Average Error: 0.3 → 0.2
Time: 4.3s
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 r4502650 = d1;
        double r4502651 = d2;
        double r4502652 = r4502650 * r4502651;
        double r4502653 = d3;
        double r4502654 = r4502650 * r4502653;
        double r4502655 = r4502652 + r4502654;
        return r4502655;
}
↓
double f(double d1, double d2, double d3) {
        double r4502656 = d3;
        double r4502657 = d2;
        double r4502658 = r4502656 + r4502657;
        double r4502659 = d1;
        double r4502660 = r4502658 * r4502659;
        return r4502660;
}

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 2019132 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))