Editing Toom–Cook multiplication (section)

==== Faster evaluation ====
Multipoint evaluation can be obtained faster than with the above formulas. The number of elementary operations (addition/subtraction) can be reduced. The sequence given by Bodrato<ref name="Bodrato2007"/> for Toom-3, executed here over the first operand (polynomial ''p'') of the running example is the following:

:{|
|-
|''p''<sub>0</sub> || ← || ''m''<sub>0</sub> + ''m''<sub>2</sub> || = || 56789012 + 123456 || = ||align="right"| 56912468
|-
|''p''(0) || = || ''m''<sub>0</sub> || = || 56789012 || = ||align="right"| 56789012
|-
|''p''(1) || = || ''p''<sub>0</sub> + ''m''<sub>1</sub> || = || 56912468 + 78901234 || = ||align="right"| 135813702
|-
|''p''(−1) || = || ''p''<sub>0</sub> − ''m''<sub>1</sub> || = || 56912468 − 78901234 || = ||align="right"| −21988766
|-
|''p''(−2) || = || (''p''(−1) + ''m''<sub>2</sub>) × 2 − ''m''<sub>0</sub> || = ||align="right"| (− 21988766 + 123456 ) × 2 − 56789012 || = || − 100519632
|-
|''p''(∞) || = || ''m''<sub>2</sub> || = || 123456 || = ||align="right"| 123456.
|}

This sequence requires five addition/subtraction operations, one less than the straightforward evaluation. Moreover the multiplication by 4 in the calculation of ''p''(−2) was saved.