Average Error: 62.0 → 62.0
Time: 891.0ms
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 r14175 = x;
        double r14176 = lo;
        double r14177 = r14175 - r14176;
        double r14178 = hi;
        double r14179 = r14178 - r14176;
        double r14180 = r14177 / r14179;
        return r14180;
}
↓
double f(double lo, double hi, double x) {
        double r14181 = x;
        double r14182 = lo;
        double r14183 = r14181 - r14182;
        double r14184 = hi;
        double r14185 = r14184 - r14182;
        double r14186 = r14183 / r14185;
        return r14186;
}

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 2020065 +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)))