Average Error: 62.0 → 62.0
Time: 779.0ms
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 r25780 = x;
        double r25781 = lo;
        double r25782 = r25780 - r25781;
        double r25783 = hi;
        double r25784 = r25783 - r25781;
        double r25785 = r25782 / r25784;
        return r25785;
}
↓
double f(double lo, double hi, double x) {
        double r25786 = x;
        double r25787 = lo;
        double r25788 = r25786 - r25787;
        double r25789 = hi;
        double r25790 = r25789 - r25787;
        double r25791 = r25788 / r25790;
        return r25791;
}

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 2019347 +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)))