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

Average Error: 62.0 → 62.0

Time: 4.0s

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 r1891723 = x;
        double r1891724 = lo;
        double r1891725 = r1891723 - r1891724;
        double r1891726 = hi;
        double r1891727 = r1891726 - r1891724;
        double r1891728 = r1891725 / r1891727;
        return r1891728;
}

↓

double f(double lo, double hi, double x) {
        double r1891729 = x;
        double r1891730 = lo;
        double r1891731 = r1891729 - r1891730;
        double r1891732 = hi;
        double r1891733 = r1891732 - r1891730;
        double r1891734 = r1891731 / r1891733;
        return r1891734;
}

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 2019174 
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))