(/ (- 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 r2300145 = x;
        double r2300146 = lo;
        double r2300147 = r2300145 - r2300146;
        double r2300148 = hi;
        double r2300149 = r2300148 - r2300146;
        double r2300150 = r2300147 / r2300149;
        return r2300150;
}

↓

double f(double lo, double hi, double x) {
        double r2300151 = x;
        double r2300152 = lo;
        double r2300153 = r2300151 - r2300152;
        double r2300154 = hi;
        double r2300155 = r2300154 - r2300152;
        double r2300156 = r2300153 / r2300155;
        return r2300156;
}

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 2019179 
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))