7 ms·
Here's a fun way to see this approximation: 1 + x ~= e^x when x is close to zero (either positive or negative). So let m be 10^-6 . Probability of survival of
by bo1024 6y ago
Here's a fun way to see this approximation: 1 + x ~= e^x when x is close to zero (either positive or negative).
So let m be 10^-6 .
Probability of survival of one event = 1 - m ~= e^-m .
Probability of survival of two events = (1 - m)^2 ~= (e^-m)^2 = e^-2m ~= 1 - 2m.
- klodolph 6y agoTo add to this, this is why we have those funny functions log1p() and expm1() in the standard library. To add micromorts: double add_micromorts(double x, double y) { return -1e6 * expm1( -log1p(x * 1e-6) - log1p(y * 1e-6) ); } This is not the most accurate way of doing things, it is much simpler to return x + y - x * y * 1e-6; But the formula with expm1 and log1p lets you easily do things like multiply 10 micromorts/day by 10.5 days.
- smabie 6y agoThey're mostly there for converting from log returns and back, but yeah they're good for any kind of probabilities as well.