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For inverse hyperbolic sine and cosine, an input of one thousand gives a finite value. But the tested MLX returns a zero derivative.

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The correct slope is about zero point zero zero one, which fits in float sixteen. Both forward and reverse differentiation lose it.

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The derivative rule first squares the input. That intermediate overflows. Taking its reciprocal square root then produces zero.

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A scaled composition makes the error about one. Finite differences of the actual forward function independently support a nonzero first derivative.

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A normalized derivative formula passes all five hundred eighteen comparisons across four types. Float thirty two and float sixty four also include higher derivatives.

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This is one shared defect in two functions. The full report includes code, source pins, and limits. GPU behavior and performance were not tested.