Arbitrary hyperbolic functions

[yerlotic]

Currently its not possible to properly plot a y = tan(x)

The plot will have either extra lines

or become even more hyperbolic:

Although it is possible to plot a simple hyperbola, it seems like it's impossible to accurately plot a slightly more complicated function

even though desmos can do it without issues:

Source code

#import "@preview/cetz:0.5.2": canvas, draw
#import "@preview/cetz-plot:0.1.4": plot

#let samples = 200
#canvas({
  import draw: *
  
  // Set-up a thin axis style
  set-style(
    axes: (stroke: .5pt, tick: (stroke: .5pt)),
    legend: (stroke: white, orientation: ttb, item: (spacing: .3), scale: 80%),
  )
  plot.plot(
    size: (10, 7),
    y-min: -4,
    y-max: 4,
    x-tick-step: 1,
    y-tick-step: 1,
    axis-style: "school-book",
    {
      let domain = (-4, 4)
      
      plot.add-contour(
        (x, y) => x * y,
        y-domain: domain,
        x-domain: domain,
        y-samples: samples,
        x-samples: samples,
        label: $x y = 1$,
      )
      plot.add(
        x => 1 / x,
        domain: domain,
        samples: samples,
        label: $y=1/x$,
        style: (stroke: (dash: "dashed", paint: red)),
      )
      
      plot.add-contour(
        (x, y) => y / calc.tan(x),
        y-domain: domain,
        x-domain: domain,
        y-samples: samples,
        x-samples: samples,
        label: $y/(tan x) = 1$,
      )
      plot.add(
        x => calc.tan(x),
        domain: domain,
        samples: samples,
        label: $y=tan x$,
        style: (stroke: (dash: "dashed", paint: purple)),
      )
      
      // problematic function
      plot.add(
        x => ((x + 2) * (x - 1)) / ((x + 3) * (x - 2)),
        domain: domain,
        samples: samples,
        label: $y=((x + 2)(x - 1)) / ((x - 2)(x + 3))$,
        style: (stroke: black),
      )
    },
  )
})