Average Error: 62.0 → 62.0
Time: 2.9s
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 r8270 = x;
        double r8271 = lo;
        double r8272 = r8270 - r8271;
        double r8273 = hi;
        double r8274 = r8273 - r8271;
        double r8275 = r8272 / r8274;
        return r8275;
}
↓
double f(double lo, double hi, double x) {
        double r8276 = x;
        double r8277 = lo;
        double r8278 = r8276 - r8277;
        double r8279 = hi;
        double r8280 = r8279 - r8277;
        double r8281 = r8278 / r8280;
        return r8281;
}

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 2020047 +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)))