Fix/set mean reversion target to d0(4) (#103)

* Set mean reversion target to D0(4)

open-spaced-repetition/fsrs-optimizer#124

* test/update test

* update default parameters

__tests__/FSRSV5.test.ts

@@ -57,7 +57,7 @@ describe('FSRS V5 ', () => {
       scheduling_cards = f.repeat(card, now)
     }
     expect(ivl_history).toEqual([
-      0, 4, 17, 57, 163, 412, 0, 0, 8, 15, 27, 49, 86,
+      0, 4, 17, 62, 198, 563, 0, 0, 9, 27, 74, 190, 457,
     ])
   })
 
@@ -135,6 +135,8 @@ describe('fsrs.next method', () => {
     const card = createEmptyCard()
     const now = new Date()
     const g = Rating.Manual as unknown as Grade
-    expect(() => fsrs.next(card, now, g)).toThrow('Cannot review a manual rating')
+    expect(() => fsrs.next(card, now, g)).toThrow(
+      'Cannot review a manual rating'
+    )
   })
 })

__tests__/algorithm.test.ts

@@ -117,10 +117,17 @@ describe('next_ds', () => {
         return Math.min(Math.max(+new Decimal(difficulty).toFixed(8), 1), 10)
       }
 
+      function init_difficulty(g: number) {
+        return +new Decimal(params.w[4])
+          .sub(new Decimal(params.w[5]).mul(new Decimal(g).sub(1)).exp())
+          .add(1)
+          .toFixed(8)
+      }
+
       const next_d = new Decimal(d)
         .sub(new Decimal(params.w[6]).mul(new Decimal(g - 3)))
         .toNumber()
-      return constrain_difficulty(mean_reversion(params.w[4], next_d))
+      return constrain_difficulty(mean_reversion(init_difficulty(4), next_d))
     }
 
     const collection: number[] = []
@@ -131,7 +138,7 @@ describe('next_ds', () => {
       collection.push(d)
       expected.push(expected_d)
     })
-    expect(collection).toEqual([7.0109708, 6.07771798, 5.14446516, 4.21121234])
+    expect(collection).toEqual([7.04017216, 5.9999955, 4.95981884, 3.91964218])
     expect(collection).toEqual(expected)
   })
 
@@ -238,15 +245,15 @@ describe('next_ds', () => {
       expected_next_s.push(next_s(d[index], s[index], r[index], grade))
     })
     expect(s_recall_collection).toEqual([
-      28.60303182, 16.24044223, 68.61087855, 237.0869306,
+      27.43740902, 15.27687386, 65.24019626, 224.35058851,
     ])
     expect(s_recall_collection).toEqual(expected_s_recall)
     expect(s_fail_collection).toEqual([
-      1.79896722, 2.0890141, 2.48973974, 2.99909845,
+      1.73909651, 2.0293769, 2.43393181, 2.95208552,
     ])
     expect(s_fail_collection).toEqual(expected_s_fail)
     expect(s_short_collection).toEqual([
-      2.57947991, 4.20673912, 6.86055123, 11.18851485,
+      2.54268521, 4.20645686, 6.95889497, 11.51235369,
     ])
     expect(s_short_collection).toEqual(expected_s_short)
 

__tests__/default.test.ts

@@ -9,9 +9,9 @@ import {
 
 describe('default params', () => {
   const expected_w = [
-    0.4197, 1.1869, 3.0412, 15.2441, 7.1434, 0.6477, 1.0007, 0.0674, 1.6597,
-    0.1712, 1.1178, 2.0225, 0.0904, 0.3025, 2.1214, 0.2498, 2.9466, 0.4891,
-    0.6468,
+    0.4072, 1.1829, 3.1262, 15.4722, 7.2102, 0.5316, 1.0651, 0.0234, 1.616,
+    0.1544, 1.0824, 1.9813, 0.0953, 0.2975, 2.2042, 0.2407, 2.9466, 0.5034,
+    0.6567,
   ]
   expect(default_request_retention).toEqual(0.9)
   expect(default_maximum_interval).toEqual(36500)

__tests__/impl/long-term_schduler.test.ts

@@ -49,15 +49,18 @@ describe('Long-term  schduler', () => {
       now = card.due
     }
 
-    expect(ivl_history).toEqual([3, 6, 17, 42, 95, 200, 8, 2, 3, 5, 8, 14, 23])
+    expect(ivl_history).toEqual([
+      3, 7, 21, 60, 158, 390, 11, 2, 5, 13, 33, 79, 184,
+    ])
     expect(s_history).toEqual([
-      0.57587467, 6.28341418, 16.83356103, 41.95128557, 95.07063986,
-      199.53765138, 8.31519008, 1.96276113, 3.06877302, 4.90880017, 8.15177579,
-      13.50873393, 22.92901865,
+      0.57587467, 6.87994283, 21.35900027, 59.97135827, 158.31738168,
+      390.28403347, 10.97158339, 2.35722772, 5.41695678, 13.11380293,
+      32.50206204, 79.19030952, 184.25083571,
     ])
     expect(d_history).toEqual([
-      7.1434, 7.1434, 7.1434, 7.1434, 7.1434, 7.1434, 9.00990564, 10,
-      9.80746516, 9.62790717, 9.46045139, 9.30428213, 9.15863867,
+      6.74032397, 6.36441526, 6.0138428, 5.68689892, 5.38199106, 5.09763399,
+      6.69894823, 8.19233389, 7.71855971, 7.27671791, 6.86465625, 6.48036755,
+      6.1219799,
     ])
   })
 
