diff --git a/src/Analysis/Abstract/BadValues.hs b/src/Analysis/Abstract/BadValues.hs
index 68eeb6b97..94b4dcd7d 100644
--- a/src/Analysis/Abstract/BadValues.hs
+++ b/src/Analysis/Abstract/BadValues.hs
@@ -38,6 +38,7 @@ instance ( Effectful m
             BitwiseError{}             -> hole >>= yield
             Bitwise2Error{}            -> hole >>= yield
             KeyValueError{}            -> hole >>= \x -> yield (x, x)
+            ArithmeticError{}          -> hole >>= yield
           )
 
   analyzeModule = liftAnalyze analyzeModule
diff --git a/src/Control/Abstract/Value.hs b/src/Control/Abstract/Value.hs
index fa7fa1908..2c02315e4 100644
--- a/src/Control/Abstract/Value.hs
+++ b/src/Control/Abstract/Value.hs
@@ -204,6 +204,8 @@ data ValueError location value resume where
   BitwiseError           :: value          -> ValueError location value value
   Bitwise2Error          :: value -> value -> ValueError location value value
   KeyValueError          :: value          -> ValueError location value (value, value)
+  -- Indicates that we encountered an arithmetic exception inside Haskell-native number crunching.
+  ArithmeticError :: ArithException -> ValueError location value value
 
 instance Eq value => Eq1 (ValueError location value) where
   liftEq _ (StringError a) (StringError b)                       = a == b
diff --git a/src/Data/Abstract/Value.hs b/src/Data/Abstract/Value.hs
index 256af31c5..d47faef94 100644
--- a/src/Data/Abstract/Value.hs
+++ b/src/Data/Abstract/Value.hs
@@ -7,6 +7,7 @@ import qualified Data.Abstract.Environment as Env
 import Data.Abstract.Evaluatable
 import qualified Data.Abstract.Number as Number
 import Data.Scientific (Scientific)
+import Data.Scientific.Exts
 import qualified Data.Set as Set
 import Prologue hiding (TypeError)
 import Prelude hiding (Float, Integer, String, Rational)
@@ -265,22 +266,25 @@ instance (Monad (m effects), MonadEvaluatable location term (Value location) eff
     | otherwise = throwValueError (NumericError arg)
 
   liftNumeric2 f left right
-    | Just (Integer  i, Integer j)  <- prjPair pair = f i j & specialize
-    | Just (Integer  i, Rational j) <- prjPair pair = f i j & specialize
-    | Just (Integer  i, Float j)    <- prjPair pair = f i j & specialize
-    | Just (Rational i, Integer j)  <- prjPair pair = f i j & specialize
-    | Just (Rational i, Rational j) <- prjPair pair = f i j & specialize
-    | Just (Rational i, Float j)    <- prjPair pair = f i j & specialize
-    | Just (Float    i, Integer j)  <- prjPair pair = f i j & specialize
-    | Just (Float    i, Rational j) <- prjPair pair = f i j & specialize
-    | Just (Float    i, Float j)    <- prjPair pair = f i j & specialize
+    | Just (Integer  i, Integer j)  <- prjPair pair = tentative f i j & specialize
+    | Just (Integer  i, Rational j) <- prjPair pair = tentative f i j & specialize
+    | Just (Integer  i, Float j)    <- prjPair pair = tentative f i j & specialize
+    | Just (Rational i, Integer j)  <- prjPair pair = tentative f i j & specialize
+    | Just (Rational i, Rational j) <- prjPair pair = tentative f i j & specialize
+    | Just (Rational i, Float j)    <- prjPair pair = tentative f i j & specialize
+    | Just (Float    i, Integer j)  <- prjPair pair = tentative f i j & specialize
+    | Just (Float    i, Rational j) <- prjPair pair = tentative f i j & specialize
+    | Just (Float    i, Float j)    <- prjPair pair = tentative f i j & specialize
     | otherwise = throwValueError (Numeric2Error left right)
       where
+        tentative x i j = attemptUnsafeArithmetic (x i j)
+
         -- Dispatch whatever's contained inside a 'Number.SomeNumber' to its appropriate 'MonadValue' ctor
-        specialize :: MonadValue location value effects m => Number.SomeNumber -> m effects value
-        specialize (Number.SomeNumber (Number.Integer i)) = integer i
-        specialize (Number.SomeNumber (Number.Ratio r))          = rational r
-        specialize (Number.SomeNumber (Number.Decimal d))        = float d
+        specialize :: MonadEvaluatable location term value effects m => Either ArithException Number.SomeNumber -> m effects value
+        specialize (Left exc) = throwValueError (ArithmeticError exc)
+        specialize (Right (Number.SomeNumber (Number.Integer i))) = integer i
+        specialize (Right (Number.SomeNumber (Number.Ratio r)))   = rational r
+        specialize (Right (Number.SomeNumber (Number.Decimal d))) = float d
         pair = (left, right)
 
   liftComparison comparator left right
diff --git a/src/Data/Scientific/Exts.hs b/src/Data/Scientific/Exts.hs
index 50df2a55d..d19d456fd 100644
--- a/src/Data/Scientific/Exts.hs
+++ b/src/Data/Scientific/Exts.hs
@@ -1,9 +1,11 @@
 module Data.Scientific.Exts
     ( module Data.Scientific
+    , attemptUnsafeArithmetic
     , parseScientific
     ) where
 
 import Control.Applicative
+import Control.Exception as Exc (evaluate, try)
 import Control.Monad hiding (fail)
 import Data.Attoparsec.ByteString.Char8
 import Data.ByteString.Char8 hiding (readInt, takeWhile)
@@ -13,6 +15,7 @@ import Numeric
 import Prelude hiding (fail, filter, null, takeWhile)
 import Prologue hiding (null)
 import Text.Read (readMaybe)
+import System.IO.Unsafe
 
 parseScientific :: ByteString -> Either String Scientific
 parseScientific = parseOnly parser
@@ -96,3 +99,10 @@ parser = signed (choice [hex, oct, bin, dec]) where
     let trail = if null trailings then "0" else trailings
 
     attempt (unpack (leads <> "." <> trail <> exponent))
+
+-- | Attempt to evaluate the given term into WHNF. If doing so raises an 'ArithException', such as
+-- 'ZeroDivisionError' or 'RatioZeroDenominator', 'Left' will be returned.
+-- Hooray for uncatchable exceptions that bubble up from third-party code.
+attemptUnsafeArithmetic :: a -> Either ArithException a
+attemptUnsafeArithmetic = unsafePerformIO . Exc.try . evaluate
+{-# NOINLINE attemptUnsafeArithmetic #-}