Average Error: 62.0 → 62.0
Time: 752.0ms
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 r6040 = x;
        double r6041 = lo;
        double r6042 = r6040 - r6041;
        double r6043 = hi;
        double r6044 = r6043 - r6041;
        double r6045 = r6042 / r6044;
        return r6045;
}
↓
double f(double lo, double hi, double x) {
        double r6046 = x;
        double r6047 = lo;
        double r6048 = r6046 - r6047;
        double r6049 = hi;
        double r6050 = r6049 - r6047;
        double r6051 = r6048 / r6050;
        return r6051;
}

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 2020001 +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)))