Average Error: 0.2 → 0
Time: 4.2s
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 r1341926 = d;
        double r1341927 = 10.0;
        double r1341928 = /* ERROR: no posit support in C */;
        double r1341929 = r1341926 * r1341928;
        double r1341930 = 20.0;
        double r1341931 = /* ERROR: no posit support in C */;
        double r1341932 = r1341926 * r1341931;
        double r1341933 = r1341929 + r1341932;
        return r1341933;
}
↓
double f(double d) {
        double r1341934 = d;
        double r1341935 = 20.0;
        double r1341936 = 10.0;
        double r1341937 = r1341935 + r1341936;
        double r1341938 = r1341934 * r1341937;
        return r1341938;
}

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 2019156 +o rules:numerics
(FPCore (d)
  :name "FastMath test1"
  (+.p16 (*.p16 d (real->posit16 10)) (*.p16 d (real->posit16 20))))