The current specialized-path evidence separates activation derivatives, Laplacians, and repeated Laplacians. These workloads have different representations and baselines.
What is recorded
The published float64 CPU figures use nine timed repeats. Activation measurements use Torch eager execution; operator measurements use JAX JIT with runtime inputs and weights, with compilation recorded separately.
For example, the order-eight tanh activation derivative records 0.1405 ms against 30.9908 ms for Torch nested autograd on 20,000 inputs. This is derivative evaluation, not a training-speed multiplier.
Accuracy is a separate measurement
Successful methods are checked against independent 80-digit references at sampled inputs. Closed-form evaluation can still suffer cancellation. An unfinished run has no measured speedup.
The general deep-network comparison includes cases where JAX Taylor-mode wins. Those results are part of a useful account of the tradeoffs.