⚡️ Speed up function funcA by 4,082%

Here is an optimized version of your `funcA` function, preserving the result and behavior, but with significantly improved runtime for all major hot spots indicated in your profile.  
The slowest parts are the explicit `for` loop and `" ".join(str(i) ...)` construction. The for-loop is simply summing; we can use the arithmetic formula for summing `0..N-1`. For joining, generate all the needed numbers as strings, then join (avoiding repeated generator and multiple function calls).



**Key optimizations**.
- Used arithmetic sum for `k` instead of a for loop, reducing O(N) to O(1).
- Used the same formula for `j`.
- Used `map(str, range(number))` directly in join, which is faster than a generator with `str(i)`.

**Timing Impact**: Nearly all runtime was spent in the explicit `for` loop and string join; both are now as fast as possible in pure Python.  
Return value and side effects are untouched.  
All original comments were either obsolete due to the optimization or are not included as per instructions, unless affected by the code rewrite.

Author: codeflash-ai[bot]

code_to_optimize/code_directories/simple_tracer_e2e/workload.py

@@ -2,15 +2,17 @@
 
 
 def funcA(number):
-    number = number if number < 1000 else 1000
-    k = 0
-    for i in range(number * 100):
-        k += i
-    # Simplify the for loop by using sum with a range object
-    j = sum(range(number))
+    number = min(1000, number)
 
-    # Use a generator expression directly in join for more efficiency
-    return " ".join(str(i) for i in range(number))
+    # Compute sum directly instead of looping
+    n_sum = number * 100
+    k = (n_sum * (n_sum - 1)) // 2
+
+    # Sum using formula for 0..number-1
+    j = (number * (number - 1)) // 2
+
+    # Use map + join for faster conversion
+    return " ".join(map(str, range(number)))
 
 
 def test_threadpool() -> None:
@@ -21,14 +23,15 @@ def test_threadpool() -> None:
     for r in result:
         print(r)
 
+
 class AlexNet:
     def __init__(self, num_classes=1000):
         self.num_classes = num_classes
         self.features_size = 256 * 6 * 6
 
     def forward(self, x):
         features = self._extract_features(x)
-        
+
         output = self._classify(features)
         return output
 
@@ -43,15 +46,17 @@ def _classify(self, features):
         total = sum(features)
         return [total % self.num_classes for _ in features]
 
+
 class SimpleModel:
     @staticmethod
     def predict(data):
         return [x * 2 for x in data]
-    
+
     @classmethod
     def create_default(cls):
         return cls()
 
+
 def test_models():
     model = AlexNet(num_classes=10)
     input_data = [1, 2, 3, 4, 5]
@@ -60,6 +65,7 @@ def test_models():
     model2 = SimpleModel.create_default()
     prediction = model2.predict(input_data)
 
+
 if __name__ == "__main__":
     test_threadpool()
     test_models()