LLM API Cost Estimator

LLM APIs charge per million tokens, with different prices for input and output, and a discount for input tokens served from the prompt cache.

Implement estimate_cost(calls, prices):

• prices maps a model name to {"input": $, "output": $, "cached_input": $}, each per 1M tokens.
• Each call is a dict with "model", "input_tokens", "output_tokens" and optionally "cached_tokens" (default 0). Cached tokens are part of input_tokens but billed at the cached rate instead of the normal one.
• Return a dict with "total" (the cost in dollars, rounded to 6 decimal places) and "by_model" (cost per model, also rounded to 6 places).
• Raise KeyError for a model that isn't in prices.

Example: 1,000,000 input tokens, 400,000 of them cached, plus 100,000 output tokens, at $3 input /$0.30 cached / $15 output: 600k ×$3 + 400k × $0.30 + 100k ×$15 = $1.80 +$0.12 + $1.50 = **$3.42**.