Average Error: 0.1 → 0.1
Time: 1.4s
Precision: binary64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[x \cdot y - y \cdot \left(x \cdot y\right)\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
x \cdot y - y \cdot \left(x \cdot y\right)
(FPCore (x y) :precision binary64 (* (* x y) (- 1.0 y)))
↓
(FPCore (x y) :precision binary64 (- (* x y) (* y (* x y))))
double code(double x, double y) {
	return (x * y) * (1.0 - y);
}
↓
double code(double x, double y) {
	return (x * y) - (y * (x * 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 sub-neg_binary640.1

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

  4. Applied distribute-rgt-in_binary640.1

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

  5. Simplified0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020233 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1.0 y)))