include binary path

[djps]

Closes #781

Greptile Summary

Adds a benchmark option and CLI argument for selecting a custom C++ solver binary, records that selection in benchmark metadata, and forwards it to solver execution.

• Extends BenchmarkOptions with cpp_binary.
• Adds --cpp-binary to the benchmark CLI.
• Passes the selected path through native benchmark runs.

Confidence Score: 4/5

The programmatic benchmark configuration should be fixed before merging because it can ignore the configured binary and record misleading benchmark provenance.

BenchmarkOptions.cpp_binary is serialized as the selected binary, while solver execution instead uses a separately defaulted run() argument, allowing the recorded configuration and actual executable to diverge.

Files Needing Attention: benchmarks/benchmark.py, benchmarks/helpers.py

Important Files Changed

Filename	Overview
benchmarks/benchmark.py	Adds custom-binary parsing, recording, and solver forwarding, but keeps the configured path in two independent parameters that can diverge for programmatic callers.
benchmarks/helpers.py	Adds the custom binary path to benchmark configuration and serialized options; this field is not directly used by benchmark execution.

_{Reviews (1): Last reviewed commit: "include binary path" | Re-trigger Greptile}

Greptile also left 1 inline comment on this PR.

Context used:

• Knowledge Base — Native solver integration

[greptile-apps]

Binary configuration values diverge

When a programmatic caller sets BenchmarkOptions.cpp_binary but does not repeat it as run(cpp_binary=...), the saved options report the custom binary while execution passes None and uses the bundled binary, causing misleading benchmark provenance or a missing-binary failure.

Knowledge Base Used: Native solver integration

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 75.83%. Comparing base (1744cf6) to head (ec8eebb).

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #782   +/-   ##
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  Coverage   75.83%   75.83%           
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  Files          58       58           
  Lines        8274     8274           
  Branches     1614     1614           
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  Hits         6275     6275           
  Misses       1373     1373           
  Partials      626      626           

Flag	Coverage Δ
3.10	75.80% <ø> (ø)
3.11	75.80% <ø> (ø)
3.12	75.80% <ø> (ø)
3.13	75.80% <ø> (ø)
macos-latest	75.71% <ø> (ø)
ubuntu-latest	75.71% <ø> (ø)
windows-latest	75.64% <ø> (ø)

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