WolframAlpha tells us that the solution of the Michaelis-Menten ODE given by

dx/dt=\frac{Vx}{K+x}

can be expressed using the Lambert W function for which we have implemented the principal branch

as

x(t)=KW(\exp(tV+x(0)/K+\log(x(0)/K))
.

**However if the argument of the exponential function is large enough we can not evaluate the solution,** with large enough meaning roughly larger than 700.

**However** W(\exp(x)) is essentially linear for “large” x as WolframAlpha tells us again.

Can we get a function that can evaluate W(\exp(x)) for large x? Implementation *should* be straightforward ™, i.e. just casting x to a higher precision type before passing it to boosts W and exp.

Might be of interest to PK models, hence the tag.