Average Error: 62.0 → 62.0
Time: 4.0s
Precision: 64
\[\frac{x - lo}{hi - lo}\]
↓
\[\frac{x - lo}{hi - lo}\]
double f(double lo, double hi, double x) {
        double r82198 = x;
        double r82199 = lo;
        double r82200 = r82198 - r82199;
        double r82201 = hi;
        double r82202 = r82201 - r82199;
        double r82203 = r82200 / r82202;
        return r82203;
}
↓
double f(double lo, double hi, double x) {
        double r82204 = x;
        double r82205 = lo;
        double r82206 = r82204 - r82205;
        double r82207 = hi;
        double r82208 = r82207 - r82205;
        double r82209 = r82206 / r82208;
        return r82209;
}


\frac{x - lo}{hi - lo}
↓
\frac{x - lo}{hi - lo}

Error

Bits error versus lo

Bits error versus hi

Bits error versus x

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 2019101 
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))