diff --git a/code_to_optimize_js/fibonacci.js b/code_to_optimize_js/fibonacci.js
index b0ab2b51c..7955faa2e 100644
--- a/code_to_optimize_js/fibonacci.js
+++ b/code_to_optimize_js/fibonacci.js
@@ -12,7 +12,57 @@ function fibonacci(n) {
     if (n <= 1) {
         return n;
     }
-    return fibonacci(n - 1) + fibonacci(n - 2);
+
+    // Fast doubling for integer n >= 2 gives O(log n) time.
+    // Iterative implementation to avoid array allocations and recursion overhead
+    if (Number.isInteger(n)) {
+        // Find the most significant bit position
+        let k = n;
+        let bitPos = 0;
+        while ((1 << (bitPos + 1)) <= k) {
+            bitPos++;
+        }
+
+        // Start with F(1) = 1, F(2) = 1
+        let a = 1;
+        let b = 1;
+
+        // Process bits from MSB to LSB (skipping the MSB itself)
+        for (let i = bitPos - 1; i >= 0; i--) {
+            // Double: F(2k) = F(k)[2*F(k+1) - F(k)], F(2k+1) = F(k)^2 + F(k+1)^2
+            const c = a * (2 * b - a);
+            const d = a * a + b * b;
+            
+            if ((k & (1 << i)) !== 0) {
+                // Bit is 1: we need F(2k+1) and F(2k+2)
+                a = d;
+                b = c + d;
+            } else {
+                // Bit is 0: we need F(2k) and F(2k+1)
+                a = c;
+                b = d;
+            }
+        }
+
+        return a;
+    }
+
+    // For non-integer n > 1, memoize the recursive definition to avoid exponential blowup.
+    const cache = new Map();
+    function memo(x) {
+        if (x <= 1) {
+            return x;
+        }
+        const cached = cache.get(x);
+        if (cached !== undefined) {
+            return cached;
+        }
+        const res = memo(x - 1) + memo(x - 2);
+        cache.set(x, res);
+        return res;
+    }
+
+    return memo(n);
 }
 
 /**