Watch an optimiser walk downhill on a function you choose, one iteration at a time.

## Steps

1. **Function** (Configure tab): pick a univariate f(x) or bivariate f(x, y) function from the list, or type your own in the box, e.g. `x^4 - 2x^2 + 0.3x` or `sin(x) cos(y)`. A function that uses `y` has two variables. You can use `sin`, `cos`, `tan`, `asin`, `acos`, `atan`, `exp`, `log` (or `ln`), `sqrt`, `abs`, `pi` and `e`; `2x` means `2*x`.
2. **Optimiser:** pick an algorithm and change its settings in the boxes below it, e.g. η, the learning rate. Hover over a box for its name, or press ⓘ for every setting with a description. The reset arrow beside it puts the settings back to their defaults.
3. **Initial point:** type it, click on the plot, or press the dice for a random one. The reset arrow beside it goes back to the function's usual initial point.
4. **Step** (bottom of the panel, in every tab): press Play, or step forward and back. Type a number in the **×** box to move several iterations per step; each one is shown in turn.

The **Metrics** tab shows the current point with f, the gradient and the Hessian (or f′ and f″ with one variable), and a chart of f at each iteration. A run stops after 1000 iterations, or earlier if it diverges.

## Two variables

The plot is a contour map of f, coloured from low (purple) to high (yellow). Tick **Gradient field** to draw ∇f as arrows (contour only); they point uphill, so the optimiser moves against them. **Surface** shows f in 3D; drag to turn it.

## Compare

In the **Compare** tab, press **+ Add optimiser** for another run on the same function. Click a run to open it and change its algorithm, settings and initial point; every run steps together, from the start again after a change. Click a run's colour to pick another, or × to remove it. Run 1 is the main run from Configure: editing it here changes it there too.

## Plot

Drag to pan and scroll to zoom. The function is redrawn for the new view.