diff --git a/devito/symbolics/printer.py b/devito/symbolics/printer.py
index 12eb2baca4..e1a3280d31 100644
--- a/devito/symbolics/printer.py
+++ b/devito/symbolics/printer.py
@@ -7,7 +7,10 @@
 
 from mpmath.libmp import prec_to_dps, to_str
 from packaging.version import Version
+from numbers import Real
 
+from sympy.core import S
+from sympy.core.numbers import equal_valued, Float
 from sympy.logic.boolalg import BooleanFunction
 from sympy.printing.precedence import PRECEDENCE_VALUES, precedence
 from sympy.printing.c import C99CodePrinter
@@ -122,15 +125,22 @@ def _print_math_func(self, expr, nest=False, known=None):
         return f'{cname}({args})'
 
     def _print_Pow(self, expr):
-        # Need to override because of issue #1627
-        # E.g., (Pow(h_x, -1) AND h_x.dtype == np.float32) => 1.0F/h_x
-        try:
-            if expr.exp == -1 and self.single_prec():
-                PREC = precedence(expr)
-                return '1.0F/%s' % self.parenthesize(expr.base, PREC)
-        except AttributeError:
-            pass
-        return super()._print_Pow(expr)
+        # Completely reimplement `_print_Pow` from sympy, since it doesn't
+        # correctly handle precision
+        if "Pow" in self.known_functions:
+            return self._print_Function(expr)
+        PREC = precedence(expr)
+        suffix = 'f' if self.single_prec(expr) else ''
+        if equal_valued(expr.exp, -1):
+            return f'{self._print_Float(Float(1.0))}/' + \
+                f'{self.parenthesize(expr.base, PREC)}'
+        elif equal_valued(expr.exp, 0.5):
+            return f'{self._ns}sqrt{suffix}({self._print(expr.base)}'
+        elif expr.exp == S.One/3 and self.standard != 'C89':
+            return f'{self._ns}cbrt{suffix}({self._print(expr.base)})'
+        else:
+            return f'{self._ns}pow{suffix}({self._print(expr.base)}, ' + \
+                f'{self._print(expr.exp)})'
 
     def _print_Mod(self, expr):
         """Print a Mod as a C-like %-based operation."""
@@ -159,7 +169,16 @@ def _print_Abs(self, expr):
         if isinstance(self.compiler, AOMPCompiler):
             return "fabs(%s)" % self._print(expr.args[0])
         # Check if argument is an integer
-        func = "abs" if has_integer_args(*expr.args[0].args) else "fabs"
+        if has_integer_args(*expr.args[0].args):
+            func = "abs"
+        elif self.single_prec(expr):
+            func = "fabsf"
+        elif any([isinstance(a, Real) for a in expr.args[0].args]):
+            # The previous condition isn't sufficient to detect case with
+            # Python `float`s in that case, fall back to the "default"
+            func = "fabsf" if self.single_prec() else "fabs"
+        else:
+            func = "fabs"
         return "%s(%s)" % (func, self._print(expr.args[0]))
 
     def _print_Add(self, expr, order=None):