Improve user experience during benchmark execution with progress indicators and intermediate results

[Copilot]

Overview

This PR enhances the user experience while running cross-library benchmarks by adding nested progress bars, intermediate results, and better informational messages. These improvements address the issue of users waiting anxiously during long-running benchmarks without visibility into what's happening.

Problem

Previously, when running benchmarks, users experienced:

• No indication of which engine/library was being tested
• A single progress bar with minimal context
• Results only visible at the very end
• Uncertainty about whether the benchmark was frozen or just slow
• No intermediate feedback during long runs

Solution

Cross-Library Benchmark (benchmarks/quadtree_bench/runner.py)

Added nested progress bars that show progress at two levels:

Running 13 experiments with 6 engines...
Experiments:  23%|██▎       | 3/13 [01:45<05:30, 33.0s/exp] (points: 8,192)
  fastquadtree (repeat 2/3):  67%|██████▋   | 12/18 [00:03<00:01, 4.5run/s]

Added intermediate results after each experiment completes:

  📊 Results for 8,192 points:
     Fastest: fastquadtree (0.342s total)
     1. fastquadtree       build=0.145s, query=0.197s, total=0.342s
     2. Rtree              build=0.189s, query=0.223s, total=0.412s
     3. PyQtree            build=0.287s, query=0.198s, total=0.485s

Added informational messages:

• "Warming up engines..." before benchmarks start
• "Running N experiments with M engines..." at start

Native vs Shim Benchmark (benchmarks/benchmark_native_vs_shim.py)

Added descriptive progress bar labels and configuration display:

Native vs Shim Benchmark
==================================================
Configuration:
  Points: 500,000
  Queries: 500
  Repeats: 5

Warming up...

Running benchmarks...
Native:  40%|████      | 2/5 [00:15<00:22, 7.5s/run]
Shim (no map):  60%|██████    | 3/5 [00:20<00:13, 6.7s/run]

Benefits

• Transparency: Users always know which engine is being tested at any moment
• Time Management: Accurate ETAs at multiple levels help users plan their time
• Early Feedback: Intermediate results show performance trends before completion
• Debugging: Easy to identify hanging or failing engines
• Professional Output: Clean, well-organized, informative display

Technical Details

• No Breaking Changes: Fully backward compatible with existing usage
• No New Dependencies: Uses existing tqdm library already in requirements.txt
• Minimal Overhead: Progress bar updates happen outside timing loops, no impact on benchmark accuracy
• Clean Implementation: Only 77 net lines added across 2 files

Testing

• ✅ Python syntax validation passed
• ✅ Code structure verification completed
• ✅ Visual demonstration shows improvements working correctly
• ✅ All existing functionality preserved

Original prompt

Find ways to improve the user experience while waiting for the cross-library benchmarks to finish ruunning

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