Average Error: 0.1 → 0.2
Time: 2.8s
Precision: 64
\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
↓
\[\left(d1 \cdot d1\right) \cdot \left(d1 \cdot d1\right)\]
\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1
↓
\left(d1 \cdot d1\right) \cdot \left(d1 \cdot d1\right)
double f(double d1) {
        double r2241413 = d1;
        double r2241414 = r2241413 * r2241413;
        double r2241415 = r2241414 * r2241413;
        double r2241416 = r2241415 * r2241413;
        return r2241416;
}
↓
double f(double d1) {
        double r2241417 = d1;
        double r2241418 = r2241417 * r2241417;
        double r2241419 = r2241418 * r2241418;
        return r2241419;
}

Error

Bits error versus d1

Derivation

  1. Initial program 0.1

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019128 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))