Average Error: 0.2 → 0.2
Time: 35.5s
Precision: 64
\[\left(x \cdot y\right) \cdot y\]
↓
\[\left(y \cdot x\right) \cdot y\]
\left(x \cdot y\right) \cdot y
↓
\left(y \cdot x\right) \cdot y
double f(double x, double y) {
        double r14269521 = x;
        double r14269522 = y;
        double r14269523 = r14269521 * r14269522;
        double r14269524 = r14269523 * r14269522;
        return r14269524;
}
↓
double f(double x, double y) {
        double r14269525 = y;
        double r14269526 = x;
        double r14269527 = r14269525 * r14269526;
        double r14269528 = r14269527 * r14269525;
        return r14269528;
}

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

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y)
  :name "Data.HyperLogLog.Config:hll from hyperloglog-0.3.4"
  (* (* x y) y))