Average Error: 62.0 → 62.0
Time: 2.6s
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 r18671 = x;
        double r18672 = lo;
        double r18673 = r18671 - r18672;
        double r18674 = hi;
        double r18675 = r18674 - r18672;
        double r18676 = r18673 / r18675;
        return r18676;
}
↓
double f(double lo, double hi, double x) {
        double r18677 = x;
        double r18678 = lo;
        double r18679 = r18677 - r18678;
        double r18680 = hi;
        double r18681 = r18680 - r18678;
        double r18682 = r18679 / r18681;
        return r18682;
}

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 2020043 +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)))