FastMath repmul

Average Error: 0.1 → 0.1

Time: 5.6s

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 r311461 = d1;
        double r311462 = r311461 * r311461;
        double r311463 = r311462 * r311461;
        double r311464 = r311463 * r311461;
        return r311464;
}

↓

double f(double d1) {
        double r311465 = d1;
        double r311466 = r311465 * r311465;
        double r311467 = r311466 * r311465;
        double r311468 = r311467 * r311465;
        return r311468;
}

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 2019152 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))