Description
For numerator / denominator, return partial derivatives 1 / denominator and -numerator / denominator².
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 numerator / denominator, return partial derivatives 1 / denominator and -numerator / denominator².
When to use this tool
Use Ratio Metric Sensitivity when you need one clearly defined metric derivative.
How to use the tool and how it works
- Enter numerator, denominator. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read numeratorDerivative, denominatorDerivative. Use the output convention below.
For numerator / denominator, return partial derivatives 1 / denominator and -numerator / denominator². Require a nonzero denominator.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| numerator | Numerator | Required. Finite number. |
| denominator | Denominator | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| numeratorDerivative | Numerator Derivative | Required. Finite number. |
| denominatorDerivative | Denominator Derivative | Required. Finite number. |
{
"input": {
"numerator": 10,
"denominator": 2
},
"output": {
"numeratorDerivative": 0.5,
"denominatorDerivative": -2.5
}
}Limitations and assumptions
- These are local derivatives, not propagated uncertainty bounds; input covariance and nonlinear effects are omitted.
- 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
- Weighted Mae One Weight Sensitivity
Subtract meanError from abs(actual - predicted) and divide by positive totalWeight for derivative.
- Mse Single Observation Gradient
Compute 2 × weight × (predicted - actual) / denominator, with nonnegative weight and positive denominator.