FastMath repmul

Average Error: 0.1 → 0.2

Time: 3.2s

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 r4181781 = d1;
        double r4181782 = r4181781 * r4181781;
        double r4181783 = r4181782 * r4181781;
        double r4181784 = r4181783 * r4181781;
        return r4181784;
}

↓

double f(double d1) {
        double r4181785 = d1;
        double r4181786 = r4181785 * r4181785;
        double r4181787 = r4181786 * r4181786;
        return r4181787;
}

Error

Bits error versus d1

Derivation

1. Initial program 0.1

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

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 2019104 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))