With the Commentary on Grahalaghava

...that 33. Divided by the "gods" original: amaraiḥ; a code-word for the number 33, the resulting intercalary month is 1. Even if an additional intercalary month is not mathematically obtained here, it should still be taken. By doing so, the intercalary months become 2. These two are added to the quantity placed in two positions: 9, multiplied by thirty: 270, added to the elapsed lunar days: 270, added to one-sixth of the cycle: 1, resulting in 271. This is placed in two positions and divided by sixty-four; the result is 4. Subtracting this from the quantity in the other position, the count of days (Ahargana) is 267. To find the desired day of the week, one is subtracted, and the day-count becomes 266, which falls on a Saturday. If the day-count were calculated using only the mathematically "obtained" intercalary month, it would be 238; therefore, that would be incorrect. This is because the resulting position of the Sun and other planets would disagree with observations. Therefore, after a "clear" calculated/true intercalary month has occurred, even if it is not mathematically "obtained" by the simplified formula, it must be included.

This was stated in the Siddhanta Shiromani A famous 12th-century astronomical text by the great teacher Bhaskaracharya:

"Whenever a 'clear' intercalary month has occurred but is not obtained by the formula, or when it is obtained but has not yet occurred;
The wise should calculate the heap of days (Ahargana) by adding or subtracting one intercalary month respectively."

There is another specific rule: In the calculation of the day-count following an intercalary month, if one is counting elapsed months from Chaitra the first month of the Hindu lunar calendar, the intercalary month itself is not counted as a separate month. However, in the middle of the day-count calculation, when taking the elapsed lunar days, the lunar days of the intercalary month must be included. Now, the method for deriving the Brahmatulya day-count from the Grahalaghava day-count is described by the venerable Ganesha Daivajña. It is as follows:

The Madhuri Commentary

"The Shaka year reduced by 1442" = the current Shaka year minus 1442. "Divided by the Lord" = divided by eleven; the "result" = the quotient, "is called the Cycle." The "remainder multiplied by the Sun" = the remainder multiplied by twelve, "added to the months starting from Chaitra" = added to the elapsed lunar months of the current year. This sum is "placed separately." From this, "added to ten" and "added to twice the cycles," "along with the intercalary months obtained by the 'gods' (33)," "multiplied by thirty" = multiplied by 30, "added to the elapsed lunar days" = including the elapsed lunar days of the desired month, "added to the sixth part of the cycle," "placed in another position." From this, "the results of dividing by sixty-four" = the number of omitted lunar days (kshaya-tithis), "subtracted," becomes the "heap of days" (Ahargana) = the collection of civil days. Here, the word vai is used for emphasis. "The day-count added to five times the cycles" gives the "day of the week" starting "from the Moon" Monday. || 4-5 ||

The Rationale (Upapatti):

By calculating the day-count from the beginning of the Kalpa a vast cosmic age up to the desired day, the planets produced are the "mean planets" for that day. Here, the planets produced from the day-count from the beginning of the Kalpa until the start of this book (Shaka 1442) are called "additive constants" (ksepa). Similarly, the planets produced by a day-count corresponding to a cycle of eleven years are called "constants" (dhruva). The planets produced by the day-count from the end of a cycle to the desired day are called "planets born of the day-count" by the Teacher. By adding these together, the mean planets from the beginning of the Kalpa to the desired day are found. Because the work was begun in Shaka 1442, and one "cycle" is defined as eleven years, one subtracts 1442 from the desired Shaka year and divides the remainder by eleven to get the number of cycles. The remainder of the cycles is multiplied by twelve to get the solar months elapsed since the end of the year (since twelve months make a year). When the elapsed lunar months from Chaitra are added to these, it becomes the total count of months. However, this is therefore? consequently? even when converting solar to lunar, the remainder of the intercalary month is taken. Right here, the intercalary months are—