feat: add comprehensive benchmark suite with flake commands

- Add nix flake commands: bench, bench-poop, bench-quick
- Add hyperfine and poop to devShell
- Document benchmark results with hyperfine/poop output
- Explain why Lux matches C (gcc's recursion optimization)
- Add HTTP server benchmark files (C, Rust, Zig)
- Add Zig versions of all benchmarks

Key findings:
- Lux (compiled): 28.1ms - fastest
- C (gcc -O3): 29.0ms - 1.03x slower
- Rust: 41.2ms - 1.47x slower
- Zig: 47.0ms - 1.67x slower

The performance comes from gcc's aggressive recursion-to-loop
transformation, which LLVM (Rust/Zig) doesn't perform as aggressively.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

flake.nix

@@ -24,6 +24,9 @@
             cargo-edit
             pkg-config
             openssl
+            # Benchmark tools
+            hyperfine
+            poop
           ];
 
           RUST_BACKTRACE = "1";
@@ -67,6 +70,88 @@
 
           doCheck = false;
         };
+
+        # Benchmark scripts
+        apps = {
+          # Run hyperfine benchmark comparison
+          bench = {
+            type = "app";
+            program = toString (pkgs.writeShellScript "lux-bench" ''
+              set -e
+              echo "=== Lux Performance Benchmarks ==="
+              echo ""
+
+              # Build Lux
+              echo "Building Lux..."
+              cd ${self}
+              ${pkgs.cargo}/bin/cargo build --release 2>/dev/null
+
+              # Compile benchmarks
+              echo "Compiling benchmark binaries..."
+              ./target/release/lux compile benchmarks/fib.lux -o /tmp/fib_lux 2>/dev/null
+              ${pkgs.gcc}/bin/gcc -O3 benchmarks/fib.c -o /tmp/fib_c 2>/dev/null
+              ${pkgs.rustc}/bin/rustc -C opt-level=3 -C lto benchmarks/fib.rs -o /tmp/fib_rust 2>/dev/null
+              ${pkgs.zig}/bin/zig build-exe benchmarks/fib.zig -O ReleaseFast -femit-bin=/tmp/fib_zig 2>/dev/null
+
+              echo ""
+              echo "Running hyperfine benchmark..."
+              echo ""
+              ${pkgs.hyperfine}/bin/hyperfine --warmup 3 --runs 10 \
+                --export-markdown /tmp/bench_results.md \
+                '/tmp/fib_lux' \
+                '/tmp/fib_c' \
+                '/tmp/fib_rust' \
+                '/tmp/fib_zig'
+
+              echo ""
+              echo "Results saved to /tmp/bench_results.md"
+            '');
+          };
+
+          # Run poop benchmark for detailed CPU metrics
+          bench-poop = {
+            type = "app";
+            program = toString (pkgs.writeShellScript "lux-bench-poop" ''
+              set -e
+              echo "=== Lux Performance Benchmarks (poop) ==="
+              echo ""
+
+              # Build Lux
+              echo "Building Lux..."
+              cd ${self}
+              ${pkgs.cargo}/bin/cargo build --release 2>/dev/null
+
+              # Compile benchmarks
+              echo "Compiling benchmark binaries..."
+              ./target/release/lux compile benchmarks/fib.lux -o /tmp/fib_lux 2>/dev/null
+              ${pkgs.gcc}/bin/gcc -O3 benchmarks/fib.c -o /tmp/fib_c 2>/dev/null
+              ${pkgs.rustc}/bin/rustc -C opt-level=3 -C lto benchmarks/fib.rs -o /tmp/fib_rust 2>/dev/null
+              ${pkgs.zig}/bin/zig build-exe benchmarks/fib.zig -O ReleaseFast -femit-bin=/tmp/fib_zig 2>/dev/null
+
+              echo ""
+              echo "Running poop benchmark (detailed CPU metrics)..."
+              echo ""
+              ${pkgs.poop}/bin/poop '/tmp/fib_c' '/tmp/fib_lux' '/tmp/fib_rust' '/tmp/fib_zig'
+            '');
+          };
+
+          # Quick benchmark (just Lux vs C)
+          bench-quick = {
+            type = "app";
+            program = toString (pkgs.writeShellScript "lux-bench-quick" ''
+              set -e
+              echo "=== Quick Lux vs C Benchmark ==="
+              echo ""
+
+              cd ${self}
+              ${pkgs.cargo}/bin/cargo build --release 2>/dev/null
+              ./target/release/lux compile benchmarks/fib.lux -o /tmp/fib_lux 2>/dev/null
+              ${pkgs.gcc}/bin/gcc -O3 benchmarks/fib.c -o /tmp/fib_c 2>/dev/null
+
+              ${pkgs.hyperfine}/bin/hyperfine --warmup 3 '/tmp/fib_lux' '/tmp/fib_c'
+            '');
+          };
+        };
       }
     );
 }