Average Error: 0.1 → 0.1
Time: 2.1s
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 r66827 = x;
        double r66828 = 1.0;
        double r66829 = y;
        double r66830 = r66827 * r66829;
        double r66831 = r66828 - r66830;
        double r66832 = r66827 * r66831;
        return r66832;
}
↓
double f(double x, double y) {
        double r66833 = x;
        double r66834 = 1.0;
        double r66835 = r66833 * r66834;
        double r66836 = y;
        double r66837 = r66833 * r66836;
        double r66838 = -r66837;
        double r66839 = r66833 * r66838;
        double r66840 = r66835 + r66839;
        return r66840;
}

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 2020065 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))