Relative error.

This is more difficult to calculate than it first appears [1,2]. The usual formula for the relative error between an actual value A and an expected value E is |(A-E)/E|, but:

1. If the expected value is 0, any other value has infinite relative error, which is counter-intuitive: if the expected voltage is 0, getting 1/10th of a volt doesn't feel like an infinitely large error.

2. This formula does not satisfy the mathematical definition of a metric [3]. [4] solved this problem by defining the relative error as |ln(|A/E|)|, but that formula only works if all values are positive: for example, it reports the relative error of -10 and 10 as 0.

Our implementation sticks with convention and returns:

• 0 if the actual and expected values are both zero
• Infinity if the actual value is non-zero and the expected value is zero
• |(A-E)/E| in all other cases

[1] https://math.stackexchange.com/questions/677852/how-to-calculate-relative-error-when-true-value-is-zero [2] https://en.wikipedia.org/wiki/Relative_change_and_difference [3] https://en.wikipedia.org/wiki/Metric_(mathematics)#Definition [4] F.W.J. Olver: "A New Approach to Error Arithmetic." SIAM Journal on Numerical Analysis, 15(2), 1978, 10.1137/0715024.