Average Error: 62.0 → 62.0
Time: 1.4s
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 r203 = x;
        double r204 = lo;
        double r205 = r203 - r204;
        double r206 = hi;
        double r207 = r206 - r204;
        double r208 = r205 / r207;
        return r208;
}
↓
double f(double lo, double hi, double x) {
        double r209 = x;
        double r210 = lo;
        double r211 = r209 - r210;
        double r212 = hi;
        double r213 = r212 - r210;
        double r214 = r211 / r213;
        return r214;
}

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 2020025 +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)))