diff --git a/pymc3/distributions/continuous.py b/pymc3/distributions/continuous.py
index 08102d2022..2d023dbfbf 100644
--- a/pymc3/distributions/continuous.py
+++ b/pymc3/distributions/continuous.py
@@ -45,7 +45,7 @@
 )
 from pymc3.distributions.distribution import Continuous, draw_values, generate_samples
 from pymc3.distributions.special import log_i0
-from pymc3.math import invlogit, logdiffexp, logit
+from pymc3.math import invlogit, log1mexp, logdiffexp, logit
 from pymc3.theanof import floatX
 
 __all__ = [
@@ -1513,12 +1513,6 @@ def logcdf(self, value):
         Compute the log of cumulative distribution function for the Exponential distribution
         at the specified value.
 
-        References
-        ----------
-        .. [Machler2012] Martin Mächler (2012).
-            "Accurately computing :math:`\log(1-\exp(-\mid a \mid))` Assessed by the Rmpfr
-            package"
-
         Parameters
         ----------
         value: numeric
@@ -1533,9 +1527,9 @@ def logcdf(self, value):
         lam = self.lam
         a = lam * value
         return tt.switch(
-            tt.le(value, 0.0),
+            tt.le(value, 0.0) | tt.le(lam, 0),
             -np.inf,
-            tt.switch(tt.le(a, tt.log(2.0)), tt.log(-tt.expm1(-a)), tt.log1p(-tt.exp(-a))),
+            log1mexp(a),
         )
 
 
@@ -2806,12 +2800,6 @@ def logcdf(self, value):
         Compute the log of the cumulative distribution function for Weibull distribution
         at the specified value.
 
-        References
-        ----------
-        .. [Machler2012] Martin Mächler (2012).
-            "Accurately computing `\log(1-\exp(- \mid a \mid))` Assessed by the Rmpfr
-            package"
-
         Parameters
         ----------
         value: numeric
@@ -2828,7 +2816,7 @@ def logcdf(self, value):
         return tt.switch(
             tt.le(value, 0.0),
             -np.inf,
-            tt.switch(tt.le(a, tt.log(2.0)), tt.log(-tt.expm1(-a)), tt.log1p(-tt.exp(-a))),
+            log1mexp(a),
         )
 
 
diff --git a/pymc3/math.py b/pymc3/math.py
index 17f286ceab..17a7a7f67d 100644
--- a/pymc3/math.py
+++ b/pymc3/math.py
@@ -219,14 +219,21 @@ def log1pexp(x):
 
 
 def log1mexp(x):
-    """Return log(1 - exp(-x)).
+    r"""Return log(1 - exp(-x)).
 
     This function is numerically more stable than the naive approach.
 
     For details, see
     https://cran.r-project.org/web/packages/Rmpfr/vignettes/log1mexp-note.pdf
+
+    References
+        ----------
+        .. [Machler2012] Martin Mächler (2012).
+            "Accurately computing `\log(1-\exp(- \mid a \mid))` Assessed by the Rmpfr
+            package"
+
     """
-    return tt.switch(tt.lt(x, 0.683), tt.log(-tt.expm1(-x)), tt.log1p(-tt.exp(-x)))
+    return tt.switch(tt.lt(x, 0.6931471805599453), tt.log(-tt.expm1(-x)), tt.log1p(-tt.exp(-x)))
 
 
 def log1mexp_numpy(x):
@@ -235,7 +242,7 @@ def log1mexp_numpy(x):
     For details, see
     https://cran.r-project.org/web/packages/Rmpfr/vignettes/log1mexp-note.pdf
     """
-    return np.where(x < 0.683, np.log(-np.expm1(-x)), np.log1p(-np.exp(-x)))
+    return np.where(x < 0.6931471805599453, np.log(-np.expm1(-x)), np.log1p(-np.exp(-x)))
 
 
 def flatten_list(tensors):