JavaScript Numerical Integration

integrate.js

//Simpsons use rule fourth derivative for error calculation and minimisation
let GR = (Math.sqrt(5)+1)/2

function maximum(f,a,b,error){
  error = error == undefined ? 1e-4 : error
  let c = b - (b-a) / GR
  let d = a + (b-a) / GR
  while (Math.abs(b-a) > error){
    if (f(c) > f(d)){
      b = d
    }
    else{
      a=c
    }
    c = b - (b-a) / GR
    d = a + (b-a) / GR
  }
  return (a+b)/2
}
function NIntegrate(f,a,b){
  //error = error == undefined ? 1e-4 : error
  let error = 1e-5
  //TODO: Make this more efficient and accurate
  //If someone can write a function to take the 4th derivative of a function at point x pls tell me
  function FourthDeriv(x){
    let h = 1e-3
    return Math.abs((f(x-2*h) - 4*f(x-h) + 6*f(x) - 4*f(x+h) + f(x+2*h))/h**4)
  }
  let M = maximum(FourthDeriv,a,b)
  let N = Math.ceil(Math.pow((M*(b-a)**5)/(180*error),1/4))+1
  let q = (b-a)/N
  let sum = 0

  for (let n=0;n<=N-1;n++){
    sum += f(a+n*q)+2*f(a+(n+0.5)*q)
  }
  return q/3*(0.5*(f(b)-f(a))+sum)
}

//Example
function integrand(x){
  return Math.sin(10*x)*Math.exp(-(x**2)) 
}
console.log(NIntegrate(integrand,0,2)) //0.10134