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

Average Error: 62.0 → 62.0

Time: 3.7s

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 r2408274 = x;
        double r2408275 = lo;
        double r2408276 = r2408274 - r2408275;
        double r2408277 = hi;
        double r2408278 = r2408277 - r2408275;
        double r2408279 = r2408276 / r2408278;
        return r2408279;
}

↓

double f(double lo, double hi, double x) {
        double r2408280 = x;
        double r2408281 = lo;
        double r2408282 = r2408280 - r2408281;
        double r2408283 = hi;
        double r2408284 = r2408283 - r2408281;
        double r2408285 = r2408282 / r2408284;
        return r2408285;
}

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