(/ (- x lo) (- hi lo))

Average Error: 62.0 → 62.0

Time: 3.2s

Precision: 64

\[lo \lt -1.000000000000000010979063629440455417405 \cdot 10^{308} \land hi \gt 1.000000000000000010979063629440455417405 \cdot 10^{308}\]

Math

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

↓

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

C

double f(double lo, double hi, double x) {
        double r2066823 = x;
        double r2066824 = lo;
        double r2066825 = r2066823 - r2066824;
        double r2066826 = hi;
        double r2066827 = r2066826 - r2066824;
        double r2066828 = r2066825 / r2066827;
        return r2066828;
}

↓

double f(double lo, double hi, double x) {
        double r2066829 = x;
        double r2066830 = lo;
        double r2066831 = r2066829 - r2066830;
        double r2066832 = hi;
        double r2066833 = r2066832 - r2066830;
        double r2066834 = r2066831 / r2066833;
        return r2066834;
}

Error

Bits error versus lo

Bits error versus hi

Bits error versus x

Derivation

1. Initial program 62.0

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

2. Final simplification 62.0

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

Reproduce

herbie shell --seed 2019172 
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))