FastMath repmul

Average Error: 0.2 → 0.2

Time: 4.0s

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 r2609882 = d1;
        double r2609883 = r2609882 * r2609882;
        double r2609884 = r2609883 * r2609882;
        double r2609885 = r2609884 * r2609882;
        return r2609885;
}

↓

double f(double d1) {
        double r2609886 = d1;
        double r2609887 = r2609886 * r2609886;
        double r2609888 = r2609887 * r2609886;
        double r2609889 = r2609888 * r2609886;
        return r2609889;
}

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 2019165 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))