FastMath repmul

Average Error: 0.2 → 0.2

Time: 2.3s

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 r4801534 = d1;
        double r4801535 = r4801534 * r4801534;
        double r4801536 = r4801535 * r4801534;
        double r4801537 = r4801536 * r4801534;
        return r4801537;
}

↓

double f(double d1) {
        double r4801538 = d1;
        double r4801539 = r4801538 * r4801538;
        double r4801540 = r4801539 * r4801538;
        double r4801541 = r4801540 * r4801538;
        return r4801541;
}

Error

Bits error versus d1

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019135 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))