3.3 Strongly Nonlinear Function

Next, consider something that would be difficult to calculate analytically, wide-ranging errors across a nonlinear function.

$pi = 3.14159 +- 1; calculate sin($pi/2);

The result is

$pi=3.14159 +- 1; calculate sin($pi/2); Result without perturbation: 1 Result with symmetric tails: 0.985588 +- 0.0796836 Result with asymmetric tails: 0.985588 (0.840605 to 0.999973)

Note that the asymmetric-tail is more meaningful in this instance.