Average Error: 62.0 → 62.0
Time: 2.8s
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 r16656 = x;
        double r16657 = lo;
        double r16658 = r16656 - r16657;
        double r16659 = hi;
        double r16660 = r16659 - r16657;
        double r16661 = r16658 / r16660;
        return r16661;
}
↓
double f(double lo, double hi, double x) {
        double r16662 = x;
        double r16663 = lo;
        double r16664 = r16662 - r16663;
        double r16665 = hi;
        double r16666 = r16665 - r16663;
        double r16667 = r16664 / r16666;
        return r16667;
}

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 2019235 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :precision binary64
  :pre (and (< lo -1e308) (> hi 1e308))
  (/ (- x lo) (- hi lo)))