Do not use bus field variables. (#3171)

Removes the special introduction and removal of bus variables because
the solver can now handle this on its own through the `LinearizedSolver`
component. It also has the benefit that we do not need to run the
optimizer twice any more (once with bus interaction variables and once
without).

Previously we would introduce a new variable type outside of the solver
and replace all bus interactions `bus_interaction(1, x + y * z)` by
`bus_interaction(1, bus_var_1)` and the algebraic constraint `bus_var_1
= x + y * z`.

Now the `LinearizedSolver` is a component inside the solver that
replaces all bus interaction fields (that are not already constants or
simple variables) and also replaces all non-linear components:

`bus_interaction(1, x + y * z)`

becomes

```
bus_interaction(1, v1)
v1 = x + v2
v2 = y * z
```

The reason behind also replacing non-linear parts is because range
constraints are only stored for variables, not for all sub-expressions.
Also if we find the same non-linear sub-expression multiple times, we
can now replace it directly by the same variable.

---------

Co-authored-by: Georg Wiese <georgwiese@gmail.com>

constraint-solver/src/indexed_constraint_system.rs

@@ -217,7 +217,7 @@ fn retain<V, Item>(
     occurrences.retain(|_, occurrences| !occurrences.is_empty());
 }
 
-impl<T: RuntimeConstant, V: Clone + Ord + Hash> IndexedConstraintSystem<T, V> {
+impl<T: RuntimeConstant, V: Clone + Eq + Hash> IndexedConstraintSystem<T, V> {
     /// Adds new algebraic constraints to the system.
     pub fn add_algebraic_constraints(
         &mut self,

constraint-solver/src/journaling_constraint_system.rs

@@ -68,6 +68,24 @@ impl<T: RuntimeConstant + Substitutable<V>, V: Ord + Clone + Eq + Hash + Display
     }
 }
 
+impl<T: RuntimeConstant, V: Clone + Eq + Hash> JournalingConstraintSystem<T, V> {
+    /// Adds new algebraic constraints to the system.
+    pub fn add_algebraic_constraints(
+        &mut self,
+        constraints: impl IntoIterator<Item = GroupedExpression<T, V>>,
+    ) {
+        self.system.add_algebraic_constraints(constraints);
+    }
+
+    /// Adds new bus interactions to the system.
+    pub fn add_bus_interactions(
+        &mut self,
+        bus_interactions: impl IntoIterator<Item = BusInteraction<GroupedExpression<T, V>>>,
+    ) {
+        self.system.add_bus_interactions(bus_interactions);
+    }
+}
+
 impl<T: RuntimeConstant, V: Clone + Eq> JournalingConstraintSystem<T, V> {
     /// Removes all algebraic constraints that do not fulfill the predicate.
     pub fn retain_algebraic_constraints(

constraint-solver/src/solver/base.rs

@@ -1,4 +1,5 @@
 use itertools::Itertools;
+use num_traits::Zero;
 use powdr_number::{ExpressionConvertible, FieldElement};
 
 use crate::constraint_system::{BusInteraction, BusInteractionHandler, ConstraintRef};
@@ -84,7 +85,7 @@ where
     ) {
         self.equivalent_expressions_cache.clear();
         self.constraint_system
-            .add_algebraic_constraints(constraints);
+            .add_algebraic_constraints(constraints.into_iter().filter(|c| !c.is_zero()));
     }
 
     fn add_bus_interactions(