Average Error: 0.1 → 0.1
Time: 4.0s
Precision: binary64
\[x \cdot \left(1 - x \cdot y\right) \]
↓
\[x - x \cdot \left(x \cdot y\right) \]
x \cdot \left(1 - x \cdot y\right)
↓
x - x \cdot \left(x \cdot y\right)

(FPCore (x y) :precision binary64 (* x (- 1.0 (* x y))))
↓
(FPCore (x y) :precision binary64 (- x (* x (* x y))))
double code(double x, double y) {
	return x * (1.0 - (x * y));
}
↓
double code(double x, double y) {
	return x - (x * (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

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

  2. Taylor expanded in x around 0 5.9

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

  3. Applied sqr-pow_binary645.9

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

  4. Applied associate-*r*_binary640.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2022068 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1.0 (* x y))))