Average Error: 0.1 → 0.1
Time: 3.3s
Precision: binary64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[y \cdot \left(x - y \cdot x\right)\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
y \cdot \left(x - y \cdot x\right)
(FPCore (x y) :precision binary64 (* (* x y) (- 1.0 y)))
↓
(FPCore (x y) :precision binary64 (* y (- x (* y x))))
double code(double x, double y) {
	return (x * y) * (1.0 - y);
}
↓
double code(double x, double y) {
	return y * (x - (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

Derivation

  1. Initial program 0.1

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

  3. Applied sub-neg_binary64_4120.1

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

  4. Applied distribute-rgt-in_binary64_3690.1

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

  5. Simplified0.1

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

  6. Simplified0.1

    \[\leadsto y \cdot x + \color{blue}{\left(-y \cdot \left(y \cdot x\right)\right)}\]
  7. Using strategy rm

  8. Applied distribute-rgt-neg-in_binary64_3770.1

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

  9. Applied distribute-lft-out_binary64_3700.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1.0 y)))