@@ -85,15 +88,15 @@ describe('Long-term  schduler', () => {
       d_history.push(card.difficulty)
       now = card.due
     }
-    expect(ivl_history).toEqual([1, 2, 3, 8, 2, 2, 4, 10])
+    expect(ivl_history).toEqual([1, 2, 3, 14, 3, 4, 8, 34])
 
     expect(s_history).toEqual([
-      0.21652154, 0.51780862, 1.8183783, 8.18593986, 1.96087115, 2.23717242,
-      3.33185406, 10.31008873,
+      0.21652154, 0.57883165, 2.75860692, 14.17790785, 2.66869241, 3.62352774,
+      7.6088889, 33.82907094,
     ])
     expect(d_history).toEqual([
-      9.00990564, 9.81735598, 9.63713135, 8.53580104, 10, 10, 9.80746516,
-      8.69465435,
+      8.60682961, 9.03837124, 8.50757415, 7.07929996, 8.54704991, 8.98262069,
+      8.45558118, 7.03081132,
     ])
   })
 
@@ -121,15 +124,15 @@ describe('Long-term  schduler', () => {
       d_history.push(card.difficulty)
       now = card.due
     }
-    expect(ivl_history).toEqual([2, 3, 17, 3, 4, 6, 18, 3])
+    expect(ivl_history).toEqual([2, 4, 26, 4, 5, 13, 67, 5])
 
     expect(s_history).toEqual([
-      0.35311368, 3.40179546, 16.86596974, 2.9223039, 3.73601023, 6.27595217,
-      18.057595, 2.96541083,
+      0.35311368, 3.82215283, 25.65963413, 3.62919153, 5.38579333, 12.54261943,
+      66.53407633, 5.47466879,
     ])
     expect(d_history).toEqual([
-      8.07665282, 8.01375158, 7.02183706, 8.89653604, 9.71162749, 9.53852896,
-      8.44384445, 10,
+      7.67357679, 7.23476684, 5.89227986, 7.44003496, 7.95021855, 7.49276295,
+      6.13288703, 7.66442521,
     ])
   })
 
@@ -158,15 +161,15 @@ describe('Long-term  schduler', () => {
       now = card.due
     }
 
-    expect(ivl_history).toEqual([3, 17, 3, 4, 8, 30, 4, 4])
+    expect(ivl_history).toEqual([3, 19, 3, 5, 13, 73, 6, 8])
 
     expect(s_history).toEqual([
-      0.57587467, 17.3937106, 2.98322161, 4.08808234, 7.99405969, 29.76078201,
-      3.78204811, 4.44627015,
+      0.57587467, 19.1514419, 3.17243454, 4.70631523, 12.88705197, 72.51830855,
+      5.70211402, 8.22198803,
     ])
     expect(d_history).toEqual([
-      7.1434, 6.21014718, 8.13955406, 9.0056661, 8.88014936, 7.82983963,
-      9.65007924, 10,
+      6.74032397, 5.43116244, 7.00999686, 7.54916502, 7.11874042, 5.78407362,
+      7.33912183, 7.85610697,
     ])
   })
   test('test5', () => {
@@ -194,15 +197,15 @@ describe('Long-term  schduler', () => {
       now = card.due
     }
 
-    expect(ivl_history).toEqual([4, 1, 2, 3, 13, 3, 3, 5])
+    expect(ivl_history).toEqual([4, 1, 2, 5, 30, 4, 6, 14])
 
     expect(s_history).toEqual([
-      0.93916394, 0.70772253, 1.16119435, 3.42301186, 12.97577367, 2.53486926,
-      3.06202367, 4.60523893,
+      0.93916394, 0.71202904, 1.28884718, 4.82236231, 29.76149698, 3.87021442,
+      5.53831177, 13.53596018,
     ])
     expect(d_history).toEqual([
-      6.21014718, 8.13955406, 9.0056661, 8.88014936, 7.82983963, 9.65007924, 10,
-      9.80746516,
+      5.80707115, 7.36056932, 7.8761089, 7.42364829, 6.0684307, 7.60431324,
+      8.10342447, 7.63564279,
     ])
   })
 
