Average Error: 62.0 → 62.0
Time: 741.0ms
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 r4257 = x;
        double r4258 = lo;
        double r4259 = r4257 - r4258;
        double r4260 = hi;
        double r4261 = r4260 - r4258;
        double r4262 = r4259 / r4261;
        return r4262;
}
↓
double f(double lo, double hi, double x) {
        double r4263 = x;
        double r4264 = lo;
        double r4265 = r4263 - r4264;
        double r4266 = hi;
        double r4267 = r4266 - r4264;
        double r4268 = r4265 / r4267;
        return r4268;
}

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 2020018 +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)))