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

Average Error: 62.0 → 62.0

Time: 3.0s

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 r927191 = x;
        double r927192 = lo;
        double r927193 = r927191 - r927192;
        double r927194 = hi;
        double r927195 = r927194 - r927192;
        double r927196 = r927193 / r927195;
        return r927196;
}

↓

double f(double lo, double hi, double x) {
        double r927197 = x;
        double r927198 = lo;
        double r927199 = r927197 - r927198;
        double r927200 = hi;
        double r927201 = r927200 - r927198;
        double r927202 = r927199 / r927201;
        return r927202;
}

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)))