FastMath dist

Average Error: 0.3 → 0.2

Time: 5.4s

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 r3584837 = d1;
        double r3584838 = d2;
        double r3584839 = r3584837 * r3584838;
        double r3584840 = d3;
        double r3584841 = r3584837 * r3584840;
        double r3584842 = r3584839 + r3584841;
        return r3584842;
}

↓

double f(double d1, double d2, double d3) {
        double r3584843 = d3;
        double r3584844 = d2;
        double r3584845 = r3584843 + r3584844;
        double r3584846 = d1;
        double r3584847 = r3584845 * r3584846;
        return r3584847;
}

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 2019162 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))