Average Error: 0.2 → 0.2
Time: 3.3s
Precision: binary64
Cost: 320
\[\left(x \cdot y\right) \cdot y\]
↓
\[y \cdot \left(y \cdot x\right)\]
\left(x \cdot y\right) \cdot y
↓
y \cdot \left(y \cdot x\right)
(FPCore (x y) :precision binary64 (* (* x y) y))
↓
(FPCore (x y) :precision binary64 (* y (* y x)))
double code(double x, double y) {
	return (x * y) * y;
}
↓
double code(double x, double y) {
	return y * (y * x);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error41.1
Cost64
\[0\]
Alternative 2
Error61.8
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.2

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

  2. Simplified0.2

    \[\leadsto \color{blue}{y \cdot \left(y \cdot x\right)}\]

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y)
  :name "Data.HyperLogLog.Config:hll from hyperloglog-0.3.4"
  :precision binary64
  (* (* x y) y))