Error propagation using Lua

The expression input("x", x, Δx) denotes a value named "x" with a value of x ± Δx. You can use all standard math operators on these values and the result will contain the propagated error as well as the expression used to obtain both the value and error. I built this tool to simplify the process of physics experiments, since error propagation calculation is often very deeply nested and complicated.

Example

test.lua contains a demo on how to create some expressions and display them within an HTML file using MathJax.

Given time t, initial positions x0, y0, initial velocities vx0, vy0 and horizontal acceleration a, the following code will calculate the distance between (0, 0) and the object after t seconds:

local t = input("t", 60, 0.01)
local x = input("x0", 0, 0.1) + input("vx0", 5, 0.5)*t + input("a", 3, 0.5)*t^2/2
local y = input("y0", 10, 0.1) + input("vy0", 5, 0.5)*t + input("g", -9.8, 0.1)*t^2/2
local length = vsqrt(x^2 + y^2) -- vsqrt is sqrt for values with error

The error and value of length can be accessed using length.val and length.err. Each of these values are tables containing the result val and textual expression name.

Using MathJax, you can beautify the expressions. The end result looks something like this: