revert relaxed root

[verheem]

Fixes #2356 by reverting to a previous implementation first introduced at #1750

Achieved performance gain:

HollandseDelta_parameterized_2025_6_0
relaxed_root_old = Computation time: 1 minute, 17 seconds, 392 milliseconds
relaxed_root = Computation time: 3 minutes, 9 seconds, 247 milliseconds

[Copilot]

Pull Request Overview

This PR updates the relaxed_root function’s threshold branch by replacing the original cubic smoothing polynomial and removing the intermediate x_scaled variable.

• Replaced the previous x_scaled-based cubic expression with a new condensed formula.
• Removed the x_scaled temporary variable.

Comments suppressed due to low confidence (2)

core/src/util.jl:713

• There aren’t any tests covering the threshold branch of relaxed_root; please add unit tests around values near threshold to validate the smoothing behavior.

if abs(x) < threshold

core/src/util.jl:714

• The new polynomial in the threshold branch no longer matches the original smoothing behavior and will produce incorrect values; please restore or correct the intended formula.

1 / 4 * (x / sqrt(threshold)) * (5 - (x / threshold)^2)

[visr]

Looks good!

Copying what you mentioned in the chat here:

HollandseDelta_parameterized_2025_6_0
relaxed_root_old = Computation time: 1 minute, 17 seconds, 392 milliseconds
relaxed_root = Computation time: 3 minutes, 9 seconds, 247 milliseconds