non-standard exponential-squared fog attenuation

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I inherited a formula that I'm hoping to simplify.

$d = \frac{\sqrt{-\log_2(t)}}{f\sqrt{\ln(2)}}$

Any ideas?

Thanks, Jason

EDIT (for context): This formula determines the exponent for exponential-squared fog attenuation. d stands for density, which is usually not so complicated, and the typical final usage is:

$\frac{1}{e^{{distance * density}^2}}$