Average Error: 0.1 → 0.1
Time: 2.1s
Precision: binary64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[x \cdot 1 - x \cdot \left(x \cdot y\right)\]
x \cdot \left(1 - x \cdot y\right)
↓
x \cdot 1 - x \cdot \left(x \cdot y\right)
(FPCore (x y) :precision binary64 (* x (- 1.0 (* x y))))
↓
(FPCore (x y) :precision binary64 (- (* x 1.0) (* x (* x y))))
double code(double x, double y) {
	return ((double) (x * ((double) (1.0 - ((double) (x * y))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (x * 1.0)) - ((double) (x * ((double) (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 Error: 0.1 bits

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

  3. Applied sub-negError: 0.1 bits

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

  4. Applied distribute-lft-inError: 0.1 bits

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

  5. SimplifiedError: 0.1 bits

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

  6. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1.0 (* x y))))