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amhayesterday at 9:40 PM2 repliesview on HN

There's a simple differential equation often taught in intro calc courses, "Newton's Law of Cooling/Heating," which basically says that the rate of heat loss is proportional to the difference in temperature between a substance and its environment. I'm curious what that'd look like here. It's a very simple model, of course, not taking into account all the variables that Dynomight points out, but if a simple model can be nearly as predictive as more complex models...

I'm also curious to see the details of the models that Dynomight's LLMs produced!


Replies

3eb7988a1663yesterday at 9:45 PM

The appendix lists the equations transcribed from the raw answers.

  LLM  T(t)  Cost
  Kimi K2.5 (reasoning)  20 + 52.9 exp(-t/3600)+ 27.1 exp(-t/80)  $0.01
  Gemini 3.1 Pro  20 + 53 exp(-t/2500) + 27 exp(-t/149.25)  $0.09
  GPT 5.4  20 + 54.6 exp(-t/2920) + 25.4 exp(-t/68.1)  $0.11
  Claude 4.6 Opus (reasoning)  20 + 55 exp(-t/1700) + 25 exp(-t/43)  $0.61 (eeek)
  Qwen3-235B  20 + 53.17 exp(-t/1414.43)  $0.009
  GLM-4.7 (reasoning)  20 + 53.2 exp(-t/2500)  $0.03
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ameliusyesterday at 10:06 PM

That model doesn't explain the relatively sharp drop in the beginning.

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