Average Error: 62.0 → 62.0
Time: 4.0s
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 r21181 = x;
        double r21182 = lo;
        double r21183 = r21181 - r21182;
        double r21184 = hi;
        double r21185 = r21184 - r21182;
        double r21186 = r21183 / r21185;
        return r21186;
}
↓
double f(double lo, double hi, double x) {
        double r21187 = x;
        double r21188 = lo;
        double r21189 = r21187 - r21188;
        double r21190 = hi;
        double r21191 = r21190 - r21188;
        double r21192 = r21189 / r21191;
        return r21192;
}

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 2019325 +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)))