## Is your feature request related to a problem?

#4947 added a new query to the backend – time to convert. It works well, just one point is kind of rough: bin width and count.

## Describe the solution you'd like

Currently the number of bins is hardcoded. Ideally we should have two options:
- return a user-specified number of bins,
- otherwise infer a reasonable number of bins using some algorithm (auto option).

@alexkim205 [suggested](https://github.com/PostHog/posthog/issues/4855#issuecomment-872423877) the [Freedman-Diaconis rule](https://en.wikipedia.org/wiki/Freedman%E2%80%93Diaconis_rule) for determining bin width (and interval based on that), but unfortunately from my testing its formula would not be the most practical – it's great for keeping a pretty constant "smoothness" of the histogram esp. with normal distribution, but we face some additional constraints that make it less than ideal:
- we can't have histograms too dense visually in the UI, from my testing a practical limit is 60 bins (above that it gets too dense),
- our data generally doesn't follow much of a normal distribution.

Clamping may help though, or maybe a different formula may work better outright – I'll be testing this.

## Additional context

Issue pertaining to the experience of time to convert: #4855

#### *Thank you* for your feature request – we love each and every one!

posthog/models/filters/mixins/common.py
DATE_FROM,
    DATE_TO,
    DISPLAY,
    EVENTS,
    FILTER_TEST_ACCOUNTS,
    FORMULA,
    INSIGHT,
    INSIGHT_TO_DISPLAY,
    INSIGHT_TRENDS,
    INTERVAL,
    OFFSET,
    SELECTOR,
    SESSION,
    SHOWN_AS,
    TREND_FILTER_TYPE_ACTIONS,
    TREND_FILTER_TYPE_EVENTS,
)
from posthog.models.entity import Entity
from posthog.models.filters.mixins.base import BaseParamMixin
from posthog.models.filters.mixins.utils import cached_property, include_dict
from posthog.utils import relative_date_parse, str_to_bool
ALLOWED_FORMULA_CHARACTERS = r"([a-zA-Z \-\*\^0-9\+\/\(\)]+)"
class IntervalMixin(BaseParamMixin):
    @cached_property
    def interval(self) -> str:
        return self._data.get(INTERVAL, "day")
    @include_dict
    def interval_to_dict(self):
        return {"interval": self.interval} if self.interval else {}
class SelectorMixin(BaseParamMixin):