(/ (- 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 r2804210 = x;
        double r2804211 = lo;
        double r2804212 = r2804210 - r2804211;
        double r2804213 = hi;
        double r2804214 = r2804213 - r2804211;
        double r2804215 = r2804212 / r2804214;
        return r2804215;
}

↓

double f(double lo, double hi, double x) {
        double r2804216 = x;
        double r2804217 = lo;
        double r2804218 = r2804216 - r2804217;
        double r2804219 = hi;
        double r2804220 = r2804219 - r2804217;
        double r2804221 = r2804218 / r2804220;
        return r2804221;
}

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 2019173 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))