General Case

Given an expression f(x₁ , ... , x_n) , create a variable E to hold its value.

• Initialize: Create code E = f(x_{1_0} , ... , x_{n_0}) to establish E for the initial values of its arguments.

• Derivative: Replace each statement dx_i that modifies some variable x_i of E by the statements: ^-E dx_i dx_i ⁺E dx_i

• Redundant Code Elimination: replace each occurrence of f(x₁ , ... , x_n) by E .

• Dead Code Elimination: remove any code that is now unused.