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

Average Error: 62.0 → 62.0

Time: 5.9s

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 r1315445 = x;
        double r1315446 = lo;
        double r1315447 = r1315445 - r1315446;
        double r1315448 = hi;
        double r1315449 = r1315448 - r1315446;
        double r1315450 = r1315447 / r1315449;
        return r1315450;
}

↓

double f(double lo, double hi, double x) {
        double r1315451 = x;
        double r1315452 = lo;
        double r1315453 = r1315451 - r1315452;
        double r1315454 = hi;
        double r1315455 = r1315454 - r1315452;
        double r1315456 = r1315453 / r1315455;
        return r1315456;
}

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