Average Error: 0.1 → 0.1
Time: 2.2s
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. Taylor expanded in x around 0 5.6

    \[\leadsto \color{blue}{\left(y - {y}^{2}\right) \cdot x} \]

  3. Taylor expanded in y around 0 5.6

    \[\leadsto \color{blue}{y \cdot x - {y}^{2} \cdot x} \]

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2022068 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1.0 y)))