Description
For strictly positive unequal actual and predicted, return sign(predicted - actual) × 4 × actual / (actual + predicted)^2.
A sensitivity is a local derivative with respect to a specified variable while other quantities are held fixed. Normalized metrics can have different derivatives from unnormalized sums.
For strictly positive unequal actual and predicted, return sign(predicted - actual) × 4 × actual / (actual + predicted)^2.
When to use this tool
Use Symmetric Percentage Error Local Slope when you need one clearly defined metric derivative.
How to use the tool and how it works
- Enter actual, predicted. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivative. Use the output convention below.
For strictly positive unequal actual and predicted, return sign(predicted - actual) × 4 × actual / (actual + predicted)^2.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| actual | Observed value on the same scale and unit as its prediction. | Required. Finite number; strictly above 0. |
| predicted | Predicted value on the same scale and unit as actual. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Derivative | Required. Finite number. |
{
"input": {
"actual": 2,
"predicted": 6
},
"output": {
"derivative": 0.125
}
}Limitations and assumptions
- This is the derivative with respect to predicted of the factor-two fractional symmetric error; equality is excluded because of the absolute-value kink.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Verify the aggregate definition and held-fixed quantities before using the derivative in optimization or uncertainty propagation.
References
Similar or alternative tools
- Symmetric Mape Denominator Convention
Divide factor × abs(predicted - actual) by abs(actual) + abs(predicted).
- Metrics: Smape Single Pair Zero Policy
Use 2 × abs(forecast - actual) / (abs(actual) + abs(forecast)) for smapeFraction.