FastMath repmul

Average Error: 0.2 → 0.2

Time: 3.6s

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 r1343463 = d1;
        double r1343464 = r1343463 * r1343463;
        double r1343465 = r1343464 * r1343463;
        double r1343466 = r1343465 * r1343463;
        return r1343466;
}

↓

double f(double d1) {
        double r1343467 = d1;
        double r1343468 = r1343467 * r1343467;
        double r1343469 = r1343468 * r1343468;
        return r1343469;
}

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 2019124 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))