diff --git a/DifferentiationInterface/docs/src/explanation/backends.md b/DifferentiationInterface/docs/src/explanation/backends.md
index 0ad276905..f1edbaad6 100644
--- a/DifferentiationInterface/docs/src/explanation/backends.md
+++ b/DifferentiationInterface/docs/src/explanation/backends.md
@@ -137,12 +137,9 @@ For every operator, preparation generates an [executable function](https://brian
 ### FiniteDiff
 
 Whenever possible, preparation creates a cache object.
-Pushforward is implemented rather slowly using a closure.
 
 ### FiniteDifferences
 
-Nothing specific to mention.
-
 ### ForwardDiff
 
 We implement [`pushforward`](@ref) directly using [`Dual` numbers](https://juliadiff.org/ForwardDiff.jl/stable/dev/how_it_works/), and preparation allocates the necessary space.
@@ -155,12 +152,9 @@ Most operators fall back on `AutoForwardDiff`.
 ### ReverseDiff
 
 Wherever possible, preparation records a [tape](https://juliadiff.org/ReverseDiff.jl/dev/api/#The-AbstractTape-API) of the function's execution.
-This tape is computed from the arguments `x` and `contexts...` provided at preparation time.
-It is control-flow dependent, so only one branch is recorded at each `if` statement.
 
-!!! danger
-    If your function has value-specific control flow (like `if x[1] > 0` or `if c == 1`), you may get silently wrong results whenever it takes new branches that were not taken during preparation.
-    You must make sure to run preparation with an input and contexts whose values trigger the correct control flow for future executions.
+!!! warning
+    This tape is specific to the control flow inside the function, and cannot be reused if the control flow is value-dependent (like `if x[1] > 0`).
 
 ### Symbolics
 
@@ -182,3 +176,4 @@ Same-point preparation runs the forward sweep and returns the pullback closure a
 
 We implement `pullback` based on `Zygote.pullback`.
 Same-point preparation runs the forward sweep and returns the pullback closure at `x`.
+
diff --git a/DifferentiationInterface/docs/src/explanation/operators.md b/DifferentiationInterface/docs/src/explanation/operators.md
index d8e257c54..1f6a2e84f 100644
--- a/DifferentiationInterface/docs/src/explanation/operators.md
+++ b/DifferentiationInterface/docs/src/explanation/operators.md
@@ -125,14 +125,13 @@ Here are the general rules that we strive to implement:
 
 For different-point preparation, the output `prep` of `prepare_op(f, b, x, [t])` can be reused in `op(f, prep, b, other_x, [other_t])`, provided that:
 
-- the inputs `x` and `other_x` have the same types and sizes
-- the tangents in `t` and `other_t` have the same types and sizes
+- the inputs `x` and `other_x` have similar types and equal shapes
+- the tangents in `t` and `other_t` have similar types and equal shapes
 
 For same-point preparation, the output `prep` of `prepare_op_same_point(f, b, x, [t])` can be reused in `op(f, prep, b, x, other_t)`, provided that:
 
-- the input `x` remains exactly the same (as well as any [`Constant`](@ref) context)
-- the tangents in `t` and `other_t` have the same types and sizes
+- the input `x` remains the same (as well as the [`Context`](@ref) constants)
+- the tangents in `t` and `other_t` have similar types and equal shapes
 
 !!! warning
-    These rules hold for the majority of backends, but there are some exceptions.
-    The most important exception is [ReverseDiff](@ref) and its taping mechanism, which is sensitive to control flow inside the function.
+    These rules hold for the majority of backends, but there are some exceptions.
\ No newline at end of file