FastMath repmul

Average Error: 0.2 → 0.2

Time: 2.0m

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 r3697609 = d1;
        double r3697610 = r3697609 * r3697609;
        double r3697611 = r3697610 * r3697609;
        double r3697612 = r3697611 * r3697609;
        return r3697612;
}

↓

double f(double d1) {
        double r3697613 = d1;
        double r3697614 = r3697613 * r3697613;
        double r3697615 = r3697614 * r3697614;
        return r3697615;
}

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 2019168 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))