Add cache to async LM call

[chenmoneygithub]

Support DSPy cache on the async LM call, and also simplify the code to avoid the redundant methods like cached_litellm_completion.

Sample testing script:

import asyncio
import time

import dspy

dspy.configure(lm=dspy.LM("openai/gpt-4o-mini", cache=True))

cot = dspy.ChainOfThought("question -> answer")


async def test_cot():
    start_time = time.time()
    result = await cot.acall(question="What is main character of Demon Slayer?")
    print(result)
    end_time = time.time()
    print(f"Time taken for the first async call: {end_time - start_time} seconds")

    start_time = time.time()
    result = await cot.acall(question="What is main character of Demon Slayer?")
    print(result)
    end_time = time.time()
    print(f"Time taken for the second async call: {end_time - start_time} seconds")


asyncio.run(test_cot())

start_time = time.time()
result = cot(question="What is main character of Tom and Jerry?")
print(result)
end_time = time.time()
print(f"Time taken for the first sync call: {end_time - start_time} seconds")

start_time = time.time()
result = cot(question="What is main character of Tom and Jerry?")
print(result)
end_time = time.time()
print(f"Time taken for the second sync call: {end_time - start_time} seconds")

output:

Prediction(
    reasoning='The main character of "Demon Slayer: Kimetsu no Yaiba" is Tanjiro Kamado. He is a young boy who becomes a demon slayer after his family is slaughtered by demons, and his younger sister Nezuko is turned into a demon. Tanjiro is characterized by his strong sense of justice, compassion, and determination to save his sister and avenge his family.',
    answer='The main character of Demon Slayer is Tanjiro Kamado.'
)
Time taken for the first async call: 2.550046920776367 seconds
Prediction(
    reasoning='The main character of "Demon Slayer: Kimetsu no Yaiba" is Tanjiro Kamado. He is a young boy who becomes a demon slayer after his family is slaughtered by demons, and his younger sister Nezuko is turned into a demon. Tanjiro is characterized by his strong sense of justice, compassion, and determination to save his sister and avenge his family.',
    answer='The main character of Demon Slayer is Tanjiro Kamado.'
)
Time taken for the second async call: 0.0007500648498535156 seconds
Prediction(
    reasoning='The main characters of "Tom and Jerry" are Tom, a cat, and Jerry, a mouse. The series revolves around the comedic rivalry between the two, with Tom often trying to catch Jerry, who always manages to outsmart him. Their interactions are central to the show\'s humor and appeal.',
    answer='The main characters of "Tom and Jerry" are Tom the cat and Jerry the mouse.'
)
Time taken for the first sync call: 2.3556289672851562 seconds
Prediction(
    reasoning='The main characters of "Tom and Jerry" are Tom, a cat, and Jerry, a mouse. The series revolves around the comedic rivalry between the two, with Tom often trying to catch Jerry, who always manages to outsmart him. Their interactions are central to the show\'s humor and appeal.',
    answer='The main characters of "Tom and Jerry" are Tom the cat and Jerry the mouse.'
)
Time taken for the second sync call: 0.0008280277252197266 seconds