Average Error: 0.1 → 0.1
Time: 2.7s
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 r65353 = x;
        double r65354 = 1.0;
        double r65355 = y;
        double r65356 = r65353 * r65355;
        double r65357 = r65354 - r65356;
        double r65358 = r65353 * r65357;
        return r65358;
}
↓
double f(double x, double y) {
        double r65359 = x;
        double r65360 = 1.0;
        double r65361 = r65359 * r65360;
        double r65362 = y;
        double r65363 = r65359 * r65362;
        double r65364 = -r65363;
        double r65365 = r65359 * r65364;
        double r65366 = r65361 + r65365;
        return r65366;
}

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 2020062 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))