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

Average Error: 62.0 → 62.0

Time: 4.0s

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 r1175315 = x;
        double r1175316 = lo;
        double r1175317 = r1175315 - r1175316;
        double r1175318 = hi;
        double r1175319 = r1175318 - r1175316;
        double r1175320 = r1175317 / r1175319;
        return r1175320;
}

↓

double f(double lo, double hi, double x) {
        double r1175321 = x;
        double r1175322 = lo;
        double r1175323 = r1175321 - r1175322;
        double r1175324 = hi;
        double r1175325 = r1175324 - r1175322;
        double r1175326 = r1175323 / r1175325;
        return r1175326;
}

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 2019192 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))