Use 'demonstrably' when you can back up your statement with clear evidence or proof. The new policy is demonstrably more efficient, as seen in the recent performance metrics.
Pro Tip 2/3
Visible Results
'Demonstrably' implies that the results of something are clearly visible, not just a matter of opinion. The company's growth is demonstrably evident in its expanding number of employees.
Pro Tip 3/3
Avoid Uncertainty
Don't use 'demonstrably' if the situation is ambiguous or open to interpretation; it should be straightforward. Their technology is demonstrably advanced, with no other rivals coming close.