there is not a day that goes by that I don’t regret saying yes
先拆分句子，把主句找出来：there is not a day，意为“没有一天”
从句1：that goes by，定语从句，修饰主句中的 a day，意为“时间流逝”
从句2：that I don’t regret，定语从句，同样修饰主句中的 a day，意为“我不后悔”
从句3：saying yes，严格来说本句不是从句，只是前面 regret 的宾语，只不过用了动名词的形式，此处单独拆开来作分析，此句意为“（后悔）说‘是’”，也可译为“答应了ta”。
补充：regret doing 表示后悔或遗憾做过某事（为已经做过的的事情感到遗憾），其后通常接动名词，且动名词可用一般式或完成式。
【总结】主句是 there is not a day，意为“没有一天”，从句1 that goes by 不能单独翻译，要结合主句一起理解，可译为“（随着时间流逝）我没有一天”，从句2 that I don’t regret 同样不能单独翻译，要结合主句一起理解，可进一步译为“（随着时间流逝）我没有一天不后悔”，从句3 behaving said yes 其实是前面 regret 的宾语，意为“（后悔）说‘是’”，结合前面的翻译即可译出全句的意思：
There is not a day that goes by that I don’t regret saying yes。
comments from native speakers:
There’s not a single day goes by that I don’t think of it.
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Yes, it’s correct. In fact, it is from classical English (Shakespeare). Here you see the subject relative pronoun missing. (There isn’t a single day (that) goes by…) This was perfectly OK in old English, and was often used by Shakespeare. Nowadays, common phrases using this structure are rare.
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Essentially it means everyday. If you say “not a day goes by that I don’t think of you” it means that I think of you every day, there isn’t one day I haven’t thought of you.
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Hardly a day goes by but I write to my family.
but在本句为关系词，等于that+not, 引导定语从句修饰主语a day.
Hardly a day goes by that I don’t write to my family.
几乎没有一天我不给家里写信。
我几乎每天都给家里写信。
通常but引导的定语从句，主句为否定句。but 为准关系代词。但本句中but为准关系副词。
这个句子还可以改写为：
Hardly a day goes by without me writing to my family.
本题答案只能选 but。
- 本题如果要选 when，则从句需用否定式，比较下面的同义句：
Hardly a day goes by but I write to my family.
=Hardly a day goes by when I don’t write to my family.
=Hardly a day goes by that I don’t write to my family.
=Hardly a day goes by without me / my writing to my family.
我几乎没有一天不给家里写信。
Hardly a day goes by but I write to my family.
**参考译文：**几乎没有一天我没有给我家人写信。
A. when B. since C. but D. before
D为正确答案but=that/which not
权威，英语常见用法大词典
but可被看作关系代词，引导定语从句，在句中作主语，在意义上相当于 who not或that not，即用在否定词或具有否定意义的词后，构成双重否定。*
There is no mother but loves her children．
=There is no mother who doesn’t love her children
没有不爱自己孩子的母亲。
There was no one present but knew the story already．
=There was no one present who didn’t know the story already
在场的人都知道这个故事。
Not a man but had tears in his eyes. 没有一个人眼睛里不含着眼泪。
There was no one but knows that. 没有人不知道这件事。
There is not one of us but wishes to help you. 我们之中没有一个人不愿意帮助你。
There is very few but admire his talents. 很少有人不敬佩他的才华。
There is no rule but has exception. 没有无例外的规则(凡规则都有例外)
but that 的省略形式，在句子中作连词
No task is so difficult but we can accomplish it. 没有什么困难的任务是我们不可能完成的。
No man is too old but he may learn.
Nothing is so hard but it becomes easy by practice. 任何难事通过练习都可以为易事。
Never a month passes but she writes to her old parents.
but 是一个连词，是 but that 的省略形式。 而 but that 在语义上相当于 except that. but (that) 与 except that 一样，引出的是例外分句。
可译为：她没有一个月不给她年老的双亲写信。(他每一个月都给年老的父母写信。)