Average Error: 0.1 → 0.1
Time: 3.0s
Precision: 64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[x \cdot 1 + x \cdot \left(-x \cdot y\right)\]
x \cdot \left(1 - x \cdot y\right)
↓
x \cdot 1 + x \cdot \left(-x \cdot y\right)
double f(double x, double y) {
        double r96534 = x;
        double r96535 = 1.0;
        double r96536 = y;
        double r96537 = r96534 * r96536;
        double r96538 = r96535 - r96537;
        double r96539 = r96534 * r96538;
        return r96539;
}
↓
double f(double x, double y) {
        double r96540 = x;
        double r96541 = 1.0;
        double r96542 = r96540 * r96541;
        double r96543 = y;
        double r96544 = r96540 * r96543;
        double r96545 = -r96544;
        double r96546 = r96540 * r96545;
        double r96547 = r96542 + r96546;
        return r96547;
}

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. Using strategy rm

  3. Applied sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))