Average Error: 0.1 → 0.1
Time: 3.9s
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 around 0 8.0

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

  3. Simplified8.0

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

  5. Applied associate-*l*_binary64_13830.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1.0 (* x y))))