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 r21908 = x;
        double r21909 = lo;
        double r21910 = r21908 - r21909;
        double r21911 = hi;
        double r21912 = r21911 - r21909;
        double r21913 = r21910 / r21912;
        return r21913;
}
↓
double f(double lo, double hi, double x) {
        double r21914 = x;
        double r21915 = lo;
        double r21916 = r21914 - r21915;
        double r21917 = hi;
        double r21918 = r21917 - r21915;
        double r21919 = r21916 / r21918;
        return r21919;
}

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)))