FastMath dist

Average Error: 0.3 → 0.2

Time: 5.5s

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 r1204607 = d1;
        double r1204608 = d2;
        double r1204609 = r1204607 * r1204608;
        double r1204610 = d3;
        double r1204611 = r1204607 * r1204610;
        double r1204612 = r1204609 + r1204611;
        return r1204612;
}

↓

double f(double d1, double d2, double d3) {
        double r1204613 = d3;
        double r1204614 = d2;
        double r1204615 = r1204613 + r1204614;
        double r1204616 = d1;
        double r1204617 = r1204615 * r1204616;
        return r1204617;
}

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 2019153 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))