Average Error: 62.0 → 62.0
Time: 1.6s
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 r17141 = x;
        double r17142 = lo;
        double r17143 = r17141 - r17142;
        double r17144 = hi;
        double r17145 = r17144 - r17142;
        double r17146 = r17143 / r17145;
        return r17146;
}
↓
double f(double lo, double hi, double x) {
        double r17147 = x;
        double r17148 = lo;
        double r17149 = r17147 - r17148;
        double r17150 = hi;
        double r17151 = r17150 - r17148;
        double r17152 = r17149 / r17151;
        return r17152;
}

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 2020045 +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)))