Editing Automatic differentiation (section)

===== Pseudocode =====
Forward accumulation calculates the function and the derivative (but only for one independent variable each) in one pass. The associated method call expects the expression ''Z'' to be derived with regard to a variable ''V''. The method returns a pair of the evaluated function and its derivative. The method traverses the expression tree recursively until a variable is reached. If the derivative with respect to this variable is requested, its derivative is 1, 0 otherwise. Then the partial function as well as the partial derivative are evaluated.<ref name=demm22>{{cite book|author = Maximilian E. Schüle, Maximilian Springer, [[Alfons Kemper]], [[Thomas Neumann]] |title=Proceedings of the Sixth Workshop on Data Management for End-To-End Machine Learning |chapter=LLVM code optimisation for automatic differentiation |date=2022|pages=1–4 |doi = 10.1145/3533028.3533302|isbn=9781450393751 |s2cid=248853034 |language=English}}</ref>
<syntaxhighlight lang="cpp">
tuple<float,float> evaluateAndDerive(Expression Z, Variable V) {
   if isVariable(Z)
      if (Z = V) return {valueOf(Z), 1};
      else return {valueOf(Z), 0};
   else if (Z = A + B)
      {a, a'} = evaluateAndDerive(A, V);
      {b, b'} = evaluateAndDerive(B, V);
      return {a + b, a' + b'};
   else if (Z = A - B)
      {a, a'} = evaluateAndDerive(A, V);
      {b, b'} = evaluateAndDerive(B, V);
      return {a - b, a' - b'};
   else if (Z = A * B)
      {a, a'} = evaluateAndDerive(A, V);
      {b, b'} = evaluateAndDerive(B, V);
      return {a * b, b * a' + a * b'};
}
</syntaxhighlight>