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The reason is because ($a, $b, $c, $d) are all strings. That means "|" works on strings, bytewise: "189" | "2" yields "389". That is unlike 189 | 2 which returns 191 — where the operands are treated as integers.
Just converting one string into a number is enough to force "|" into numerical mode.
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| & || & |
| < || < |
| > || > |
| [ || [ |
| ] || ] ||