Average Error: 62.0 → 62.0
Time: 740.0ms
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 r4449 = x;
        double r4450 = lo;
        double r4451 = r4449 - r4450;
        double r4452 = hi;
        double r4453 = r4452 - r4450;
        double r4454 = r4451 / r4453;
        return r4454;
}
↓
double f(double lo, double hi, double x) {
        double r4455 = x;
        double r4456 = lo;
        double r4457 = r4455 - r4456;
        double r4458 = hi;
        double r4459 = r4458 - r4456;
        double r4460 = r4457 / r4459;
        return r4460;
}

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 2020020 +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)))