Average Error: 0.3 → 0.2
Time: 4.0s
Precision: 64
\[\frac{\left(d1 \cdot d2\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(d3 + d2\right) \cdot d1\]
\frac{\left(d1 \cdot d2\right)}{\left(d1 \cdot d3\right)}
↓
\left(d3 + d2\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r1608887 = d1;
        double r1608888 = d2;
        double r1608889 = r1608887 * r1608888;
        double r1608890 = d3;
        double r1608891 = r1608887 * r1608890;
        double r1608892 = r1608889 + r1608891;
        return r1608892;
}
↓
double f(double d1, double d2, double d3) {
        double r1608893 = d3;
        double r1608894 = d2;
        double r1608895 = r1608893 + r1608894;
        double r1608896 = d1;
        double r1608897 = r1608895 * r1608896;
        return r1608897;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.3

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))