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

Average Error: 62.0 → 62.0

Time: 3.6s

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 r2450673 = x;
        double r2450674 = lo;
        double r2450675 = r2450673 - r2450674;
        double r2450676 = hi;
        double r2450677 = r2450676 - r2450674;
        double r2450678 = r2450675 / r2450677;
        return r2450678;
}

↓

double f(double lo, double hi, double x) {
        double r2450679 = x;
        double r2450680 = lo;
        double r2450681 = r2450679 - r2450680;
        double r2450682 = hi;
        double r2450683 = r2450682 - r2450680;
        double r2450684 = r2450681 / r2450683;
        return r2450684;
}

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 2019179 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))