(12C Platinum) Normal Distribution

[Dieter]

(12-02-2018 08:14 PM)Albert Chan Wrote:  

(12-02-2018 06:59 PM)Dieter Wrote:  There now is a new approximation with focus on the absolute error. But in a somewhat different way: With the following coefficients the error is less than 6,5 units in the 7th significant digit ...

For x = 0 to 5, confirmed on the 6.5e-7 maximum absolute error ...

However, the old constants did even better, max abs. error = 5.1e-7

It's 6,5 units in the 7th significant (!) digit. Not an absolute error of 6,5 E-7. The previous approximation had a largest error of about 1 unit in the 6th significant digit, now this is down to 65% of that.

Compare the results for x=3,1:

Result for the coefficients in post #6: 9,676022 E-04
Compare this to the true result 9,676032 E-04
The error is about -1 unit in the 6th significant digit.

Result for the coefficients in post #7: 9,676026 E-04
Compare this to the true result 9,676032 E-04
The error is about -6 units in the 7th significant digit.

The coefficients in post #7 limit this kind of error to less than 6,5 units in the 7th digit. These are simply two different targets both approximations are designed for.

Dieter