tanh rule in v1.74.11 fails on symbolic inputs ("non-boolean (Num) used in boolean context") #871

Since v1.74.11 (#864), the tanh rule picks between two formulas with a ternary:

@scalar_rule tanh(x) abs(real(x)) < 1 ? 1 - Ω ^ 2 : sech(x) ^ 2

The ternary needs a Bool. For a symbolic x (e.g. Symbolics.Num), abs(real(x)) < 1 is a symbolic expression, so frule / derivatives_given_output throws.

Reproducer

using ChainRules, ChainRulesCore, Symbolics
@variables x
frule((NoTangent(), true), tanh, x)

ERROR: TypeError: non-boolean (Symbolics.Num) used in boolean context
Stacktrace:
 [1] derivatives_given_output(Ω::Num, ::typeof(tanh), x::Num)
   @ ChainRules ~/.julia/packages/ChainRules/.../src/rulesets/Base/fastmath_able.jl:42
 [2] frule(::Tuple{NoTangent, Bool}, ::typeof(tanh), x::Num)
   @ ChainRules ~/.julia/packages/ChainRules/.../src/rulesets/Base/fastmath_able.jl:42

The stack trace is from a CI failure in which TaylorDiff.jl hit this while precompiling (log). The snippet above reconstructs that call and hasn't been run on its own.

Impact

TaylorDiff.jl (v0.3.5) evaluates ChainRules rules on Symbolics variables while it precompiles, so it now fails to precompile. That in turn breaks everything that depends on it, e.g. NonlinearSolveHomotopyContinuation and the ModelingToolkit HomotopyContinuation extension tests. We see this in downstream CI: v1.74.10 passes, v1.74.11 and later fail, and v1.74.13 still has the ternary.

Suggested fix

Use ifelse instead of the ternary. Symbolics and similar packages overload it for symbolic conditions:

@scalar_rule tanh(x) ifelse(abs(real(x)) < 1, 1 - Ω ^ 2, sech(x) ^ 2)

ifelse always computes both branches, which costs one extra sech for ordinary numbers, but gives the same result. The other rules changed in #864 may be worth checking for the same problem with non-Bool comparisons.

(Diagnosed with the help of Claude Code.)