Average Error: 0.1 → 0.1
Time: 2.5s
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 r104555 = x;
        double r104556 = 1.0;
        double r104557 = y;
        double r104558 = r104555 * r104557;
        double r104559 = r104556 - r104558;
        double r104560 = r104555 * r104559;
        return r104560;
}
↓
double f(double x, double y) {
        double r104561 = x;
        double r104562 = 1.0;
        double r104563 = r104561 * r104562;
        double r104564 = y;
        double r104565 = r104561 * r104564;
        double r104566 = -r104565;
        double r104567 = r104561 * r104566;
        double r104568 = r104563 + r104567;
        return r104568;
}

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 2020056 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))