(expr, optimizations)
return expr
Preprocess an expression to optimize for common subexpression
    elimination.

    Parameters
    ----------
    expr : sympy expression
        The target expression to optimize.
    optimizations : list of (callable, callable) pairs
        The (preprocessor, postprocessor) pairs.

    Returns
    -------
    expr : sympy expression
        The transformed expression.
Preprocess an expression to optimize for common subexpression
    elimination.
Preprocess an expression to optimize for common subexpression elimination .
def preprocess_for_cse(expr, optimizations):
    """ Preprocess an expression to optimize for common subexpression
    elimination.

    Parameters
    ----------
    expr : sympy expression
        The target expression to optimize.
    optimizations : list of (callable, callable) pairs
        The (preprocessor, postprocessor) pairs.

    Returns
    -------
    expr : sympy expression
        The transformed expression.
    """
    for pre, post in optimizations:
        if pre is not None:
            expr = pre(expr)
    return expr
def preprocess_for_cse ( expr , optimizations ) : for pre , post in optimizations : if pre is not None : expr = pre ( expr ) return expr