Average Error: 62.0 → 62.0
Time: 780.0ms
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 r6676 = x;
        double r6677 = lo;
        double r6678 = r6676 - r6677;
        double r6679 = hi;
        double r6680 = r6679 - r6677;
        double r6681 = r6678 / r6680;
        return r6681;
}
↓
double f(double lo, double hi, double x) {
        double r6682 = x;
        double r6683 = lo;
        double r6684 = r6682 - r6683;
        double r6685 = hi;
        double r6686 = r6685 - r6683;
        double r6687 = r6684 / r6686;
        return r6687;
}

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 2020003 +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)))