FastMath dist

Average Error: 0.3 → 0.2

Time: 3.8s

Precision: 64

Math

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

↓

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

C

double f(double d1, double d2, double d3) {
        double r5208688 = d1;
        double r5208689 = d2;
        double r5208690 = r5208688 * r5208689;
        double r5208691 = d3;
        double r5208692 = r5208688 * r5208691;
        double r5208693 = r5208690 + r5208692;
        return r5208693;
}

↓

double f(double d1, double d2, double d3) {
        double r5208694 = d3;
        double r5208695 = d2;
        double r5208696 = r5208694 + r5208695;
        double r5208697 = d1;
        double r5208698 = r5208696 * r5208697;
        return r5208698;
}

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. Simplified 0.2

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

3. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))