Average Error: 0.1 → 0.1
Time: 2.9s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[y \cdot \left(x \cdot \left(1 - y\right)\right)\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
y \cdot \left(x \cdot \left(1 - y\right)\right)
double code(double x, double y) {
	return ((double) (((double) (x * y)) * ((double) (1.0 - y))));
}
↓
double code(double x, double y) {
	return ((double) (y * ((double) (x * ((double) (1.0 - y))))));
}

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 0.1

    \[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
  2. Using strategy rm

  3. Applied *-commutative0.1

    \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot \left(1 - y\right)\]

  4. Applied associate-*l*0.1

    \[\leadsto \color{blue}{y \cdot \left(x \cdot \left(1 - y\right)\right)}\]

  5. Final simplification0.1

    \[\leadsto y \cdot \left(x \cdot \left(1 - y\right)\right)\]

Reproduce

herbie shell --seed 2020114 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))