FastMath repmul

Average Error: 0.2 → 0.2

Time: 5.9s

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 r565413 = d1;
        double r565414 = r565413 * r565413;
        double r565415 = r565414 * r565413;
        double r565416 = r565415 * r565413;
        return r565416;
}

↓

double f(double d1) {
        double r565417 = d1;
        double r565418 = r565417 * r565417;
        double r565419 = r565418 * r565418;
        return r565419;
}

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 2019153 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))