Average Error: 62.0 → 62.0
Time: 739.0ms
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 r7480 = x;
        double r7481 = lo;
        double r7482 = r7480 - r7481;
        double r7483 = hi;
        double r7484 = r7483 - r7481;
        double r7485 = r7482 / r7484;
        return r7485;
}
↓
double f(double lo, double hi, double x) {
        double r7486 = x;
        double r7487 = lo;
        double r7488 = r7486 - r7487;
        double r7489 = hi;
        double r7490 = r7489 - r7487;
        double r7491 = r7488 / r7490;
        return r7491;
}

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 2020024 +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)))