Average Error: 0.2 → 0.2
Time: 2.1s
Precision: 64
\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
↓
\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1
↓
\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1
double f(double d1) {
        double r2830982 = d1;
        double r2830983 = r2830982 * r2830982;
        double r2830984 = r2830983 * r2830982;
        double r2830985 = r2830984 * r2830982;
        return r2830985;
}
↓
double f(double d1) {
        double r2830986 = d1;
        double r2830987 = r2830986 * r2830986;
        double r2830988 = r2830987 * r2830986;
        double r2830989 = r2830988 * r2830986;
        return r2830989;
}

Error

Bits error versus d1

Derivation

  1. Initial program 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019107 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))