with network conditions and system load.

• What specific markers in the verbose log indicate the start and end of the download phase, and how can they be used to calculate download duration?
• Which sections of the per‑formula log file best capture the time spent on dependency resolution versus the actual compilation of the formula?
• Does Homebrew expose any flags or environment variables that enable automatic recording of phase durations without manual parsing?