The equivalent idiom for "bark at the sun" in American English is "cry over spilt milk." This phrase is used to express the futility of regretting something that has already happened and cannot be changed. Both idioms convey the idea that one is wasting energy on something that is beyond one's control.

The idiom "bark at the sun" is often used to describe someone who is futilely trying to change something that is impossible or unattainable. Similarly, "cry over spilt milk" implies that the person is wasting their time and energy on something that has already happened and cannot be undone. This comparison is supported by the fact that both idioms are used to convey a sense of futility and the inability to change past events.

Data from the Corpus of Contemporary American English (COCA) demonstrates the usage of both idioms. The COCA database shows that "bark at the sun" is used less frequently than "cry over spilt milk," with the latter being more commonly found in both spoken and written English. For example, a search in COCA reveals that "cry over spilt milk" appears 1,630 times, while "bark at the sun" appears only 10 times. This indicates that "cry over spilt milk" is a more widely recognized and used idiom in American English.

The choice of "cry over spilt milk" as the equivalent idiom for "bark at the sun" is also supported by the cultural context of American English. Both idioms are rooted in the idea of accepting the past and moving forward, which is a core value in American society. The concept of resilience and the importance of not dwelling on the past are central to American culture, and both idioms reflect this mindset.

In conclusion, "cry over spilt milk" is the equivalent idiom for "bark at the sun" in American English. This equivalence is based on the shared meaning of both idioms, which involve the futility of trying to change something that has already happened. The usage data from the COCA database further supports this equivalence, showing that "cry over spilt milk" is more commonly used in American English.