Average Error: 62.0 → 52.1
Time: 1.9s
Precision: 64
\[lo \lt -1 \cdot 10^{308} \land hi \gt 10^{308}\]
\[\frac{x - lo}{hi - lo}\]
↓
\[1\]
\frac{x - lo}{hi - lo}
↓
1
double f(double lo, double hi, double x) {
        double r10400 = x;
        double r10401 = lo;
        double r10402 = r10400 - r10401;
        double r10403 = hi;
        double r10404 = r10403 - r10401;
        double r10405 = r10402 / r10404;
        return r10405;
}
↓
double f(double __attribute__((unused)) lo, double __attribute__((unused)) hi, double __attribute__((unused)) x) {
        double r10406 = 1.0;
        return r10406;
}

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. Using strategy rm

  3. Applied div-sub62.0

    \[\leadsto \color{blue}{\frac{x}{hi - lo} - \frac{lo}{hi - lo}}\]

  4. Taylor expanded around 0 52.1

    \[\leadsto \color{blue}{1}\]

  5. Final simplification52.1

    \[\leadsto 1\]

Reproduce

herbie shell --seed 2020033 +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)))