FastMath dist

Average Error: 0.3 → 0.2

Time: 4.1s

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 r6004869 = d1;
        double r6004870 = d2;
        double r6004871 = r6004869 * r6004870;
        double r6004872 = d3;
        double r6004873 = r6004869 * r6004872;
        double r6004874 = r6004871 + r6004873;
        return r6004874;
}

↓

double f(double d1, double d2, double d3) {
        double r6004875 = d3;
        double r6004876 = d2;
        double r6004877 = r6004875 + r6004876;
        double r6004878 = d1;
        double r6004879 = r6004877 * r6004878;
        return r6004879;
}

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 2019134 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))