Average Error: 62.0 → 62.0
Time: 719.0ms
Precision: 64
\[lo \lt -1 \cdot 10^{308} \land hi \gt 10^{308}\]
\[\frac{x - lo}{hi - lo}\]
↓
\[\frac{x - lo}{hi - lo}\]
\frac{x - lo}{hi - lo}
↓
\frac{x - lo}{hi - lo}
double f(double lo, double hi, double x) {
        double r9697 = x;
        double r9698 = lo;
        double r9699 = r9697 - r9698;
        double r9700 = hi;
        double r9701 = r9700 - r9698;
        double r9702 = r9699 / r9701;
        return r9702;
}
↓
double f(double lo, double hi, double x) {
        double r9703 = x;
        double r9704 = lo;
        double r9705 = r9703 - r9704;
        double r9706 = hi;
        double r9707 = r9706 - r9704;
        double r9708 = r9705 / r9707;
        return r9708;
}

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 2020057 +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)))