Average Error: 62.0 → 62.0
Time: 3.5s
Precision: 64
\[lo \lt -1.000000000000000010979063629440455417405 \cdot 10^{308} \land hi \gt 1.000000000000000010979063629440455417405 \cdot 10^{308}\]
\[\frac{x - lo}{hi - lo}\]
↓
\[\frac{x - lo}{hi - lo}\]
\frac{x - lo}{hi - lo}
↓
\frac{x - lo}{hi - lo}
double f(double lo, double hi, double x) {
        double r17026 = x;
        double r17027 = lo;
        double r17028 = r17026 - r17027;
        double r17029 = hi;
        double r17030 = r17029 - r17027;
        double r17031 = r17028 / r17030;
        return r17031;
}
↓
double f(double lo, double hi, double x) {
        double r17032 = x;
        double r17033 = lo;
        double r17034 = r17032 - r17033;
        double r17035 = hi;
        double r17036 = r17035 - r17033;
        double r17037 = r17034 / r17036;
        return r17037;
}

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 2019212 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :precision binary64
  :pre (and (< lo -1e308) (> hi 1e308))
  (/ (- x lo) (- hi lo)))