this is the grammar:

expr -> <number> | <sum> | <product> | <quotient>

<sum> -> <term> + <term> | <term> - <term> | <sum> + <term> | <sum> - <term>

<term> -> <number> | <product> | <quotient>

<product> -> <factor> x <factor> | <product> x <factor> | (<quotient>) x <factor>

<quotient> -> <factor> / <factor> | <product> / <factor> | (<quotient>) / <factor>

<factor> -> <number> | (<sum>)

<number> -> <digit>

so we see how brackets are carefully placed

(b) extends number with:

<number> -> <digit> | <number><digit>

(c) extends number with (Knuth errata):

<number> -> <digit string> | .<digit string> | <digit string>.<digit string>

<digit string> -> <digit> | <digit string><digit>

errata note (TAOCP 4A, answer 122(c), 24.01.08):

cases = 9,875,514,240

solutions = 137,375

reduced cases considered = 586,220,150 (was 739,361,319)