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

Average Error: 62.0 → 62.0

Time: 3.8s

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 r2013379 = x;
        double r2013380 = lo;
        double r2013381 = r2013379 - r2013380;
        double r2013382 = hi;
        double r2013383 = r2013382 - r2013380;
        double r2013384 = r2013381 / r2013383;
        return r2013384;
}

↓

double f(double lo, double hi, double x) {
        double r2013385 = x;
        double r2013386 = lo;
        double r2013387 = r2013385 - r2013386;
        double r2013388 = hi;
        double r2013389 = r2013388 - r2013386;
        double r2013390 = r2013387 / r2013389;
        return r2013390;
}

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 2019174 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))