Average Error: 62.0 → 62.0
Time: 805.0ms
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 r13962 = x;
        double r13963 = lo;
        double r13964 = r13962 - r13963;
        double r13965 = hi;
        double r13966 = r13965 - r13963;
        double r13967 = r13964 / r13966;
        return r13967;
}
↓
double f(double lo, double hi, double x) {
        double r13968 = x;
        double r13969 = lo;
        double r13970 = r13968 - r13969;
        double r13971 = hi;
        double r13972 = r13971 - r13969;
        double r13973 = r13970 / r13972;
        return r13973;
}

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 2019346 +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)))