Average Error: 62.0 → 62.0
Time: 982.0ms
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 r6690 = x;
        double r6691 = lo;
        double r6692 = r6690 - r6691;
        double r6693 = hi;
        double r6694 = r6693 - r6691;
        double r6695 = r6692 / r6694;
        return r6695;
}
↓
double f(double lo, double hi, double x) {
        double r6696 = x;
        double r6697 = lo;
        double r6698 = r6696 - r6697;
        double r6699 = hi;
        double r6700 = r6699 - r6697;
        double r6701 = r6698 / r6700;
        return r6701;
}

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 2020035 +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)))