Description
Evaluate sinh(x)/(cosh(x)+1) using its equivalent tanh(x/2), avoiding direct formation of potentially overflowing hyperbolic functions.
Hyperbolic tangent maps a real argument to values between -1 and 1. Input scaling or temperature changes its slope and location in input coordinates. A derivative with respect to temperature differs from differentiation with respect to the scalar input.
Evaluate sinh(x)/(cosh(x)+1) using its equivalent tanh(x/2), avoiding direct formation of potentially overflowing hyperbolic functions.
When to use this tool
Use Tanh Half Angle Ratio when checking the stated hyperbolic-tangent coordinate or derivative convention.
How to use the tool and how it works
- Enter x. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read ratio. Use the output convention below.
Evaluate sinh(x)/(cosh(x)+1) using its equivalent tanh(x/2), avoiding direct formation of potentially overflowing hyperbolic functions.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | Finite scalar input coordinate; use the mathematical scale specified above. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| ratio | Ratio | Required. Finite number. |
{
"input": {
"x": 1.0986122886681096
},
"output": {
"ratio": 0.49999999999999994
}
}Limitations and assumptions
- Returns a scalar identity; finite-precision saturation can return exactly -1 or 1 at large magnitudes.
- 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
Use the complete explicit function and the intended parameter, branch and numerical conventions for symbolic, tensor or model-level differentiation; assess training behavior independently.
References
Similar or alternative tools
- Tanh Inflection Distance
Return inflectionX=-bias/slope, signedDistance=x-inflectionX and argumentDistance=abs(slope)*abs(signedDistance).
- Activation: Tanh Scalar Second Derivative
Let t=tanh(x).