The accuracy of the result can be influenced in a considerable way by the word width. For instance when the word width is 32 bits and the integration step h=1s, only the accuracy of computation of the equation (20) shown in Tab.6 can be reached.
| Reduced value y(1) | ORD | Absolute error |
| 2. | 1 | -7.183E-0001 |
| 2. | 2 | -2.183E-0001 |
| 2.7 | 3 | -5.162E-0002 |
| 2.71 | 4 | -9.948E-0003 |
| 2.718 | 5 | -1.615E-0003 |
| 2.7182 | 6 | -2.263E-0004 |
| 2.7182 | 7 | -2.785E-0005 |
| 2.718281 | 8 | -3.053E-0006 |
| 2.718281 | 9 | -2.980E-0007 |
| 2.7182818 | 10 | -2.421E-0008 |
| 2.71828182 | 11 | 1.863E-0009 |
| 2.71828182 | 12 | 1.863E-0009 |
| 2.71828182 | 13 | 1.863E-0009 |
Tab.6: 32 bit arithmetic
With a specially constructed 128-bit arithmetic a very high computation accuracy for the equation (20) can be reached even with the integration step h=1s (Tab.7).
Given an integration step h, it is very important
| Reduced value y(1) | ORD | Abs err |
| 2. | 1 | -7.183E-0001 |
| 2. | 2 | -2.183E-0001 |
| 2.7 | 3 | -5.162E-0002 |
| 2.71 | 4 | -9.948E-0003 |
| 2.718 | 5 | -1.615E-0003 |
| 2.7182 | 6 | -2.663E-0004 |
| 2.7182 | 7 | -2.786E-0005 |
| 2.718281 | 8 | -3.059E-0006 |
| 2.7182818 | 9 | -3.029E-0007 |
| 2.71828182 | 10 | -2.731E-0008 |
| 2.718281828 | 11 | -2.261E-0009 |
| 2.7182818284 | 12 | -1.729E-0010 |
| 2.71828182845 | 13 | -1.229E-0011 |
| 2.71828182845 | 14 | -8.155E-0013 |
| 2.71828182845904 | 15 | -5.077E-0014 |
| 2.718281828459045 | 16 | -2.976E-0015 |
| 2.7182818284590452 | 17 | -1.648E-0016 |
| 2.71828182845904523 | 18 | -8.652E-0018 |
| 2.7182818284590452353 | 19 | -4.315E-0019 |
| 2.7182818284590452353 | 20 | -2.050E-0020 |
| 2.7182818284590452353602 | 21 | -9.300E-0022 |
| 2.71828182845904523536028 | 22 | -4.036E-0023 |
| 2.7182818284590452353602874 | 23 | -1.679E-0024 |
| 2.7182818284590452353602874 | 24 | -6.704E-0026 |
| 2.718281828459045235360287471 | 25 | -2.575E-0027 |
| 2.7182818284590452353602874713 | 26 | -9.523E-0029 |
| 2.718281828459045235360287471352 | 27 | -3.397E-0030 |
| 2.7182818284590452353602874713526 | 28 | -1.170E-0031 |
| 2.718281828459045235360287471352662 | 29 | -3.896E-0033 |
| 2.71828182845904523536028747135266249 | 30 | -1.255E-0034 |
| 2.718281828459045235360287471352662497 | 31 | -3.910E-0036 |
| 2.7182818284590452353602874713526624977 | 32 | -1.102E-0037 |
| 2.7182818284590452353602874713526624977 | 33 | 4.408E-0039 |
| 2.7182818284590452353602874713526624977 | 34 | 4.408E-0039 |
| 2.7182818284590452353602874713526624977 | 35 | 4.408E-0039 |
Tab.7: 128 bit arithmetic