Average Error: 0.2 → 0.2
Time: 3.4s
Precision: 64
\[\left(x \cdot y\right) \cdot y\]
↓
\[\left(x \cdot y\right) \cdot y\]
\left(x \cdot y\right) \cdot y
↓
\left(x \cdot y\right) \cdot y
double f(double x, double y) {
        double r233732 = x;
        double r233733 = y;
        double r233734 = r233732 * r233733;
        double r233735 = r233734 * r233733;
        return r233735;
}
↓
double f(double x, double y) {
        double r233736 = x;
        double r233737 = y;
        double r233738 = r233736 * r233737;
        double r233739 = r233738 * r233737;
        return r233739;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(x \cdot y\right) \cdot y\]

  2. Final simplification0.2

    \[\leadsto \left(x \cdot y\right) \cdot y\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y)
  :name "Data.HyperLogLog.Config:hll from hyperloglog-0.3.4"
  :precision binary64
  (* (* x y) y))