FastMath repmul

Average Error: 0.1 → 0.1

Time: 53.0s

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 r4523900 = d1;
        double r4523901 = r4523900 * r4523900;
        double r4523902 = r4523901 * r4523900;
        double r4523903 = r4523902 * r4523900;
        return r4523903;
}

↓

double f(double d1) {
        double r4523904 = d1;
        double r4523905 = r4523904 * r4523904;
        double r4523906 = r4523905 * r4523904;
        double r4523907 = r4523906 * r4523904;
        return r4523907;
}

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 2019163 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))