Trace-Based Compiler in JavaScript

This challenge asks you to implement a simplified trace-based compiler. Trace-based compilation is a technique where a program's execution is traced, and the trace is then used to generate optimized code. This is particularly useful for dynamic languages or situations where ahead-of-time compilation is impractical.

Problem Description

You are tasked with building a trace-based compiler that takes a simple expression language as input and generates optimized JavaScript code. The input will be a list of execution traces, where each trace represents a single execution path through the expression. Each trace consists of a series of operations, and your compiler should analyze these traces to identify common subexpressions and generate code that reuses them, minimizing redundant calculations.

What needs to be achieved:

1. Trace Parsing: Parse the input traces, which are represented as arrays of operation objects. Each operation object has a type (e.g., "literal", "add", "variable") and a value (if applicable).
2. Common Subexpression Identification: Identify common subexpressions across the traces. A subexpression is considered common if it appears in multiple traces with the same operands.
3. Code Generation: Generate optimized JavaScript code that reuses the identified common subexpressions. Introduce temporary variables to store the results of these subexpressions.
4. Output: The output should be a string containing the generated JavaScript code.

Key Requirements:

• The compiler should handle basic arithmetic operations: addition (+), subtraction (-), multiplication (*), and division (/).
• The expression language should support literal values (numbers) and variables (represented by strings).
• The compiler should prioritize re-using common subexpressions to improve performance.
• The generated code should be readable and maintainable.

Expected Behavior:

The compiler should take a list of traces as input and produce a JavaScript code string that efficiently evaluates the expressions represented by those traces. The generated code should produce the same results as executing the original traces.

Edge Cases to Consider:

• Empty traces: Should return an empty string or a reasonable default.
• Traces with different variable names: The compiler should handle this gracefully, potentially introducing new variables.
• Division by zero: The compiler should not generate code that results in division by zero. (This is a simplification; full error handling is not required).
• Complex expressions: The compiler should be able to handle expressions with multiple operations.

Examples

Example 1:

Input: [
  [{ type: 'literal', value: 2 }, { type: 'add', value: 3 }],
  [{ type: 'literal', value: 2 }, { type: 'add', value: 3 }]
]
Output:
```javascript
let tempVar = 2 + 3;
tempVar

Explanation: The expression 2 + 3 appears in both traces. The compiler introduces a temporary variable tempVar to store the result of this subexpression and then returns the variable.

Example 2:

Input: [
  [{ type: 'literal', value: 2 }, { type: 'add', value: 3 }, { type: 'literal', value: 4 }],
  [{ type: 'literal', value: 2 }, { type: 'add', value: 3 }, { type: 'literal', value: 5 }]
]
Output:
```javascript
let tempVar = 2 + 3;
tempVar + 4

Explanation: The expression 2 + 3 is common to both traces. It's stored in tempVar, and then the result is added to 4 in both cases.

Example 3: (Edge Case - Empty Trace)

Input: []
Output:
```javascript
undefined

Explanation: An empty trace should result in a reasonable default, such as undefined.

Constraints

• Input Size: The number of traces will be between 1 and 100.
• Trace Length: Each trace will contain between 1 and 20 operations.
• Operation Types: The type field of an operation object will be one of: "literal", "add", "subtract", "multiply", "divide", "variable".
• Literal Values: Literal values will be numbers.
• Variable Names: Variable names will be strings consisting of alphanumeric characters.
• Performance: The code generation should be reasonably efficient. While absolute performance is not the primary focus, avoid excessively complex or inefficient algorithms.
• Output Length: The generated JavaScript code should not exceed 500 characters.

Notes

• This is a simplified trace-based compiler. A real-world compiler would be significantly more complex.
• Focus on identifying and reusing common subexpressions.
• Consider using a data structure like a hash map to efficiently store and retrieve common subexpressions.
• The generated code does not need to be perfectly formatted (e.g., whitespace is not critical). Correctness and functionality are the primary concerns.
• You can assume that the input traces are valid and well-formed.
• Error handling (e.g., for invalid operation types or division by zero) is not required for this challenge. Focus on the core compilation logic.