Average Error: 0.2 → 0
Time: 2.7s
Precision: 64
\[\frac{\left(d \cdot \left(10\right)\right)}{\left(d \cdot \left(20\right)\right)}\]
↓
\[d \cdot \left(20 + 10\right)\]
\frac{\left(d \cdot \left(10\right)\right)}{\left(d \cdot \left(20\right)\right)}
↓
d \cdot \left(20 + 10\right)
double f(double d) {
        double r1015359 = d;
        double r1015360 = 10.0;
        double r1015361 = /* ERROR: no posit support in C */;
        double r1015362 = r1015359 * r1015361;
        double r1015363 = 20.0;
        double r1015364 = /* ERROR: no posit support in C */;
        double r1015365 = r1015359 * r1015364;
        double r1015366 = r1015362 + r1015365;
        return r1015366;
}
↓
double f(double d) {
        double r1015367 = d;
        double r1015368 = 20.0;
        double r1015369 = 10.0;
        double r1015370 = r1015368 + r1015369;
        double r1015371 = r1015367 * r1015370;
        return r1015371;
}

Error

Bits error versus d

Derivation

  1. Initial program 0.2

    \[\frac{\left(d \cdot \left(10\right)\right)}{\left(d \cdot \left(20\right)\right)}\]

  2. Simplified0

    \[\leadsto \color{blue}{d \cdot \left(\frac{\left(20\right)}{\left(10\right)}\right)}\]

  3. Final simplification0

    \[\leadsto d \cdot \left(20 + 10\right)\]

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (d)
  :name "FastMath test1"
  (+.p16 (*.p16 d (real->posit16 10)) (*.p16 d (real->posit16 20))))