Find the correct code optimization technique that can be applied to the…

Explanation: all four listed optimizations can be applied if performed in the right order. Below are the stepwise transformations and why each optimization applies.

• Constant folding — evaluate expressions involving known constants.

  Original (normalized):

  x = 1

  z = 3

  y = x * 3 + a

  b = z + a

  c = y * c + b

  After constant folding (x = 1 makes x*3 = 3; z is 3):

  y = 3 + a

  b = 3 + a

  c = y * c + b

• Common subexpression elimination — detect that y and b compute the same expression.

  Since both y and b are 3 + a, compute it once and reuse the result (introduce a single definition or make one variable copy the other).

  Example transform:

  y = 3 + a

  b = y // reuse the computed value

• Copy propagation — substitute the copy where it is used.

  Replace uses of b with y in later code to eliminate the extra variable:

  c = y * c + y

• Dead code elimination — remove assignments that are no longer needed.

  After propagation the assignments to x and z are unused and can be removed. The temporary b is also eliminated.

  Final optimized code (after these passes):

  y = 3 + a

  c = y * c + y

Notes:

• The optimizations interact: constant folding exposes the common subexpression; eliminating the common subexpression creates a copy that can be propagated; propagation enables dead-code elimination.

• Further algebraic simplification (e.g., factoring c = y*c + y into c = y * (c + 1)) is possible but is a different transformation (algebraic simplification/strength reduction).