Average Error: 62.0 → 62.0
Time: 731.0ms
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 r4015 = x;
        double r4016 = lo;
        double r4017 = r4015 - r4016;
        double r4018 = hi;
        double r4019 = r4018 - r4016;
        double r4020 = r4017 / r4019;
        return r4020;
}
↓
double f(double lo, double hi, double x) {
        double r4021 = x;
        double r4022 = lo;
        double r4023 = r4021 - r4022;
        double r4024 = hi;
        double r4025 = r4024 - r4022;
        double r4026 = r4023 / r4025;
        return r4026;
}

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 2020064 +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)))