FastMath repmul

Average Error: 0.2 → 0.2

Time: 7.9s

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 r1227728 = d1;
        double r1227729 = r1227728 * r1227728;
        double r1227730 = r1227729 * r1227728;
        double r1227731 = r1227730 * r1227728;
        return r1227731;
}

↓

double f(double d1) {
        double r1227732 = d1;
        double r1227733 = r1227732 * r1227732;
        double r1227734 = r1227733 * r1227732;
        double r1227735 = r1227734 * r1227732;
        return r1227735;
}

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 2019155 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))