FastMath repmul

Average Error: 0.2 → 0.2

Time: 2.6s

Precision: 64

Math

\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]

↓

\[\left(d1 \cdot d1\right) \cdot \left(d1 \cdot d1\right)\]

C

double f(double d1) {
        double r5458523 = d1;
        double r5458524 = r5458523 * r5458523;
        double r5458525 = r5458524 * r5458523;
        double r5458526 = r5458525 * r5458523;
        return r5458526;
}

↓

double f(double d1) {
        double r5458527 = d1;
        double r5458528 = r5458527 * r5458527;
        double r5458529 = r5458528 * r5458528;
        return r5458529;
}

Error

Bits error versus d1

Derivation

1. Initial program 0.2

   \[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]

2. Simplified 0.2

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

3. Final simplification 0.2

   \[\leadsto \left(d1 \cdot d1\right) \cdot \left(d1 \cdot d1\right)\]

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))