pH buffer other than TA?

It seems that things go astray once the magnitude of pH change is beyond 0.4 and/or the pH is above 7.6. The app warns of this, but the magnitude of the estimation error surprised me. If I understand correctly, this is how it's calculated (for 31.45% HCl and no borates):

1. Calculate the difference between current pH and target pH.
2. Multiply the result by the pool volume (in US gallons) and keep the result as variable a.
3. Calculate the median of current pH and target pH and keep the result as variable b.
4. Store the pool's TA value as variable c.
5. Solve 0.008726(-0.1943b3 + 6.0752b2 - 60.1221b + 192.163) × (c + 13.91) and store the result as variable d.
6. Solve (d × a) / 240.15

In my case this gives:

((192.1626 - 60.1221×7.85 + 6.0752×7.85×7.85 - 0.1943×7.85×7.85×7.85)×(80 + 13.91)/114.6) × 14000) / 241.15 = 27.78

I'm wondering why the much simpler approach used in the "Effects of Adding" isn't used in all cases? For instance, in my case we could calculate it as:

a = ((200 b - 1) g)/48030

Where a is the amount of 31.45% HCl to add in oz., b is the magnitude of pH change desired (i.e., 0.7), and g is the pool volume in gallons.

I'm sure it's because there's something in the chemistry I don't understand. This is going to be a discussion for the Deep End.
 
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