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Precision Error
Precision Error
The plots in this Demonstration show precision error. The formula is true for all real . To plot for various , Mathematica correctly finds numerical values very close to 0. In the plot, these infinitesimal deviations are magnified a quadrillion-fold.
arctan(x)+arctan(1/x)=π/2
x≠0
arctan(kx)+arctan(1/(kx))-π/2
k
Various types of machine error—round-off, precision, accumulated—have led to the loss of lives and fortunes. For example, the Patriot missile system relies on a .1 second internal clock. The binary machine considers this as a 209715/2097152 second clock. In a 1991 incident during Operation Desert Storm, after being on for 100 hours, the missile tracking timing had accumulated a .34 second error. This rendered it unable to track an incoming missile, which subsequently fell intact on a barracks and killed 28 people.