How much will US draw down on its petroleum reserves to ease the price shock from the Iran war?
The US Strategic Petroleum Reserve as of April 24th is 397.9 million barrels, down from 415 million pre-war.
President Trump authorized the Department of Energy to release 172 million barrels from the Strategic Petroleum Reserve, beginning next week. This will take approximately 120 days to deliver based on planned discharge rates (March 11th, https://www.energy.gov/articles/united-states-release-172-million-barrels-oil-strategic-petroleum-reserve)
This market resolves based on the values officially reported by EIA - currently at https://www.eia.gov/petroleum/supply/weekly/ under "Petroleum Balance Sheet" (will update if the source changes). Only values for May 2026 or later count for the question
Some historical trends below: (source: https://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=pet&s=mcsstus1&f=m, note that this is in thousands of barrels)

The lowest value in recent history is 347.1 million barrels from June 2023