Average Error: 0.1 → 0.1
Time: 2.9s
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 r77778 = x;
        double r77779 = 1.0;
        double r77780 = y;
        double r77781 = r77778 * r77780;
        double r77782 = r77779 - r77781;
        double r77783 = r77778 * r77782;
        return r77783;
}
↓
double f(double x, double y) {
        double r77784 = x;
        double r77785 = 1.0;
        double r77786 = r77784 * r77785;
        double r77787 = y;
        double r77788 = r77784 * r77787;
        double r77789 = -r77788;
        double r77790 = r77784 * r77789;
        double r77791 = r77786 + r77790;
        return r77791;
}

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 2020100 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))