Clarification on input tokens

[Specy]

I'm using the vercel AI sdk and wanted to calculate the pricing of each turn but i get error:

Error: Uncached text input tokens cannot be negative

My code:

export function calculateAiUsage(model: LLMModels, usage: LanguageModelUsage) {
    console.log(usage)
    console.log({
        input_tokens: usage.inputTokenDetails.noCacheTokens,
        cache_read_tokens: usage.inputTokenDetails.cacheReadTokens,
        cache_write_tokens: usage.inputTokenDetails.cacheWriteTokens,
        output_tokens: usage.outputTokens,
    });
    try{
        const price = calcPrice(
            {
                input_tokens: usage.inputTokenDetails.noCacheTokens,
                cache_read_tokens: usage.inputTokenDetails.cacheReadTokens,
                cache_write_tokens: usage.inputTokenDetails.cacheWriteTokens,
                output_tokens: usage.outputTokens,
            },
            LLM_MODELS_TO_NAME[model],
        );

        return price
            ? {
                  total: price.total_price,
                  input: price.input_price,
                  output: price.output_price,
              }
            : null;
    }catch (e){
        console.error(e);
        return null
    }
}

This is the result:

{
  inputTokens: 4740,
  inputTokenDetails: { noCacheTokens: 5, cacheReadTokens: 0, cacheWriteTokens: 4735 },
  outputTokens: 255,
  outputTokenDetails: { textTokens: undefined, reasoningTokens: undefined },
  totalTokens: 4995,
  raw: {
    input_tokens: 5,
    cache_creation_input_tokens: 4735,
    cache_read_input_tokens: 0,
    cache_creation: { ephemeral_5m_input_tokens: 4735, ephemeral_1h_input_tokens: 0 },
    output_tokens: 255,
    service_tier: 'standard',
    inference_geo: 'not_available'
  },
  reasoningTokens: undefined,
  cachedInputTokens: 0
}
{
  input_tokens: 5,
  cache_read_tokens: 0,
  cache_write_tokens: 4735,
  output_tokens: 255
}

I'm confused as of how i'm supposed to map the input tokens to what the library expects, is it supposed to be:

        const price = calcPrice(
            {
                //ALL tokens
                input_tokens: usage.inputToken, 
                //out of which, those were cache read
                cache_read_tokens: usage.inputTokenDetails.cacheReadTokens,
                //out of which those were cache writes
                cache_write_tokens: usage.inputTokenDetails.cacheWriteTokens,
                output_tokens: usage.outputTokens,
            },
            LLM_MODELS_TO_NAME[model],
        );

is input_tokens supposed to be the total number of input tokens (regardless if they were uncached, cache read or written) or only tokens that were not cache read or writes?

EDIT:
looking at the code of the library, yes it seems like input_tokens is supposed to be the total and then cache_read_tokens and cache_write_tokens are partitions of the input_tokens. Maybe it could be made more clear on the docs?