Update development log

LOG.md

@@ -193,3 +193,48 @@ the evaluators were run in sequence on any input expression.
 To combine more than two evaluators, I created a `pipeline` macro that
 constructs nested compositions of evaluators with Rust's `macro_rules`
 system.
+
+### Differentiator
+
+The differentiation pass itself was very easy to implement given the
+simplications made by first having a normalisation pass.  I also had
+decided to only support constant exponents, which simplifies things
+too.  In the end, it ended up being more-or-less a fairly direct
+translation of the sum rule and product rule into code, along with the
+power rule and chain rule combined for handling exponents.
+
+### Simplification
+
+The output of the differentiation pass was correct but contained a lot
+of noise such as terms multiplied by zero and other similar things.  I
+therefore implemented a basic simplification pass that applied various
+identities such as `x + 0 = x`, `0x = 0` and `1x = 1`.  Expression
+simplification is famously a very complex problem, but I kept this
+pass quite limited in scope and only implemented the most high-payoff
+features.
+
+### Canonicalisation
+
+To make the output a little easier to read, the final evaluation pass
+I implemented was a limited multiplication reordering canonicalisation
+pass that ensured that products had the constants first.  This is
+still incomplete as the re-ordering only takes place within binary
+products (so `x*4` becomes `4x`, but `x*(y*4)` would become `x*4y` not
+`4xy`), and terms in a sum were not re-ordered at all.  However, I
+decided full canonicalisation would be excessively complex for this
+project and decided to leave it there, as the output was acceptably
+readable at this point anyway.
+
+### Wrapping up
+
+The final pipeline I ended up with was:
+
+1. Normalisation
+2. Differentiation
+3. Constant folding
+4. Simplification
+5. Constant folding again
+6. Canonicalisation
+
+I then created an `evaluator` function to wrap this up in the `eval`
+module, to allow for a simple interface to the whole library.