Average Error: 62.0 → 62.0
Time: 4.8s
Precision: 64
\[lo \lt -1.000000000000000010979063629440455417405 \cdot 10^{308} \land hi \gt 1.000000000000000010979063629440455417405 \cdot 10^{308}\]
\[\frac{x - lo}{hi - lo}\]
↓
\[\frac{x - lo}{hi - lo}\]
\frac{x - lo}{hi - lo}
↓
\frac{x - lo}{hi - lo}
double f(double lo, double hi, double x) {
        double r21917 = x;
        double r21918 = lo;
        double r21919 = r21917 - r21918;
        double r21920 = hi;
        double r21921 = r21920 - r21918;
        double r21922 = r21919 / r21921;
        return r21922;
}
↓
double f(double lo, double hi, double x) {
        double r21923 = x;
        double r21924 = lo;
        double r21925 = r21923 - r21924;
        double r21926 = hi;
        double r21927 = r21926 - r21924;
        double r21928 = r21925 / r21927;
        return r21928;
}

Error

Bits error versus lo

Bits error versus hi

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 62.0

    \[\frac{x - lo}{hi - lo}\]

  2. Final simplification62.0

    \[\leadsto \frac{x - lo}{hi - lo}\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :precision binary64
  :pre (and (< lo -1e308) (> hi 1e308))
  (/ (- x lo) (- hi lo)))