Custom function in Desmos, including custom autoOperatorNames. Warning: currently incompatible with other scripts that manipulate the worker, such as desmos god mode.

custom-function.user.js

// ==UserScript==
// @name        Custom Desmos Function
// @namespace   github.com/jared-hughes
// @match       *://www.desmos.com/calculator*
// @description Custom function in Desmos, including custom autoOperatorNames. Warning: currently incompatible with other scripts that manipulate the worker, such as desmos god mode.
// @grant       none
// @version     0.1.1
// @run-at      document-start
// @author      fireflame241 (Jared Hughes)
// ==/UserScript==

/* To change the function, ctrl+F for "squiggle" and edit */


// the function definition itself
function squiggle(x) {
  return 8*Math.sin(x) + 3*Math.sin(4*x)
}

window.Worker = new Proxy(Worker, {
  construct(target, args) {
    if (args[0].startsWith("blob:")) {
      const xhr = new XMLHttpRequest
      xhr.open("GET", args[0], false)
      xhr.send()
      const hooked = xhr.responseText
        // Define BuiltIn.squiggle to be the above function
        .replace(/Object.defineProperty\((?<exports>.),"sinh"/g, `
Object.defineProperty($<exports>, "squiggle", {
  enumerable: true,
  get: function() {
    return ${squiggle.toString()}
  }
}), $&`)
        // Mark squiggle as a builtin that calls BuiltIn.squiggle(x)
        .replace(/sinh:(?<func>.)\("BuiltIn","sinh"/, `squiggle:$<func>("BuiltIn","squiggle"), $&`)
      args[0] = URL.createObjectURL(new Blob([hooked]))
    }
    return new target(...args)
  }
})

function applyNames() {
  /* see https://github.com/jared-hughes/DesThree/blob/master/src/View.js#L66 for more info, including forcing a rerender */
  const fields = document.querySelectorAll('.dcg-mq-editable-field')
  fields.forEach(field => {
    const opt = field._mqMathFieldInstance.__controller.root.cursor.options;
    // allow squiggle to be written without manipulating LaTeX in the console
    opt.autoOperatorNames.squiggle = 'squiggle'
  })
}


function initialRerender() {
  window.Calc.getExpressions()
    .filter(e => e.type === 'expression')
    .forEach(e => {
      const selector = `.dcg-expressionitem[expr-id='${e.id}'] .dcg-mq-editable-field`
      const mqField = document.querySelector(selector)
      mqField._mqMathFieldInstance.__controller.renderLatexMath(e.latex)
    })
}

function init() {
  window.Calc.controller.dispatcher.register(e => {
    if (
      ['tick', 'new-expression', 'new-expression-at-end'].includes(e.type) ||
      (e.type === 'on-special-key-pressed' && e.key === 'Enter')
    ) {
      // update the math field of new expression elements
      applyNames()
    }
  })
  applyNames()
  initialRerender()
}

const interval = setInterval(() => {
  if (window.Calc && window.Calc.controller) {
    clearInterval(interval)
    init()
  }
}, 50)