@@ -238,11 +241,20 @@ describe('Long-term  schduler', () => {
       d_history.push(card.difficulty)
       state_history.push(State[card.state])
     }
-    expect(ivl_history).toEqual([0, 4, 1, 4, 12, 0])
+    expect(ivl_history).toEqual([0, 4, 1, 4, 15, 0])
     expect(s_history).toEqual([
-      3.0412, 3.0412, 1.20788692, 3.83856852, 12.23542321, 2.48288917,
+      3.0412, 3.0412, 1.21778427, 4.32308454, 14.84659978, 2.81505627,
+    ])
+    expect(d_history).toEqual([
+      4.49094334, 4.26664289, 5.92396593, 5.60307975, 5.3038213, 6.89123851,
+    ])
+    expect(state_history).toEqual([
+      'Learning',
+      'Review',
+      'Review',
+      'Review',
+      'Review',
+      'Relearning',
     ])
-    expect(d_history).toEqual([4.49094334, 4.66971892, 6.70295066, 6.73263695,6.76032238,8.65264745])
-    expect(state_history).toEqual(['Learning', 'Review', 'Review', 'Review','Review','Relearning'])
   })
 })

debug/short-term.ts

@@ -35,22 +35,22 @@ function test1() {
 
   assert.deepStrictEqual(
     ivl_history,
-    [0, 4, 17, 57, 163, 412, 0, 0, 8, 15, 27, 49, 86]
+    [0, 4, 15, 48, 136, 351, 0, 0, 7, 13, 24, 43, 77]
   )
   assert.deepStrictEqual(
     s_history,
     [
-      3.0412, 4.17286168, 16.55123695, 56.74378762, 163.35708827, 411.77071586,
-      11.15423471, 5.75442486, 7.89570531, 14.90748589, 27.437534, 48.90521597,
-      85.82782993,
+      3.1262, 4.35097949, 14.94870008, 47.78790366, 136.29251941, 351.35118365,
+      9.99090459, 5.08074507, 7.07127426, 13.09253023, 23.92805755, 43.23645988,
+      76.59611345,
     ]
   )
   assert.deepStrictEqual(
     d_history,
     [
-      4.49094334, 4.66971892, 4.83644502, 4.99193379, 5.13694261, 5.27217784,
-      7.26480385, 9.12312687, 8.98969328, 8.86525311, 8.74920021, 8.64096928,
-      8.54003311,
+      5.31457783, 5.26703555, 5.22060576, 5.17526243, 5.13098013, 5.08773404,
+      7.12585323, 9.11628043, 8.97977831, 8.84647034, 8.71628178, 8.58913963,
+      8.4649726,
     ]
   )
 }

src/fsrs/algorithm.ts

@@ -165,16 +165,16 @@ export class FSRSAlgorithm {
 
   /**
    * The formula used is :
-   * $$\text{next}_d = D - w_6 \cdot (R - 2)$$
-   * $$D^\prime(D,R) = w_5 \cdot D_0(2) +(1 - w_5) \cdot \text{next}_d$$
+   * $$\text{next}_d = D - w_6 \cdot (g - 3)$$
+   * $$D^\prime(D,R) = w_7 \cdot D_0(4) +(1 - w_7) \cdot \text{next}_d$$
    * @param {number} d Difficulty $$D \in [1,10]$$
    * @param {Grade} g Grade (rating at Anki) [1.again,2.hard,3.good,4.easy]
    * @return {number} $$\text{next}_D$$
    */
   next_difficulty(d: number, g: Grade): number {
     const next_d = d - this.param.w[6] * (g - 3)
     return this.constrain_difficulty(
-      this.mean_reversion(this.param.w[4], next_d)
+      this.mean_reversion(this.init_difficulty(Rating.Easy), next_d)
     )
   }
 

src/fsrs/default.ts

@@ -4,9 +4,9 @@ import { TypeConvert } from './convert'
 export const default_request_retention = 0.9
 export const default_maximum_interval = 36500
 export const default_w = [
-  0.4197, 1.1869, 3.0412, 15.2441, 7.1434, 0.6477, 1.0007, 0.0674, 1.6597,
-  0.1712, 1.1178, 2.0225, 0.0904, 0.3025, 2.1214, 0.2498, 2.9466, 0.4891,
-  0.6468,
+  0.4072, 1.1829, 3.1262, 15.4722, 7.2102, 0.5316, 1.0651, 0.0234, 1.616,
+  0.1544, 1.0824, 1.9813, 0.0953, 0.2975, 2.2042, 0.2407, 2.9466, 0.5034,
+  0.6567,
 ]
 export const default_enable_fuzz = false
 export const defualt_enable_short_term = true
@@ -30,8 +30,7 @@ export const generatorParameters = (
     maximum_interval: props?.maximum_interval || default_maximum_interval,
     w: w,
     enable_fuzz: props?.enable_fuzz ?? default_enable_fuzz,
-    enable_short_term:
-      props?.enable_short_term ?? defualt_enable_short_term,
+    enable_short_term: props?.enable_short_term ?? defualt_enable_short_term,
   } satisfies FSRSParameters
 }