Average Error: 0.2 → 0.2
Time: 3.1s
Precision: 64
\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
↓
\[\left(d1 \cdot d1\right) \cdot \left(d1 \cdot d1\right)\]
\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1
↓
\left(d1 \cdot d1\right) \cdot \left(d1 \cdot d1\right)
double f(double d1) {
        double r1610770 = d1;
        double r1610771 = r1610770 * r1610770;
        double r1610772 = r1610771 * r1610770;
        double r1610773 = r1610772 * r1610770;
        return r1610773;
}
↓
double f(double d1) {
        double r1610774 = d1;
        double r1610775 = r1610774 * r1610774;
        double r1610776 = r1610775 * r1610775;
        return r1610776;
}

Error

Bits error versus d1

Derivation

  1. Initial program 0.2

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))