diff --git a/qupulse/program/__init__.py b/qupulse/program/__init__.py
index b5040676..a1b52b7c 100644
--- a/qupulse/program/__init__.py
+++ b/qupulse/program/__init__.py
@@ -1,16 +1,17 @@
 import contextlib
 from abc import ABC, abstractmethod
 from dataclasses import dataclass
-from typing import Optional, Union, Sequence, ContextManager, Mapping, Tuple, Generic, TypeVar, Iterable
-from numbers import Real
+from typing import Optional, Union, Sequence, ContextManager, Mapping, Tuple, Generic, TypeVar, Iterable, Dict
+from numbers import Real, Number
 
 import numpy as np
 
 from qupulse._program.waveforms import Waveform
-from qupulse.utils.types import MeasurementWindow, TimeType
+from qupulse.utils.types import MeasurementWindow, TimeType, FrozenMapping
 from qupulse._program.volatile import VolatileRepetitionCount
 from qupulse.parameter_scope import Scope
-from qupulse.expressions import sympy as sym_expr
+from qupulse.expressions import sympy as sym_expr, Expression
+from qupulse.utils.sympy import _lambdify_modules
 
 from typing import Protocol, runtime_checkable
 
@@ -30,7 +31,7 @@ class SimpleExpression(Generic[NumVal]):
     """
 
     base: NumVal
-    offsets: Sequence[Tuple[str, NumVal]]
+    offsets: Dict[str, NumVal]
 
     def value(self, scope: Mapping[str, NumVal]) -> NumVal:
         value = self.base
@@ -43,7 +44,10 @@ def __add__(self, other):
             return SimpleExpression(self.base + other, self.offsets)
 
         if type(other) == type(self):
-            return SimpleExpression(self.base + other.base, self.offsets + other.offsets)
+            offsets = self.offsets.copy()
+            for name, value in other.offsets.items():
+                offsets[name] = value + offsets.get(name, 0)
+            return SimpleExpression(self.base + other.base, offsets)
 
         return NotImplemented
 
@@ -57,22 +61,40 @@ def __rsub__(self, other):
         (-self).__add__(other)
 
     def __neg__(self):
-        return SimpleExpression(-self.base, tuple((name, -value) for name, value in self.offsets))
+        return SimpleExpression(-self.base, {name: -value for name, value in self.offsets.items()})
 
     def __mul__(self, other: NumVal):
-        if isinstance(other, SimpleExpression):
-            return NotImplemented
-        return SimpleExpression(self.base * other, tuple((name, value * other) for name, value in self.offsets))
+        if isinstance(other, (float, int, TimeType)):
+            return SimpleExpression(self.base * other, {name: other * value for name, value in self.offsets.items()})
+
+        return NotImplemented
 
     def __rmul__(self, other):
         return self.__mul__(other)
 
-    def evaluate_in_scope(self, *args, **kwargs):
+    def __truediv__(self, other):
+        inv = 1 / other
+        return self.__mul__(inv)
+
+    @property
+    def free_symbols(self):
+        return ()
+
+    def _sympy_(self):
+        return self
+
+    def replace(self, r, s):
+        return self
+
+    def evaluate_in_scope_(self, *args, **kwargs):
         # TODO: remove. It is currently required to avoid nesting this class in an expression for the MappedScope
         # We can maybe replace is with a HardwareScope or something along those lines
         return self
 
 
+_lambdify_modules.append({'SimpleExpression': SimpleExpression})
+
+
 RepetitionCount = Union[int, VolatileRepetitionCount, SimpleExpression[int]]
 HardwareTime = Union[TimeType, SimpleExpression[TimeType]]
 HardwareVoltage = Union[float, SimpleExpression[float]]
diff --git a/qupulse/program/linspace.py b/qupulse/program/linspace.py
index 7dc3ddc6..d224648b 100644
--- a/qupulse/program/linspace.py
+++ b/qupulse/program/linspace.py
@@ -124,7 +124,7 @@ def inner_scope(self, scope: Scope) -> Scope:
         process."""
         if self._ranges:
             name, _ = self._ranges[-1]
-            return MappedScope(scope, FrozenDict({name: SimpleExpression(base=0, offsets=[(name, 1)])}))
+            return scope.overwrite({name: SimpleExpression(base=0, offsets=[(name, 1)])})
         else:
             return scope