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

Average Error: 62.0 → 62.0

Time: 6.3s

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 r1294130 = x;
        double r1294131 = lo;
        double r1294132 = r1294130 - r1294131;
        double r1294133 = hi;
        double r1294134 = r1294133 - r1294131;
        double r1294135 = r1294132 / r1294134;
        return r1294135;
}

↓

double f(double lo, double hi, double x) {
        double r1294136 = x;
        double r1294137 = lo;
        double r1294138 = r1294136 - r1294137;
        double r1294139 = hi;
        double r1294140 = r1294139 - r1294137;
        double r1294141 = r1294138 / r1294140;
        return r1294141;
}

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 2019168 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))