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

↓

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

double f(double lo, double hi, double x) {
        double r83764 = x;
        double r83765 = lo;
        double r83766 = r83764 - r83765;
        double r83767 = hi;
        double r83768 = r83767 - r83765;
        double r83769 = r83766 / r83768;
        return r83769;
}

↓

double f(double lo, double hi, double x) {
        double r83770 = x;
        double r83771 = lo;
        double r83772 = r83770 - r83771;
        double r83773 = hi;
        double r83774 = r83773 - r83771;
        double r83775 = r83772 / r83774;
        return r83775;
}

\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 2019102 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))