Average Error: 0.5 → 0.3
Time: 7.9s
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 r1616089 = d1;
        double r1616090 = 3.0;
        double r1616091 = r1616089 * r1616090;
        double r1616092 = d2;
        double r1616093 = r1616089 * r1616092;
        double r1616094 = r1616091 + r1616093;
        double r1616095 = d3;
        double r1616096 = r1616089 * r1616095;
        double r1616097 = r1616094 + r1616096;
        return r1616097;
}
↓
double f(double d1, double d2, double d3) {
        double r1616098 = 3.0;
        double r1616099 = d2;
        double r1616100 = r1616098 + r1616099;
        double r1616101 = d3;
        double r1616102 = r1616100 + r1616101;
        double r1616103 = d1;
        double r1616104 = r1616102 * r1616103;
        return r1616104;
}


\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 0.5

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

  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 2019101 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))