Fine-tune the sample size for CMRR.py (#136)

* Fine-tune sample size for CMRR.py

So here's the idea: the amount of time it takes to run CMRR for small values of days_to_simulate is very small. Which means that we can increase the sample size without having to worry about CMRR taking too long to annoy the user.
Instead of writing a whole bunch of else-if statements, I made a function that calculates the "best" sample size. Specifically, it calculates what sample size would make CMRR run roughly as long as it owuld with sample_size=4 and days_to_simulate=365.
sample_size=4 and days_to_simulate=365 is used as the default, and then if days_to_simulate is lower, sample size is increased to make the total run time approximately constant.

* Update fsrs_simulator.py

* Update fsrs_simulator.py

* Change the coefficients.py

* Fixed a problem where the output was 3 instead of 4.py

* Update fsrs_simulator.py

I don't know how I managed to delete "best" twice today

* Update fsrs_simulator.py

* set loss_aversion to 1 when plotting workload

* Update ylim.py

Don't mind me, I'm just trying things

* Update fsrs_simulator.py

* min -> minimum.py

* Decrease ylim.py

* Update fsrs_simulator.py

Ensure that nothing is plotted above the box with the graph

* bump version

---------

Co-authored-by: Jarrett Ye <jarrett.ye@outlook.com>

pyproject.toml

@@ -4,7 +4,7 @@ build-backend = "setuptools.build_meta"
 
 [project]
 name = "FSRS-Optimizer"
-version = "5.0.7"
+version = "5.0.8"
 readme = "README.md"
 dependencies = [
     "matplotlib>=3.7.0",

src/fsrs_optimizer/fsrs_simulator.py

@@ -263,12 +263,19 @@ def sample(
     workload_only=False,
 ):
     results = []
-    if learn_span < 100:
-        SAMPLE_SIZE = 16
-    elif learn_span < 365:
-        SAMPLE_SIZE = 8
-    else:
-        SAMPLE_SIZE = 4
+
+    def best_sample_size(days_to_simulate):
+        if days_to_simulate <= 30:
+            return 45
+        elif days_to_simulate >= 365:
+            return 4
+        else:
+            a1, a2, a3 = 8.20e-07, 2.41e-03, 1.30e-02
+            factor = a1 * np.power(days_to_simulate, 2) + a2 * days_to_simulate + a3
+            default_sample_size = 4
+            return int(default_sample_size/factor)
+
+    SAMPLE_SIZE = best_sample_size(learn_span)
 
     for i in range(SAMPLE_SIZE):
         _, _, _, memorized_cnt_per_day, cost_per_day = simulate(
@@ -422,6 +429,7 @@ def workload_graph(default_params, sampling_size=30):
         default_params["deck_size"] / default_params["learn_span"]
     )
     default_params["review_limit_perday"] = math.inf
+    default_params["loss_aversion"] = 1
     workload = [sample(r=r, workload_only=True, **default_params) for r in R]
 
     # this is for testing
@@ -513,10 +521,14 @@ def workload_graph(default_params, sampling_size=30):
     ax.xaxis.set_tick_params(labelsize=14)
     ax.set_xlim(0.7, 0.99)
 
-    if max_w >= 4.5 * min_w:
-        lim = 4.5 * min_w
-    elif max_w >= 3.5 * min_w:
+    if max_w >= 3.5 * min_w:
         lim = 3.5 * min_w
+    elif max_w >= 3 * min_w:
+        lim = 3 * min_w
+    elif max_w >= 2.5 * min_w:
+        lim = 2.5 * min_w
+    elif max_w >= 2 * min_w:
+        lim = 2 * min_w
     else:
         lim = 1.1 * max_w
 
@@ -527,13 +539,13 @@ def workload_graph(default_params, sampling_size=30):
     ax.text(
         0.701,
         min_w,
-        "min. workload",
+        "minimum workload",
         ha="left",
         va="bottom",
         color="black",
         fontsize=12,
     )
-    if max_w >= 1.8 * min_w:
+    if lim >= 1.8 * min_w:
         ax.axhline(y=1.5 * min_w, color="black", alpha=0.75, ls="--")
         ax.text(
             0.701,
@@ -544,7 +556,7 @@ def workload_graph(default_params, sampling_size=30):
             color="black",
             fontsize=12,
         )
-    if max_w >= 2.3 * min_w:
+    if lim >= 2.3 * min_w:
         ax.axhline(y=2 * min_w, color="black", alpha=0.75, ls="--")
         ax.text(
             0.701,
@@ -555,7 +567,7 @@ def workload_graph(default_params, sampling_size=30):
             color="black",
             fontsize=12,
         )
-    if max_w >= 2.8 * min_w:
+    if lim >= 2.8 * min_w:
         ax.axhline(y=2.5 * min_w, color="black", alpha=0.75, ls="--")
         ax.text(
             0.701,
@@ -566,7 +578,7 @@ def workload_graph(default_params, sampling_size=30):
             color="black",
             fontsize=12,
         )
-    if max_w >= 3.3 * min_w:
+    if lim >= 3.3 * min_w:
         ax.axhline(y=3 * min_w, color="black", alpha=0.75, ls="--")
         ax.text(
             0.701,