Generates timestamps that increase following an exponential function

increasing_timestamps.sql

-- Generates timestamps that follow a function: y = r^x 
with
increasing_timestamps as (
    select
        '2020-01-01'::timestamp as time_start,
        sysdate as time_end,
        date_diff('minute', time_start, time_end) as time_span_minutes,

        random() as x,  -- generate a random value from 0 to 1 for x
        2^x - 1 as y,   -- get our y, in this case also between 0 and 1 for simplicity

        -- Note that when we're creating the timestamp for each row we're starting at time_end
        -- and working backwords -- effectively flipping y on the x axis
        -- We do this because we want the distribution of timestamps to look like our exponential function:
        -- fewer sessions in the beginning and more towards the end
        -- Think of y as the distance the timestamp is from the start time. Because our function is exponential,
        -- bigger y values are futher and further apart from each other. This means the distance between timestamps
        -- increases with bigger y. Flipping it gets us what we want: fewer timestamps at the start and more at the end
  
        date_add('minute',  -(time_span_minutes * y)::integer, time_end) as ts
    from dw_demo.numbers n 
    where n.number < time_span_minutes / 2  -- one timestamp every two minutes
)

select
    date_trunc('day', ts)::date AS day,
    count(1) as total_timestamps
from increasing_timestamps
group by day
order by day asc