Test a conversion together with its intended inverse. Equality of representations may need normalization, while equality of numerical values can be limited by floating-point rounding or truncation. Distinct strings can encode the same value, so a value round trip and a character-for-character round trip are different properties.
An independent oracle is still needed: the wrong functions and satisfy both composition identities on integers, although neither implements an intended identity conversion. Thus passing inverse-consistency tests does not alone establish the specification of either conversion.
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