{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0b82ab56-4995-480e-93bd-9780abcfe64b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\frac{a^{2} \\operatorname{asinh}{\\left(\\frac{x}{a} \\right)}}{2} + \\frac{x \\sqrt{a^{2} + x^{2}}}{2}$"
      ],
      "text/plain": [
       " 2      /x\\        _________\n",
       "a *asinh|-|       /  2    2 \n",
       "        \\a/   x*\\/  a  + x  \n",
       "----------- + --------------\n",
       "     2              2       "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using SymPy\n",
    "using QuadGK\n",
    "using BenchmarkTools\n",
    "\n",
    "@vars x real=true\n",
    "@vars a positive=true\n",
    "\n",
    "f(a, x) = √(a^2 + x^2)\n",
    "expr_sym = sympy.Integral(f(a, x), x).doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5f1a61ac-d3fe-4030-88e2-1b354c7d1f3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"a^2*asinh(x/a)/2 + x*sqrt(a^2 + x^2)/2\""
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str_sym = string(expr_sym)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "294b1c22-1222-416b-b60c-2d612bdf2dda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":(F(a, x) = begin\n",
       "          \u001b[90m#= none:1 =#\u001b[39m\n",
       "          (a ^ 2 * asinh(x / a)) / 2 + (x * sqrt(a ^ 2 + x ^ 2)) / 2\n",
       "      end)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr_julia = Meta.parse(\"F(a, x) = $expr_sym\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "eb9f3db3-1d73-466f-a8ac-01455d6a98bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "F (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@eval $expr_julia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4d900e83-5a34-436f-a380-2ab4ab5aaf69",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  6.352 ms (19995 allocations: 3.58 MiB)\n",
      "  314.800 μs (5 allocations: 78.27 KiB)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x) = f(2, x)\n",
    "F_quadgk(t) = quadgk(f, 0, t)[1]\n",
    "F(t) = F(2, t) - F(2, 0)\n",
    "t = 1:10^4\n",
    "A = @btime F_quadgk.(t)\n",
    "B = @btime F.(t);\n",
    "A ≈ B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7e533e6c-e255-4265-b7a5-b393c3788fcf",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "jupytext": {
   "formats": "ipynb,jl:hydrogen"
  },
  "kernelspec": {
   "display_name": "Julia 1.9.2",
   "language": "julia",
   "name": "julia-1.9"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.9.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}