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

Average Error: 62.0 → 62.0

Time: 3.0s

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 r1174746 = x;
        double r1174747 = lo;
        double r1174748 = r1174746 - r1174747;
        double r1174749 = hi;
        double r1174750 = r1174749 - r1174747;
        double r1174751 = r1174748 / r1174750;
        return r1174751;
}

↓

double f(double lo, double hi, double x) {
        double r1174752 = x;
        double r1174753 = lo;
        double r1174754 = r1174752 - r1174753;
        double r1174755 = hi;
        double r1174756 = r1174755 - r1174753;
        double r1174757 = r1174754 / r1174756;
        return r1174757;
}

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)))