Application of fuzz to interval is not deterministic

[winghouchan]

Steps to reproduce

1. Schedule the same card with enable_fuzz: true and the same review date time and rating.

JSFiddle

Code

const {
  createEmptyCard,
  fsrs,
  Grades,
  Rating,
} = window.FSRS

const MOCK_NOW = new Date(2024, 7, 15)
const MOCK_TOMORROW = new Date(2024, 7, 16)
const { card } = fsrs().next(createEmptyCard(), MOCK_NOW, Rating.Good)

for (let count = 0; count < 10; count++) {
  const scheduler = fsrs({ enable_fuzz: true })
  console.log(scheduler.next(card, MOCK_TOMORROW, Rating.Good).card)
}

<script src="https://unpkg.com/ts-fsrs@4.1.1/dist/index.umd.js"></script>

Expected behaviour

All the next cards should be in the same state.

Actual behaviour

The next cards are not in the same state. They have different due dates. An example:

[winghouchan]

Investigation notes

• When enable_fuzz is true, the algorithm applies a fuzz factor to the next interval. The fuzz factor is generated with a pseudo-random number generator. When initialising the generator, a seed is passed to it.

  ts-fsrs/src/fsrs/algorithm.ts

  Lines 130 to 147 in eee4f0c

  	/**
  	* If fuzzing is disabled or ivl is less than 2.5, it returns the original interval.
  	* @param {number} ivl - The interval to be fuzzed.
  	* @param {number} elapsed_days t days since the last review
  	* @param {number} enable_fuzz - This adds a small random delay to the new interval time to prevent cards from sticking together and always being reviewed on the same day.
  	* @return {number} - The fuzzed interval.
  	**/
  	apply_fuzz(ivl: number, elapsed_days: number, enable_fuzz?: boolean): int {
  	if (!enable_fuzz || ivl < 2.5) return Math.round(ivl) as int
  	const generator = alea(this.seed)
  	const fuzz_factor = generator()
  	const { min_ivl, max_ivl } = get_fuzz_range(
  	ivl,
  	elapsed_days,
  	this.param.maximum_interval
  	)
  	return Math.floor(fuzz_factor * (max_ivl - min_ivl + 1) + min_ivl) as int
  	}

• The seed is generated from the time of the review, number of reps, and the product of card's current difficulty and stability.

  ts-fsrs/src/fsrs/abstract_schduler.ts

  Lines 83 to 88 in eee4f0c

  	private initSeed() {
  	const time = this.review_time.getTime()
  	const reps = this.current.reps
  	const mul = this.current.difficulty * this.current.stability
  	this.algorithm.seed = `${time}_${reps}_${mul}`
  	}

• The inputs to the seed should be the same for all the cards in the test however the output due date can be different across runs.
• When inspecting the state while apply_fuzz is run, it can be seen that this.seed is undefined. This means the pseudo-random number generator was initialised with no seed. It looks like the seed is available on this._seed.
• The root cause is the FSRSAlgorithm class having a setter for seed which assigns the value to this._seed. As there is no getter, this.seed returns undefined.

  ts-fsrs/src/fsrs/algorithm.ts

  Lines 41 to 43 in eee4f0c

  	set seed(seed: string) {
  	this._seed = seed
  	}

Resolution

One of:

• Remove the setter for seed.
• Add a getter for seed to return this._seed.
• Update references to this.seed to this._seed.

[ishiko732]

Thank you for identifying the issue; I am now checking and will fix it!

[ishiko732]

• Remove the setter for seed.

I cannot remove set seed because it is used in abstract_scheduler.ts :

ts-fsrs/src/fsrs/abstract_schduler.ts

Lines 83 to 88 in eee4f0c

	private initSeed() {
	const time = this.review_time.getTime()
	const reps = this.current.reps
	const mul = this.current.difficulty * this.current.stability
	this.algorithm.seed = `${time}_${reps}_${mul}`
	}