Average Error: 62.0 → 62.0
Time: 934.0ms
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 r5134 = x;
        double r5135 = lo;
        double r5136 = r5134 - r5135;
        double r5137 = hi;
        double r5138 = r5137 - r5135;
        double r5139 = r5136 / r5138;
        return r5139;
}
↓
double f(double lo, double hi, double x) {
        double r5140 = x;
        double r5141 = lo;
        double r5142 = r5140 - r5141;
        double r5143 = hi;
        double r5144 = r5143 - r5141;
        double r5145 = r5142 / r5144;
        return r5145;
}

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 2020034 +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)))