logic.py

    if op == '+':
        if v == 0:
            return u
        if u == 0:
            return v
        if u == v:
            return 2 * u
        if u == -v or v == -u:
            return 0
    elif op == '-' and len(args) == 1:
        if u.op == '-' and len(u.args) == 1:
            return u.args[0]  # --y ==> y
    elif op == '-':
        if v == 0:
            return u
        if u == 0:
            return -v
        if u == v:
            return 0
        if u == -v or v == -u:
            return 0
    elif op == '*':
        if u == 0 or v == 0:
            return 0
        if u == 1:
            return v
        if v == 1:
            return u
        if u == v:
            return u ** 2
    elif op == '/':
        if u == 0:
            return 0
        if v == 0:
            return Expr('Undefined')
        if u == v:
            return 1
        if u == -v or v == -u:
            return 0
    elif op == '**':
        if u == 0:
            return 0
        if v == 0:
            return 1
        if u == 1:
            return 1
        if v == 1:
            return u
    elif op == 'log':
        if u == 1:
            return 0
    else:
        raise ValueError("Unknown op: " + op)
    # If we fall through to here, we can not simplify further
    return Expr(op, *args)


def d(y, x):
    """Differentiate and then simplify."""
    return simp(diff(y, x))