Average Error: 0.1 → 0.1
Time: 3.1s
Precision: binary64
Cost: 448
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[x - x \cdot \left(x \cdot y\right)\]
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

Alternatives

Alternative 1
Error14.5
Cost712
\[\begin{array}{l} \mathbf{if}\;y \leq -1.580540693828247 \cdot 10^{+41} \lor \neg \left(y \leq 2.120353431922988 \cdot 10^{+93}\right):\\ \;\;\;\;x \cdot \left(-x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
Alternative 2
Error21.1
Cost64
\[x\]
Alternative 3
Error61.3
Cost64
\[0\]
Alternative 4
Error61.7
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.1

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

  3. Applied sub-neg_binary64_17760.1

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

  4. Applied distribute-rgt-in_binary64_17330.1

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

  5. Simplified0.1

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

  6. Simplified0.1

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

  7. Simplified0.1

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

  8. 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))))