(/ (- 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 r1271045 = x;
        double r1271046 = lo;
        double r1271047 = r1271045 - r1271046;
        double r1271048 = hi;
        double r1271049 = r1271048 - r1271046;
        double r1271050 = r1271047 / r1271049;
        return r1271050;
}

↓

double f(double lo, double hi, double x) {
        double r1271051 = x;
        double r1271052 = lo;
        double r1271053 = r1271051 - r1271052;
        double r1271054 = hi;
        double r1271055 = r1271054 - r1271052;
        double r1271056 = r1271053 / r1271055;
        return r1271056;
}

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