diff -ru sage-7.3.orig/src/sage/coding/code_bounds.py sage-7.3/src/sage/coding/code_bounds.py
--- sage-7.3.orig/src/sage/coding/code_bounds.py        2016-08-05 20:26:10.033204091 +0200
+++ sage-7.3/src/sage/coding/code_bounds.py     2016-08-05 20:32:27.276579565 +0200
@@ -554,7 +554,7 @@
     if q < 2:   # Here we check that q is actually at least 2
         raise ValueError("The value q must be an integer greater than 1")
 
-    eps  = 4.5e-16 # find_root has about this as the default xtol
+    eps  = 4.5e-15 # find_root has about this as the default xtol
     ymax = 1 - 1/q
     if x <= eps:
         return 0
diff -ru sage-7.3.orig/src/sage/numerical/optimize.py sage-7.3/src/sage/numerical/optimize.py
--- sage-7.3.orig/src/sage/numerical/optimize.py        2016-08-05 20:26:10.816536625 +0200
+++ sage-7.3/src/sage/numerical/optimize.py     2016-08-05 20:32:21.449907130 +0200
@@ -15,7 +15,7 @@
 from sage.rings.real_double import RDF
 
 
-def find_root(f, a, b, xtol=10e-13, rtol=4.5e-16, maxiter=100, full_output=False):
+def find_root(f, a, b, xtol=10e-13, rtol=4.5e-15, maxiter=100, full_output=False):
     """
     Numerically find a root of ``f`` on the closed interval `[a,b]`
     (or `[b,a]`) if possible, where ``f`` is a function in the one variable.
diff -ru sage-7.3.orig/src/sage/symbolic/expression.pyx sage-7.3/src/sage/symbolic/expression.pyx
--- sage-7.3.orig/src/sage/symbolic/expression.pyx      2016-08-05 20:26:11.333202767 +0200
+++ sage-7.3/src/sage/symbolic/expression.pyx   2016-08-05 20:32:14.236566826 +0200
@@ -10884,7 +10884,7 @@
             ret = ret[0]
         return ret
 
-    def find_root(self, a, b, var=None, xtol=10e-13, rtol=4.5e-16, maxiter=100, full_output=False):
+    def find_root(self, a, b, var=None, xtol=10e-13, rtol=4.5e-15, maxiter=100, full_output=False):
         """
         Numerically find a root of self on the closed interval [a,b] (or
         [b,a]) if possible, where self is a function in the one variable.