I have only recently discovered the source code to the ZX Spectrum was put online during lockdown. Steven comments that he calculated the coefficients for the Chebyshev series himself for LN and EXP. I think he was trying to improve the accuracy when used together for roots. Note his last page words

This is the division error. As Dr Frank O’Hara stated the final jump back should be to the position I have indicated in red. He names it DIV-34TH. Implementation would create multiple errors because the parsing of fractional numbers uses fuzzy logic building numbers from repeating decimals.

The first computer Steve Vickers saw was Turing's Pilot Ace and when the Daily Mirror's reporter "Ruggles" asked Jim Wilkinson at NPL what happens when an error occurs he was told it blows a Raspberry. :-)

Steady, they own the rights to the Jupiter Ace. A USB Jupiter Ace keyboard would be nice for The Spectrum. The ZX Printer used silver paper that was burnt off by high voltage electric stylus to reveal black. Thermals use heat to release ink embedded in paper. Requires mains power or a battery.

“The Spectrum” is for sale at £79.99 now (up £20). Rampant ZX inflation Rachel.

Chris Curry’s Red Boxes that controlled switches via signals in the mains.
Set up using the ZX Spectrum and other computers e.g. Acorn. All done by bluetooth and radio now. I did have a mesh system that spread via the mains.

Amazon sold out. smythstoys still has ‘em for £59.99. Second best is PLAION at £67.49 until tonight.
Get your ZX Spectrum clone here.

I have just checked arounsband PLAION have it for 67.50 while Smyths Toys and Amazon Prime have it for £59.99 although check out the Amazon delivery. It says February. Probably a mistake.

And there is more from Andrew on Page 167

This is the one I bought first but it was £15. If you leave a good review it goes up. There are plenty of others but this does have an extra 13 rolls of paper.

ebay.us/m/AfMpvl

These bluetooth printers cost between £8 and £15 and could be adapted to USB data. They need the occasional recharge. My Alphacom 32 buffered the ZX81 and ZX Spectrum output until it had received two lines and then output them shimmying right and left.
Adapting would not cost much.
Jolly useful.

THE PRINTER. They can then do a ZX81/TS1000/TS1500 combination with the same printer. It would sell stateside.

The Acorn BBC Computer has a very respectable speed and accuracy rating. The ZX Spectrum and Timex machines are not bad for accuracy considering the maths is based on fuzzy logic. It is good to see David Ahl is still going. He put all his work in the public domain.
www.swapmeetdave.com/Ahl/DHA.htm

I go for precision at every turn. I have just made the ZX81 as accurate as the IBM PC. Imagine that back in 1981. Sinclair lost out because of deadlines and a fixation with forward compatibility. For a few bytes more or respite to find the space required. The math pack was frozen for the ZX Spectrum

On the ZX Spectrum Looking Glass ROM I had more room and after removing the red Z80 lines I added an iteration counter in K-DATA 23565. Many roots only require 1 try while most take 5 loops for a perfect solution.
The accompanying BASIC program shows the binary roots and loop counter.

I wrote that routine over 20 years ago on the sg81.rom which is preserved on wayback. The routines that use sqr - asn,acs use mem-0 to mem-2 for several Chebyshev series generations as does the original sqr function which uses to_power,ln and exp. The original ZX81 sqr uses mem-3 indirectly (exp).