Granted, I’m not familiar with analog circuits, but $13 for something single purpose that’s easily done in digital circuits seems kind of expensive. What’s involved that makes that a reasonable price?
Reasonable for AD, I should have qualified. 
Creating an accurate analog multiplier with the characteristics declared by the AD633 is not easy.
At first glance, the translinear part needs a very good process to guarantee its component transistors are exactly matched, on which the precision and linearity of the product depends.
The linearity is also singularly tested on each IC.
The buried zener diode is laser trimmed.
As a single block, that chip is very easy to use: no external components, no calibrations etc - doing the same with discrete components, while possible, would be far more expensive, both for material costs and for calibration.
That might be enough of a schematic to throw at the circuit sim, thanks!
The Multiplier Application Guide that AD links to from the 633 datasheet goes into various purposes that multipliers can serve.
The fact that the document is a scan of a scuffed and faded 1978 print copy just…might…be a metalevel commentary on the state of applications for analog multipliers.
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Hee hee. I studied chemical engineering. I used to taunt my EE friends: “Aww, you’ve got equations an undergrad can solve. That’s so sweet!” Then I’d duck and run the fuck away, because objects were flying at me.
Of course, I never had to solve those massive equations, because undergrads couldn’t, so I had it easier. But I didn’t dwell on that with my EE peers. 
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I 100% would have been on the throwing side.
Nerd stuff follows.
TLDR: I had first hand experience of math in electronics.
My Electronics I c(o)urse was led by a professor who, to put it gently, didn’t give a fuck.
Always late for lessons, for the whole year he rambled about Gunn diodes and explained little else.
His assistants did 90% of the work.
When I got to the written test, we were given a quite simple circuit, a transistor based current source charging a capacitor, to analyze.
I wrote the analysis in the linear section (result: a straight rising line), and completed with an analysis in the saturation regime (the line tapered off to an horizontal).
I was confident I was going to get good grades (in fact, I went home and replicated the circuit…).
I go to the orals, and my test was rated barely sufficient (18/30).
The professor had just looked at the graph, saw it was not a straight line, and graded without reading, expecting only the linear part.
I complained quite vehemently, and he had to concede.
BUT he took his revenge:
“It’s quite clear you understand the practical side of electronics, let’s have some theory”.
He started from Schrodinger’s equation and went down from there.
After 30’ I managed to rip a 28/30 by mutual exhaustion.
But I had my revenge too: at the second session (I was not there, a fried related this to me) he publicly said:
“It’s possible that the guy with two surnames (that’d be me) was right, there’s some tests that need to be graded again…”.
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