Average Error: 62.0 → 62.0
Time: 754.0ms
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 r4138 = x;
        double r4139 = lo;
        double r4140 = r4138 - r4139;
        double r4141 = hi;
        double r4142 = r4141 - r4139;
        double r4143 = r4140 / r4142;
        return r4143;
}
↓
double f(double lo, double hi, double x) {
        double r4144 = x;
        double r4145 = lo;
        double r4146 = r4144 - r4145;
        double r4147 = hi;
        double r4148 = r4147 - r4145;
        double r4149 = r4146 / r4148;
        return r4149;
}

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 2020060 
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :precision binary64
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))