# Evaluating Composite Functions import { Tabs, Tab } from 'nextra/components' ## Background This prompt tests an LLM's mathematical capabilities by prompting it to evaluate a given composition function. ## Prompt Suppose $$g(x) = f^{-1}(x), g(0) = 5, g(4) = 7, g(3) = 2, g(7) = 9, g(9) = 6$$ what is $$f(f(f(6)))$$? ## Code / API ```python from openai import OpenAI client = OpenAI() response = client.chat.completions.create( model="gpt-4", messages=[ { "role": "user", "content": "Suppose g(x) = f^{-1}(x), g(0) = 5, g(4) = 7, g(3) = 2, g(7) = 9, g(9) = 6 what is f(f(f(6)))?\n" } ], temperature=1, max_tokens=256, top_p=1, frequency_penalty=0, presence_penalty=0 ) ``` ```python import fireworks.client fireworks.client.api_key = "" completion = fireworks.client.ChatCompletion.create( model="accounts/fireworks/models/mixtral-8x7b-instruct", messages=[ { "role": "user", "content": "Suppose g(x) = f^{-1}(x), g(0) = 5, g(4) = 7, g(3) = 2, g(7) = 9, g(9) = 6 what is f(f(f(6)))?", } ], stop=["<|im_start|>","<|im_end|>","<|endoftext|>"], stream=True, n=1, top_p=1, top_k=40, presence_penalty=0, frequency_penalty=0, prompt_truncate_len=1024, context_length_exceeded_behavior="truncate", temperature=0.9, max_tokens=4000 ) ``` ## Reference - [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://arxiv.org/abs/2303.12712) (13 April 2023)