FastMath dist

Average Error: 0.3 → 0.2

Time: 4.5s

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 r1854356 = d1;
        double r1854357 = d2;
        double r1854358 = r1854356 * r1854357;
        double r1854359 = d3;
        double r1854360 = r1854356 * r1854359;
        double r1854361 = r1854358 + r1854360;
        return r1854361;
}

↓

double f(double d1, double d2, double d3) {
        double r1854362 = d3;
        double r1854363 = d2;
        double r1854364 = r1854362 + r1854363;
        double r1854365 = d1;
        double r1854366 = r1854364 * r1854365;
        return r1854366;
}

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 2019128 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))