Tbh, I'm really not sure why something like this should take 15 seconds to compute. That's roughly a few trillion floating point ops for a problem that has been solvable for decades. I have trouble imagining any reasonable model for mapping price -> sales needing that much compute.
Also, fwiw, I really wouldn't expect clients slider clicks to follow a normal distribution. A normal distribution occurs when you have the sum of a large number of random variables with Finite (and bounded) expectation and variance; or alternatively, when you're modelling a process with known Expectation and Variance, but not any higher order moments. If anything, I'd expect human beings to play with the slider more around extremal points, like the start and end.
Also, fwiw, I really wouldn't expect clients slider clicks to follow a normal distribution. A normal distribution occurs when you have the sum of a large number of random variables with Finite (and bounded) expectation and variance; or alternatively, when you're modelling a process with known Expectation and Variance, but not any higher order moments. If anything, I'd expect human beings to play with the slider more around extremal points, like the start and end.