add cua replay example script (#1162)

# why

Update example script to show benefits from using cached actions 

image of what the final log looks like 
<img width="948" height="506" alt="image"
src="https://github.com/user-attachments/assets/2307e7c2-6a59-4173-b459-14e062800f4c"
/>

# what changed

# test plan

---------

Co-authored-by: Sean McGuire <[email protected]>

Author: tkattkat

packages/core/examples/v3/cuaReplay.ts

@@ -1,29 +1,97 @@
-import { V3 } from "../../lib/v3";
+import { Stagehand } from "../../lib/v3";
+import { v3Logger } from "../../lib/v3/logger";
+import dotenv from "dotenv";
 
-async function main() {
-  const v3 = new V3({
+dotenv.config();
+
+async function runDemo(runNumber: number) {
+  const startTime = Date.now();
+
+  v3Logger({
+    level: 1,
+    category: "demo",
+    message: `RUN ${runNumber}: ${runNumber === 1 ? "BUILDING CACHE" : "USING CACHE"}`,
+  });
+
+  const stagehand = new Stagehand({
     env: "LOCAL",
     verbose: 1,
     cacheDir: "cua-agent-cache",
   });
 
-  await v3.init();
+  await stagehand.init();
+
+  const page = stagehand.context.pages()[0];
 
-  const startPage = v3.context.pages()[0];
-  await startPage.goto(
-    "https://browserbase.github.io/stagehand-eval-sites/sites/drag-drop/",
-  );
-  const agent = v3.agent({
+  await page.goto("https://v0-modern-login-flow.vercel.app/", {
+    waitUntil: "networkidle",
+  });
+
+  const agent = stagehand.agent({
     cua: true,
     model: "anthropic/claude-sonnet-4-20250514",
   });
 
   const result = await agent.execute({
-    instruction: "drag 'text' to zone A.",
+    instruction: `Sign in with the email address '[email protected]' and the password 'stagehand=goated'`,
     maxSteps: 20,
   });
 
-  console.log(JSON.stringify(result, null, 2));
+  const endTime = Date.now();
+  const duration = (endTime - startTime) / 1000;
+
+  await stagehand.close();
+
+  return {
+    duration,
+    success: result.success,
+    result,
+  };
+}
+
+async function main() {
+  const metrics1 = await runDemo(1);
+
+  v3Logger({
+    level: 1,
+    category: "demo",
+    message: "⏳ Waiting 2 seconds before cached run...",
+  });
+  await new Promise((resolve) => setTimeout(resolve, 2000));
+
+  v3Logger({
+    level: 1,
+    category: "demo",
+    message: "Starting second run with cache...",
+  });
+  const metrics2 = await runDemo(2);
+
+  const duration1 = `${metrics1.duration.toFixed(2)}s`;
+  const duration2 = `${metrics2.duration.toFixed(2)}s`;
+
+  v3Logger({
+    level: 1,
+    category: "demo",
+    message: `
+╔════════════════════════════════════════════════════════════╗
+║                  📊 PERFORMANCE COMPARISON                 ║
+╚════════════════════════════════════════════════════════════╝
+
+┌─────────────────────┬──────────────────┬──────────────────┐
+│     Metric          │   Run 1 (Cold)   │  Run 2 (Cached)  │
+├─────────────────────┼──────────────────┼──────────────────┤
+│ Duration            │ ${duration1.padEnd(16)} │ ${duration2.padEnd(16)} │
+└─────────────────────┴──────────────────┴──────────────────┘
+
+ Performance Comparison:
+   • Speed: ${((1 - metrics2.duration / metrics1.duration) * 100).toFixed(1)}% faster with cache
+   • Time saved: ${(metrics1.duration - metrics2.duration).toFixed(2)} seconds
+
+ Insights:
+   • First run establishes the CUA action cache
+   • Second run reuses cached actions for instant execution
+   • Zero LLM tokens used on cached run`,
+  });
 }
 
-main();
+main().catch(console.error);