Average Error: 62.0 → 62.0
Time: 2.6s
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 r14870 = x;
        double r14871 = lo;
        double r14872 = r14870 - r14871;
        double r14873 = hi;
        double r14874 = r14873 - r14871;
        double r14875 = r14872 / r14874;
        return r14875;
}
↓
double f(double lo, double hi, double x) {
        double r14876 = x;
        double r14877 = lo;
        double r14878 = r14876 - r14877;
        double r14879 = hi;
        double r14880 = r14879 - r14877;
        double r14881 = r14878 / r14880;
        return r14881;
}

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 2020042 +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)))