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

Average Error: 62.0 → 62.0

Time: 10.9s

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 r1504589 = x;
        double r1504590 = lo;
        double r1504591 = r1504589 - r1504590;
        double r1504592 = hi;
        double r1504593 = r1504592 - r1504590;
        double r1504594 = r1504591 / r1504593;
        return r1504594;
}

↓

double f(double lo, double hi, double x) {
        double r1504595 = x;
        double r1504596 = lo;
        double r1504597 = r1504595 - r1504596;
        double r1504598 = hi;
        double r1504599 = r1504598 - r1504596;
        double r1504600 = r1504597 / r1504599;
        return r1504600;
}

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 2019200 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))