Feat/add fuzz option to simulator (#160)

* Feat/add fuzz option to simulator

* bump version

src/fsrs_optimizer/fsrs_simulator.py

@@ -12,11 +12,54 @@ def power_forgetting_curve(t, s):
     return (1 + FACTOR * t / s) ** DECAY
 
 
-def next_interval(s, r, float_ivl: bool = False):
+def next_interval(s, r, float_ivl: bool = False, fuzz: bool = False):
     ivl = s / FACTOR * (r ** (1 / DECAY) - 1)
-    return (
-        np.maximum(1, np.round(ivl).astype(int)) if not float_ivl else np.round(ivl, 6)
-    )
+    if float_ivl:
+        ivl = np.round(ivl, 6)
+    else:
+        ivl = np.maximum(1, np.round(ivl).astype(int))
+        if fuzz:
+            fuzz_mask = ivl >= 3
+            ivl[fuzz_mask] = fuzz_interval(ivl[fuzz_mask])
+    return ivl
+
+
+FUZZ_RANGES = [
+    {
+        "start": 2.5,
+        "end": 7.0,
+        "factor": 0.15,
+    },
+    {
+        "start": 7.0,
+        "end": 20.0,
+        "factor": 0.1,
+    },
+    {
+        "start": 20.0,
+        "end": math.inf,
+        "factor": 0.05,
+    },
+]
+
+
+def get_fuzz_range(interval):
+    delta = np.ones_like(interval, dtype=float)
+    for range in FUZZ_RANGES:
+        delta += range["factor"] * np.maximum(
+            np.minimum(interval, range["end"]) - range["start"], 0.0
+        )
+    min_ivl = np.round(interval - delta).astype(int)
+    max_ivl = np.round(interval + delta).astype(int)
+    min_ivl = np.maximum(2, min_ivl)
+    min_ivl = np.minimum(min_ivl, max_ivl)
+    return min_ivl, max_ivl
+
+
+def fuzz_interval(interval):
+    min_ivl, max_ivl = get_fuzz_range(interval)
+    # max_ivl + 1 because randint upper bound is exclusive
+    return np.random.randint(min_ivl, max_ivl + 1, size=min_ivl.shape)
 
 
 columns = [
@@ -64,6 +107,7 @@ def simulate(
     forget_session_len=DEFAULT_FORGET_SESSION_LEN,
     loss_aversion=2.5,
     seed=42,
+    fuzz=False,
 ):
     np.random.seed(seed)
     card_table = np.zeros((len(columns), deck_size))
@@ -224,6 +268,7 @@ def mean_reversion(init, current):
             next_interval(
                 card_table[col["stability"]][true_review | true_learn],
                 request_retention,
+                fuzz=fuzz,
             ),
             1,
             max_ivl,