you will need to use a hashing algorithm that can handle a sufficiently large number of items
I didn't expect SHA256 to be so slow. I just tested a simple bash loop, and get less than 1000 hashes per second. That won't scale well to 40 billion inputs.As @vjudeu said, you used un-optimized tool. You should use optimized tool such as hashcat. Even on single core VPS, i managed to get ~5000 kH/s.
Currently I work on piece of software for someone who has lost access to his brainwallet. He knows the way how to produce the phrase, but as it contains some (unknown) number, we must check many possible phrases. The list of potential addresses is very small (just a few), so it is not a factor which slows us down - it is rather priv->pub generation. Initial sha256 and later Hash160 are very fast. The main problem would be to compare generated hash160 against huge database of addresses (& of course generation for both compressed and uncompressed keys). At this stage of project we have speed 47Mkey on RTX 3060 and a little more than 100Mkeys on 3090 - but we are progressing every day
