($define! real->inexact
  ($λ (real)
    ($if (inexact? real) real
         (zero? real)    0.0
         ($let* ((absolute    (abs real))
                 ;; When absolute = 1, it doesn't matter: pick
                 ;; the lowest of the two.
                 (exponent    ($if (>=? absolute 1)
                                   (- (integer-length (floor absolute)) 53)
                                   (max -1074 (- -52 (integer-length (floor (/ 1 absolute)))))))
                 (scaled      (* real (expt 2 (- 0 exponent))))
                 (significand (round-quotient (numerator scaled)
                                              (denominator scaled))))
           (* (expt 2.0 exponent) significand)))))