Average Error: 62.0 → 62.0
Time: 2.5s
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 r20705 = x;
        double r20706 = lo;
        double r20707 = r20705 - r20706;
        double r20708 = hi;
        double r20709 = r20708 - r20706;
        double r20710 = r20707 / r20709;
        return r20710;
}
↓
double f(double lo, double hi, double x) {
        double r20711 = x;
        double r20712 = lo;
        double r20713 = r20711 - r20712;
        double r20714 = hi;
        double r20715 = r20714 - r20712;
        double r20716 = r20713 / r20715;
        return r20716;
}

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)))