alt Hacker NewsThe 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
It looks like a lot of them are missing something big. I'd think the two big ones are the evaporative cooling as you pour into the cup, and heating up the cup (by convection) itself. The convective cooling to the air is tertiary, but important (and conduction of the mug to the table probably isn't completely negligible). If there's only one exponential, they're definitely doing something wrong.
I'd like to see a sensitivity study to see how much those terms would need to be changed to match within a few %. Exponentials are really tweaky!