FastMath repmul

Average Error: 0.1 → 0.1

Time: 1.8m

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 r3984757 = d1;
        double r3984758 = r3984757 * r3984757;
        double r3984759 = r3984758 * r3984757;
        double r3984760 = r3984759 * r3984757;
        return r3984760;
}

↓

double f(double d1) {
        double r3984761 = d1;
        double r3984762 = r3984761 * r3984761;
        double r3984763 = r3984762 * r3984761;
        double r3984764 = r3984763 * r3984761;
        return r3984764;
}

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