diff --git a/manimlib/utils/rate_functions.py b/manimlib/utils/rate_functions.py
index 32fda05f..6f51bda0 100644
--- a/manimlib/utils/rate_functions.py
+++ b/manimlib/utils/rate_functions.py
@@ -1,28 +1,25 @@
 import numpy as np
 
 from manimlib.utils.bezier import bezier
-from manimlib.utils.simple_functions import sigmoid
-from manimlib.utils.simple_functions import clip
 
 
 def linear(t):
     return t
 
 
-def smooth(t, inflection=10.0):
-    error = sigmoid(-inflection / 2)
-    return clip(
-        (sigmoid(inflection * (t - 0.5)) - error) / (1 - 2 * error),
-        0, 1,
-    )
+def smooth(t):
+    # Zero first and second derivatives at t=0 and t=1.
+    # Equivalent to bezier([0, 0, 0, 1, 1, 1])
+    s = 1 - t
+    return (t**3) * (10 * s * s + 5 * s * t + t * t)
 
 
-def rush_into(t, inflection=10.0):
-    return 2 * smooth(t / 2.0, inflection)
+def rush_into(t):
+    return 2 * smooth(0.5 * t)
 
 
-def rush_from(t, inflection=10.0):
-    return 2 * smooth(t / 2.0 + 0.5, inflection) - 1
+def rush_from(t):
+    return 2 * smooth(0.5 * (t + 1)) - 1
 
 
 def slow_into(t):
@@ -36,9 +33,9 @@ def double_smooth(t):
         return 0.5 * (1 + smooth(2 * t - 1))
 
 
-def there_and_back(t, inflection=10.0):
+def there_and_back(t):
     new_t = 2 * t if t < 0.5 else 2 * (1 - t)
-    return smooth(new_t, inflection)
+    return smooth(new_t)
 
 
 def there_and_back_with_pause(t, pause_ratio=1. / 3):
@@ -69,8 +66,7 @@ def squish_rate_func(func, a=0.4, b=0.6):
     def result(t):
         if a == b:
             return a
-
-        if t < a:
+        elif t < a:
             return func(0)
         elif t > b:
             return func(1)