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

Average Error: 62.0 → 62.0

Time: 2.7s

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 r1987437 = x;
        double r1987438 = lo;
        double r1987439 = r1987437 - r1987438;
        double r1987440 = hi;
        double r1987441 = r1987440 - r1987438;
        double r1987442 = r1987439 / r1987441;
        return r1987442;
}

↓

double f(double lo, double hi, double x) {
        double r1987443 = x;
        double r1987444 = lo;
        double r1987445 = r1987443 - r1987444;
        double r1987446 = hi;
        double r1987447 = r1987446 - r1987444;
        double r1987448 = r1987445 / r1987447;
        return r1987448;
}

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