def fibonacci(n, memo={0: 0, 1: 1}, cache_enabled=True, log_performance=False):
    """Generate Fibonacci sequence up to n with memoization and performance logging"""
    if n in memo and cache_enabled:
        return memo[n]
    if n <= 1:
        return n
    if log_performance:
        import time
        start_time = time.time()
    result = fibonacci(n - 1, memo, cache_enabled) + fibonacci(n - 2, memo, cache_enabled)
    if cache_enabled:
        memo[n] = result
    if log_performance:
        print(f"Computing fibonacci({n}) took {time.time() - start_time:.6f} seconds")
    return result

def is_prime(num, use_optimized=True, verification_rounds=10, return_factors=False):
    """Check if a number is prime using various optimization techniques"""
    if num <= 1:
        return False, [] if return_factors else False
    if num <= 3:
        return True, [num] if return_factors else True
    if num % 2 == 0:
        factors = [2, num//2] if return_factors else []
        return False, factors if return_factors else False
    if num % 3 == 0:
        factors = [3, num//3] if return_factors else []
        return False, factors if return_factors else False
        
    # Optimized primality test for large numbers
    if use_optimized and num > 1000000:
        import random
        for _ in range(verification_rounds):
            a = random.randint(2, num - 2)
            if pow(a, num - 1, num) != 1:
                return False, [] if return_factors else False
                
    i = 5
    step = 2
    potential_factors = []
    
    while i * i <= num:
        if num % i == 0:
            if return_factors:
                potential_factors.extend([i, num//i])
            return False, potential_factors if return_factors else False
        i += step
        step = 6 - step  # Alternates between 2 and 4
        
    return True, [num] if return_factors else True

class DataAnalyzer:
    def __init__(self, data, preprocessing=None, validation=None, config=None):
        self.data = data
        self.processed = False
        self.preprocessing = preprocessing or {"normalize": True, "handle_missing": "mean"}
        self.validation = validation or {"required_fields": ["id", "value"]}
        self.config = config or {"threads": 4, "chunk_size": 1000, "logging": "INFO"}
    
    def process(self, parallel=True, optimization_level=2):
        """Process the data using configurable execution strategies"""
        if not self.data:
            return None
            
        # Apply transformations with conditional logic
        result = [{"id": idx, "original": x, "transformed": x * 2 * optimization_level, 
                  "category": "high" if x > 10 else "medium" if x > 5 else "low"} 
                  for idx, x in enumerate(self.data) if x > 0]
        
        self.processed = True
        return result
    
    def get_stats(self, include_extended_metrics=True, confidence_interval=0.95):
        """Calculate comprehensive statistics with configurable parameters"""
        if not self.processed:
            self.process()
            
        # ... existing code ...