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

Average Error: 62.0 → 62.0

Time: 3.4s

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 r1935393 = x;
        double r1935394 = lo;
        double r1935395 = r1935393 - r1935394;
        double r1935396 = hi;
        double r1935397 = r1935396 - r1935394;
        double r1935398 = r1935395 / r1935397;
        return r1935398;
}

↓

double f(double lo, double hi, double x) {
        double r1935399 = x;
        double r1935400 = lo;
        double r1935401 = r1935399 - r1935400;
        double r1935402 = hi;
        double r1935403 = r1935402 - r1935400;
        double r1935404 = r1935401 / r1935403;
        return r1935404;
}

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 2019173 
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))