```python
import re


def dose_totals(log: list) -> dict:
    """Exact per-reagent totals of a pour log, counted in thousandths."""
    thousandths = {}
    places = {}
    for reagent, amount in log:
        written = re.fullmatch(r"[+-]?\d+(?:\.(\d{1,3}))?", amount)
        if written is None:
            raise ValueError("amount is not a decimal of at most three places: " + amount)
        digits = written.group(1) or ""
        sign = -1 if amount.startswith("-") else 1
        bare = amount.replace("+", "").replace("-", "").replace(".", "")
        thousandths[reagent] = thousandths.get(reagent, 0) + sign * int(bare) * 10 ** (3 - len(digits))
        places[reagent] = max(places.get(reagent, 0), len(digits))
    totals = {}
    for reagent, total in thousandths.items():
        if total % 10 == 0:
            total //= 10
            digits = 0
        else:
            digits = places[reagent]
        totals[reagent] = f"{total:+'.{digits}f'}"
    return totals
```