Average Error: 62.0 → 62.0
Time: 763.0ms
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 r7917 = x;
        double r7918 = lo;
        double r7919 = r7917 - r7918;
        double r7920 = hi;
        double r7921 = r7920 - r7918;
        double r7922 = r7919 / r7921;
        return r7922;
}
↓
double f(double lo, double hi, double x) {
        double r7923 = x;
        double r7924 = lo;
        double r7925 = r7923 - r7924;
        double r7926 = hi;
        double r7927 = r7926 - r7924;
        double r7928 = r7925 / r7927;
        return r7928;
}

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 2019353 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :precision binary64
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))