How to parse JS code into one-operation-per-line with fewest temp variables?

Say I have this code:

// Walk GF(2^8)
var x = 0;
var xi = 0;
for (var i = 0; i < 256; i++) {
    // Compute sbox
    var sx = xi ^ (xi << 1) ^ (xi << 2) ^ (xi << 3) ^ (xi << 4);
    sx = (sx >>> 8) ^ (sx & 0xff) ^ 0x63;
    SBOX[x] = sx;
    INV_SBOX[sx] = x;

    // Compute multiplication
    var x2 = d[x];
    var x4 = d[x2];
    var x8 = d[x4];

    // Compute sub bytes, mix columns tables
    var t = (d[sx] * 0x101) ^ (sx * 0x1010100);
    SUB_MIX_0[x] = (t << 24) | (t >>> 8);
    SUB_MIX_1[x] = (t << 16) | (t >>> 16);
    SUB_MIX_2[x] = (t << 8)  | (t >>> 24);
    SUB_MIX_3[x] = t;

    // Compute inv sub bytes, inv mix columns tables
    var t = (x8 * 0x1010101) ^ (x4 * 0x10001) ^ (x2 * 0x101) ^ (x * 0x1010100);
    INV_SUB_MIX_0[sx] = (t << 24) | (t >>> 8);
    INV_SUB_MIX_1[sx] = (t << 16) | (t >>> 16);
    INV_SUB_MIX_2[sx] = (t << 8)  | (t >>> 24);
    INV_SUB_MIX_3[sx] = t;

    // Compute next counter
    if (!x) {
        x = xi = 1;
    } else {
        x = x2 ^ d[d[d[x8 ^ x2]]];
        xi ^= d[d[xi]];
    }
}

I am using meriyah to parse the AST. But just generally, since this is rather involved, how do you go about figuring out how many temp variables you need if you were to put every operation on one line?

So the first line of the loop:

var sx = xi ^ (xi << 1) ^ (xi << 2) ^ (xi << 3) ^ (xi << 4);

It would be made like:

var foo1 = xi << 1
var foo2 = xi << 2
var foo3 = xi << 3
var foo4 = xi << 4
var sx = xi ^ (foo1) ^ (foo2) ^ (foo3) ^ (foo4);

To become something like:

var foo1 = xi << 1
var foo2 = xi << 2
var foo3 = xi << 3
var foo4 = xi << 4
var foo6 = (foo3) ^ (foo4)
var foo7 = (foo2) ^ foo6
var foo8 = (foo1) ^ foo7
var sx = xi ^ foo8;

But better would be:

var foo1 = xi << 1
var foo2 = xi << 2
var foo3 = xi << 3
var foo4 = xi << 4
foo4 = (foo3) ^ (foo4)
foo4 = (foo2) ^ foo4
foo4 = (foo1) ^ foo4
var sx = xi ^ foo4;

So we minimize how many variables we create. How do you do this or even think about it programmatically?

AST for the line of code I tried is here:

{
  "type": "Program",
  "sourceType": "script",
  "body": [
    {
      "type": "VariableDeclaration",
      "kind": "var",
      "declarations": [
        {
          "type": "VariableDeclarator",
          "id": {
            "type": "Identifier",
            "name": "sx"
          },
          "init": {
            "type": "BinaryExpression",
            "left": {
              "type": "BinaryExpression",
              "left": {
                "type": "BinaryExpression",
                "left": {
                  "type": "BinaryExpression",
                  "left": {
                    "type": "Identifier",
                    "name": "xi"
                  },
                  "right": {
                    "type": "BinaryExpression",
                    "left": {
                      "type": "Identifier",
                      "name": "xi"
                    },
                    "right": {
                      "type": "Literal",
                      "value": 1
                    },
                    "operator": "<<"
                  },
                  "operator": "^"
                },
                "right": {
                  "type": "BinaryExpression",
                  "left": {
                    "type": "Identifier",
                    "name": "xi"
                  },
                  "right": {
                    "type": "Literal",
                    "value": 2
                  },
                  "operator": "<<"
                },
                "operator": "^"
              },
              "right": {
                "type": "BinaryExpression",
                "left": {
                  "type": "Identifier",
                  "name": "xi"
                },
                "right": {
                  "type": "Literal",
                  "value": 3
                },
                "operator": "<<"
              },
              "operator": "^"
            },
            "right": {
              "type": "BinaryExpression",
              "left": {
                "type": "Identifier",
                "name": "xi"
              },
              "right": {
                "type": "Literal",
                "value": 4
              },
              "operator": "<<"
            },
            "operator": "^"
          }
        }
      ]
    }
  ]
}

How would you handle this specific case in a generic way, so it could be generalized and used elsewhere (with a bit more work)?

from How to parse JS code into one-operation-per-line with fewest temp variables?