Average Error: 62.0 → 62.0
Time: 746.0ms
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 r4228 = x;
        double r4229 = lo;
        double r4230 = r4228 - r4229;
        double r4231 = hi;
        double r4232 = r4231 - r4229;
        double r4233 = r4230 / r4232;
        return r4233;
}
↓
double f(double lo, double hi, double x) {
        double r4234 = x;
        double r4235 = lo;
        double r4236 = r4234 - r4235;
        double r4237 = hi;
        double r4238 = r4237 - r4235;
        double r4239 = r4236 / r4238;
        return r4239;
}

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 2020062 +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)))