Finite-strain viscoelastic models require internal variables to represent material memory. Storing a history tensor for every Prony branch at each quadrature point can become costly in large finite element simulations. We assess how reduced-precision history storage affects memory requirements and displacement accuracy, separating storage precision from computational precision. A Mooney--Rivlin--Prony model is evaluated in a three-dimensional torsion--hold--release benchmark on three HEX8 meshes. We compare 64-bit double-precision (FP64), 32-bit single-precision (FP32), unscaled 16-bit half-precision (FP16) storage, and two scaled FP16 policies. Unscaled FP16 converts history components directly to FP16 without rescaling. Constitutive evaluation and mechanical solution remain in FP64. The scaled policies use shared FP32 scales for individual history tensors or element--branch groups. We also assess elementwise constant histories updated from projected driving stresses. Displacement errors are measured against per-quadrature-point FP64 on the same mesh using global relative and maximum component errors. Per-quadrature-point FP32 reduces history storage while keeping relative displacement errors below 1.6e-5 % over the saved configurations. Unscaled FP16 reduces storage to 25% of the baseline, with peak relative errors of approximately 6--7%. Scaling extends the representation to the effective FP16 range but provides little improvement in displacement accuracy in this benchmark. Elementwise FP32 reduces storage to 6.25% of the baseline, with a peak relative error of 1.07% on the finest mesh. Errors due to elementwise history approximation decreased with mesh refinement. These results support FP32 history storage for the tested problem and quantify the accuracy trade-off associated with further compression.