The fact that evaluating ∇f(x) is as fast as f(x) is very important and often misunderstood http://timvieira.github.io/blog/post/2016/09/25/evaluating-fx-is-as-fast-as-fx/ …https://twitter.com/gabrielpeyre/status/1167663307668373504 …
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got it. I thought misunderstanding was on computing the gradient not on the asymptotic complexity.
The analysis can be stated more tightly BTW. It's something like FLOPS{ ∇f } ≤ 4*FLOPS{ f }, but I have to look it up in Griewank and Walther.
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