reloadium.com

showFormula

Show a calculation as formula -> your numbers plugged in -> result, instead of writing the derivation as prose. Trigger rule: if your final answer is about to contain a bolded label followed by a computed value and its derivation — e.g. 'Cost per Customer (CAC): You spent $68,200 to get 55 customers. That is $1,240 per customer.' or 'Profit per Month: $95 x 72% = $68.40' — stop, call this tool for that value instead, and keep the surrounding prose to what it means rather than re-deriving it in text. This applies every time that pattern occurs, including when your answer already includes other cards (a gauge, a chart, a zone grid) — those show the verdict, this shows the math behind one specific number, and they're not substitutes for each other. Use it whenever you compute a value the user might want to check or learn from — especially when the user's own phrasing suggests they're not fluent in the underlying jargon/domain — since seeing the real numbers substituted into the formula is what makes an opaque result like 'LTV is $2,850' actually verifiable and teachable. Skip this for values you didn't derive from a formula (a number the user told you directly) or for fluent/expert users who don't need the derivation shown. Provide `label` (what's being computed, e.g. 'Customer Lifetime Value' or 'Compound Interest'), `formula` (the general formula in symbolic form, e.g. 'ARPU x margin / churn' or 'P(1 + r/n)^(nt)'), `substituted` (that same formula with the user's actual numbers plugged in, e.g. '$95 x 72% / 2.4%'), and `result` (the computed value, e.g. '$2,850'). Optionally add `note` — one short plain-language line on what the result means or why it matters, e.g. 'How much revenue you can expect from one customer over their whole subscription.'

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Input schema

{
  "type": "object",
  "properties": {
    "label": {
      "type": "string"
    },
    "formula": {
      "type": "string",
      "description": "Symbolic form, e.g. 'ARPU x margin / churn'."
    },
    "substituted": {
      "type": "string",
      "description": "Same formula with real numbers plugged in, e.g. '$95 x 72% / 2.4%'."
    },
    "result": {
      "type": "string",
      "description": "The computed value, e.g. '$2,850'."
    },
    "note": {
      "type": "string",
      "description": "Optional one-line plain-language explanation of what this value means."
    }
  },
  "required": [
    "label",
    "formula",
    "substituted",
    "result"
  ]
}