预匹配以捕获简单的数学问题

我有一个preg_match()来尝试捕捉数学问题，但它只能部分工作。虽然它捕获了"加号"和最后一个"加号"，但由于某种原因，它没有捕获第一个"号"。我做错了什么？

$string = "one plus one";
if (preg_match("~([0-9]|one|two|three|four|five|six|seven|eight|nine|ten|eleven|twelve|thirteen|fourteen|fifteen|sixteen|seventeen|eighteen|nineteen|twenty|thirty|forty|fifty|sixty|seventy|eighty|ninety|hundred|thousand|million|'-| )+('+|'-|'*|'/|plus|add|minus|subtract|time|multiply|divide)([0-9]|one|two|three|four|five|six|seven|eight|nine|ten|eleven|twelve|thirteen|fourteen|fifteen|sixteen|seventeen|eighteen|nineteen|twenty|thirty|forty|fifty|sixty|seventy|eighty|ninety|hundred|thousand|million|'-| )+~", $string, $match)) {    
    print_r($match);
}

结果：

Array ( [0] => one plus one [1] => [2] => plus [3] => one )

预期结果：

Array ( [0] => one plus one [1] => one [2] => plus [3] => one )