\[\frac{x - lo}{hi - lo}\]

↓

\[\frac{x - lo}{hi - lo}\]

double f(double lo, double hi, double x) {
        double r83765 = x;
        double r83766 = lo;
        double r83767 = r83765 - r83766;
        double r83768 = hi;
        double r83769 = r83768 - r83766;
        double r83770 = r83767 / r83769;
        return r83770;
}

↓

double f(double lo, double hi, double x) {
        double r83771 = x;
        double r83772 = lo;
        double r83773 = r83771 - r83772;
        double r83774 = hi;
        double r83775 = r83774 - r83772;
        double r83776 = r83773 / r83775;
        return r83776;
}

\frac{x - lo}{hi - lo}

↓

\frac{x - lo}{hi - lo}

Error

The X axis uses an exponential scale — Bits error versus `lo`

Derivation

Initial program 62.0
\[\frac{x - lo}{hi - lo}\]
Final simplification62.0
\[\leadsto \frac{x - lo}{hi - lo}\]

Reproduce

herbie shell --seed 2019101 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))