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

Average Error: 62.0 → 62.0

Time: 3.3s

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 r2236895 = x;
        double r2236896 = lo;
        double r2236897 = r2236895 - r2236896;
        double r2236898 = hi;
        double r2236899 = r2236898 - r2236896;
        double r2236900 = r2236897 / r2236899;
        return r2236900;
}

↓

double f(double lo, double hi, double x) {
        double r2236901 = x;
        double r2236902 = lo;
        double r2236903 = r2236901 - r2236902;
        double r2236904 = hi;
        double r2236905 = r2236904 - r2236902;
        double r2236906 = r2236903 / r2236905;
        return r2236906;
}

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 2019169 
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))