Average Error: 0.6 → 0.3
Time: 7.4s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[\left(\left(3 + d2\right) + d3\right) \cdot d1\]
double f(double d1, double d2, double d3) {
        double r2308970 = d1;
        double r2308971 = 3.0;
        double r2308972 = r2308970 * r2308971;
        double r2308973 = d2;
        double r2308974 = r2308970 * r2308973;
        double r2308975 = r2308972 + r2308974;
        double r2308976 = d3;
        double r2308977 = r2308970 * r2308976;
        double r2308978 = r2308975 + r2308977;
        return r2308978;
}
↓
double f(double d1, double d2, double d3) {
        double r2308979 = 3.0;
        double r2308980 = d2;
        double r2308981 = r2308979 + r2308980;
        double r2308982 = d3;
        double r2308983 = r2308981 + r2308982;
        double r2308984 = d1;
        double r2308985 = r2308983 * r2308984;
        return r2308985;
}


\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
\left(\left(3 + d2\right) + d3\right) \cdot d1

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.6

    \[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\left(\frac{\left(3\right)}{\left(\frac{d2}{d3}\right)}\right) \cdot d1}\]
  3. Using strategy rm

  4. Applied associate-+r+0.3

    \[\leadsto \color{blue}{\left(\frac{\left(\frac{\left(3\right)}{d2}\right)}{d3}\right)} \cdot d1\]

  5. Final simplification0.3

    \[\leadsto \left(\left(3 + d2\right) + d3\right) \cdot d1\]

Reproduce

herbie shell --seed 2019102 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))