Common subexpression elimination in Compiler Design - Step-by-Step Execution

Concept Flow - Common subexpression elimination

Start: Code with expressions

↓

Identify repeated expressions

↓

Check if operands unchanged

Yes No↓

Replace with temp

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Use temp variable instead

↓

Optimized code output

The process finds repeated expressions, checks if their inputs stay the same, then replaces duplicates with a temporary variable to avoid recomputing.

Execution Sample

Compiler Design

a = b + c
x = b + c
y = a * 2
z = b + c + y

This code has the expression 'b + c' repeated three times, which can be optimized by computing it once and reusing.

Analysis Table

Step	Action	Expression Found	Operands Unchanged?	Replace with Temp?	Resulting Code
1	Scan first expression	b + c	N/A	No	a = b + c
2	Scan second expression	b + c	Yes	Yes	x = temp1
3	Create temp1 = b + c	b + c	N/A	No	temp1 = b + c
4	Scan third expression	a * 2	N/A	No	y = a * 2
5	Scan fourth expression	b + c	Yes	Yes	z = temp1 + y
6	Final optimized code	N/A	N/A	N/A	temp1 = b + c a = temp1 x = temp1 y = a * 2 z = temp1 + y

💡 All repeated expressions replaced with temp1 where operands unchanged, optimization complete.

State Tracker

Variable	Start	After Step 1	After Step 3	After Step 6
a	undefined	b + c	b + c	temp1
x	undefined	undefined	undefined	temp1
y	undefined	undefined	undefined	a * 2
z	undefined	undefined	undefined	temp1 + y
temp1	undefined	undefined	b + c	b + c

Key Insights - 2 Insights

Why do we need to check if operands are unchanged before replacing expressions?

Because if operands changed, the repeated expression would produce different results. The execution_table rows 2 and 5 show replacement only when operands are unchanged.

Why create a temporary variable for the common expression?

To store the computed value once and reuse it, avoiding repeated calculations. Step 3 in the execution_table shows creating temp1 for this purpose.

Visual Quiz - 3 Questions

According to the execution_table, at which step is the temporary variable created?

A Step 2

B Step 3

C Step 5

D Step 6

💡 Hint

Look at the 'Action' and 'Resulting Code' columns in the execution_table for step 3.

In the variable_tracker, what is the value of 'x' after step 6?

A temp1

B undefined

C b + c

D a * 2

💡 Hint

Check the 'After Step 6' column for variable 'x' in variable_tracker.

If operands changed between expressions, what would happen according to the concept_flow?

A Replace with temp variable anyway

B Create multiple temp variables

C Do not replace repeated expression

D Stop optimization

💡 Hint

Refer to the decision branch 'Operands Unchanged?' in concept_flow ASCII diagram.

Concept Snapshot

Common subexpression elimination:
- Find repeated expressions in code
- Check if operands are unchanged
- If yes, compute once and store in temp variable
- Replace repeated expressions with temp variable
- Saves computation time by avoiding repeats

Full Transcript

Common subexpression elimination is a compiler optimization that finds expressions repeated multiple times in code. It checks if the inputs to these expressions remain the same. If they do, the compiler computes the expression once, stores the result in a temporary variable, and replaces all repeated occurrences with this variable. This reduces redundant calculations and improves efficiency. The process involves scanning code, identifying repeated expressions, verifying operand stability, creating temporary variables, and rewriting code accordingly.