Average Error: 0.1 → 0.2
Time: 2.0s
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 r2626736 = d1;
        double r2626737 = r2626736 * r2626736;
        double r2626738 = r2626737 * r2626736;
        double r2626739 = r2626738 * r2626736;
        return r2626739;
}
↓
double f(double d1) {
        double r2626740 = d1;
        double r2626741 = r2626740 * r2626740;
        double r2626742 = r2626741 * r2626741;
        return r2626742;
}

Error

Bits error versus d1

Derivation

  1. Initial program 0.1

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

  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 2019128 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))