FastMath repmul

Average Error: 0.2 → 0.2

Time: 2.7s

Precision: 64

Math

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

↓

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

C

double f(double d1) {
        double r6003989 = d1;
        double r6003990 = r6003989 * r6003989;
        double r6003991 = r6003990 * r6003989;
        double r6003992 = r6003991 * r6003989;
        return r6003992;
}

↓

double f(double d1) {
        double r6003993 = d1;
        double r6003994 = r6003993 * r6003993;
        double r6003995 = r6003994 * r6003994;
        return r6003995;
}

Error

Bits error versus d1

Derivation

1. Initial program 0.2

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

2. Simplified 0.2

   \[\leadsto \color{blue}{\left(d1 \cdot d1\right) \cdot \left(d1 \cdot d1\right)}\]

3. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))