Wolfram Mathematica – it is designed for smart and highly educated people – CAS with M-expr LISP frontend isn't for everybody. Math Notes is designed for children of ages 6-99.
Handheld calculators that calculate logs require a human to hit buttons; that's the rate limiting process.
Both the calculator and slide rule are fast at the actual table lookup. The hairline mark on the slide rule's cursor performs a fast lookup; it instantaneously links the input value with its logarithm.
It's the button punching on the calculator, or sliding of the cursor of the slide rule, and the reading of the result, that are slow.
The limitations of slide rules compared to calculators are:
- precision: you can't get anywhere near a six figure logarithm or product. In engineering, you usually don't need this; but you do need intuition for being in the right ballpark. Forget slide rules for accounting/finance though.
- variety of functions: there are only so many tables you can fit on a slide rule before it becomes unwieldy.
- lack of registers for recalling prior values, such as frequently reused intermediaries. Even the cheapest, simples calculators usually have an accumulator register you can add to or subtract from, recall and clear. The user can have several slide rules to have multiple cursors left at different values.
The actual speed of calculating what is available, with the available precision, is not bad. The game-changing speed difference comes with programmable calculators.