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

Average Error: 62.0 → 62.0

Time: 3.1s

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 r1927644 = x;
        double r1927645 = lo;
        double r1927646 = r1927644 - r1927645;
        double r1927647 = hi;
        double r1927648 = r1927647 - r1927645;
        double r1927649 = r1927646 / r1927648;
        return r1927649;
}

↓

double f(double lo, double hi, double x) {
        double r1927650 = x;
        double r1927651 = lo;
        double r1927652 = r1927650 - r1927651;
        double r1927653 = hi;
        double r1927654 = r1927653 - r1927651;
        double r1927655 = r1927652 / r1927654;
        return r1927655;
}

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 2019169 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))