(/ (- x lo) (- hi lo))

Average Error: 62.0 → 62.0

Time: 3.0s

Precision: 64

\[lo \lt -1.000000000000000010979063629440455417405 \cdot 10^{308} \land hi \gt 1.000000000000000010979063629440455417405 \cdot 10^{308}\]

Math

\[\frac{x - lo}{hi - lo}\]

↓

\[\frac{x - lo}{hi - lo}\]

C

double f(double lo, double hi, double x) {
        double r1902097 = x;
        double r1902098 = lo;
        double r1902099 = r1902097 - r1902098;
        double r1902100 = hi;
        double r1902101 = r1902100 - r1902098;
        double r1902102 = r1902099 / r1902101;
        return r1902102;
}

↓

double f(double lo, double hi, double x) {
        double r1902103 = x;
        double r1902104 = lo;
        double r1902105 = r1902103 - r1902104;
        double r1902106 = hi;
        double r1902107 = r1902106 - r1902104;
        double r1902108 = r1902105 / r1902107;
        return r1902108;
}

Error

Bits error versus lo

Bits error versus hi

Bits error versus x

Derivation

1. Initial program 62.0

   \[\frac{x - lo}{hi - lo}\]

2. Final simplification 62.0

   \[\leadsto \frac{x - lo}{hi - lo}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))