commit d7ec2c509b
Author: Sergey B Kirpichev <skirpichev@gmail.com>
Date:   Mon Mar 1 11:29:16 2021 +0300

    bpo-43420 Simple optimizations for Fraction._add/sub()

diff --git a/Lib/fractions.py b/Lib/fractions.py
index de3e23b759..12150f91e8 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -382,30 +382,53 @@ def reverse(b, a):
 
     def _add(a, b):
         """a + b"""
+        na, nb = a.numerator, b.numerator
         da, db = a.denominator, b.denominator
-        return Fraction(a.numerator * db + b.numerator * da,
-                        da * db)
+        g = math.gcd(da, db)
+        if g == 1:
+            # This is the case with probability 6/pi**2 ~ 60.8%.
+            return Fraction(na * db + da * nb, da * db, _normalize=False)
+        else:
+            q1, q2 = da // g, db // g
+            n, d = na * q2 + nb * q1, q1 * q2
+            g2 = math.gcd(n, g)
+            return Fraction(n // g2, d * (g // g2), _normalize=False)
 
     __add__, __radd__ = _operator_fallbacks(_add, operator.add)
 
     def _sub(a, b):
         """a - b"""
+        na, nb = a.numerator, b.numerator
         da, db = a.denominator, b.denominator
-        return Fraction(a.numerator * db - b.numerator * da,
-                        da * db)
+        g = math.gcd(da, db)
+        if g == 1:
+            # This is the case with probability 6/pi**2 ~ 60.8%.
+            return Fraction(na * db - da * nb, da * db, _normalize=False)
+        else:
+            q1, q2 = da // g, db // g
+            n, d = na * q2 - nb * q1, q1 * q2
+            g2 = math.gcd(n, g)
+            return Fraction(n // g2, d * (g // g2), _normalize=False)
 
     __sub__, __rsub__ = _operator_fallbacks(_sub, operator.sub)
 
     def _mul(a, b):
         """a * b"""
-        return Fraction(a.numerator * b.numerator, a.denominator * b.denominator)
+        na, da = a.numerator, a.denominator
+        nb, db = b.numerator, b.denominator
+        x1 = math.gcd(na, db)
+        x2 = math.gcd(nb, da)
+        return Fraction((na//x1)*(nb//x2), (da//x2)*(db//x1), _normalize=False)
 
     __mul__, __rmul__ = _operator_fallbacks(_mul, operator.mul)
 
     def _div(a, b):
         """a / b"""
-        return Fraction(a.numerator * b.denominator,
-                        a.denominator * b.numerator)
+        na, da = a.numerator, a.denominator
+        nb, db = b.numerator, b.denominator
+        x1 = math.gcd(na, nb)
+        x2 = math.gcd(db, da)
+        return Fraction((na//x1)*(db//x2), (da//x2)*(nb//x1), _normalize=False)
 
     __truediv__, __rtruediv__ = _operator_fallbacks(_div, operator.truediv)