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

Average Error: 62.0 → 62.0

Time: 2.4s

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 r902190 = x;
        double r902191 = lo;
        double r902192 = r902190 - r902191;
        double r902193 = hi;
        double r902194 = r902193 - r902191;
        double r902195 = r902192 / r902194;
        return r902195;
}

↓

double f(double lo, double hi, double x) {
        double r902196 = x;
        double r902197 = lo;
        double r902198 = r902196 - r902197;
        double r902199 = hi;
        double r902200 = r902199 - r902197;
        double r902201 = r902198 / r902200;
        return r902201;
}

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)))