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

Average Error: 62.0 → 62.0

Time: 3.9s

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 r1935841 = x;
        double r1935842 = lo;
        double r1935843 = r1935841 - r1935842;
        double r1935844 = hi;
        double r1935845 = r1935844 - r1935842;
        double r1935846 = r1935843 / r1935845;
        return r1935846;
}

↓

double f(double lo, double hi, double x) {
        double r1935847 = x;
        double r1935848 = lo;
        double r1935849 = r1935847 - r1935848;
        double r1935850 = hi;
        double r1935851 = r1935850 - r1935848;
        double r1935852 = r1935849 / r1935851;
        return r1935852;
}

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 2019171 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))