Average Error: 62.0 → 62.0
Time: 814.0ms
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 r4407 = x;
        double r4408 = lo;
        double r4409 = r4407 - r4408;
        double r4410 = hi;
        double r4411 = r4410 - r4408;
        double r4412 = r4409 / r4411;
        return r4412;
}
↓
double f(double lo, double hi, double x) {
        double r4413 = x;
        double r4414 = lo;
        double r4415 = r4413 - r4414;
        double r4416 = hi;
        double r4417 = r4416 - r4414;
        double r4418 = r4415 / r4417;
        return r4418;
}

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 2019354 +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)))