FastMath repmul

Average Error: 0.1 → 0.1

Time: 5.7s

Precision: 64

Math

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

↓

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

C

double f(double d1) {
        double r350791 = d1;
        double r350792 = r350791 * r350791;
        double r350793 = r350792 * r350791;
        double r350794 = r350793 * r350791;
        return r350794;
}

↓

double f(double d1) {
        double r350795 = d1;
        double r350796 = r350795 * r350795;
        double r350797 = r350796 * r350795;
        double r350798 = r350797 * r350795;
        return r350798;
}

Error

Bits error versus d1

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))