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 r49832 = x;
        double r49833 = 1.0;
        double r49834 = y;
        double r49835 = r49832 * r49834;
        double r49836 = r49833 - r49835;
        double r49837 = r49832 * r49836;
        return r49837;
}
↓
double f(double x, double y) {
        double r49838 = x;
        double r49839 = 1.0;
        double r49840 = r49838 * r49839;
        double r49841 = y;
        double r49842 = r49838 * r49841;
        double r49843 = -r49842;
        double r49844 = r49838 * r49843;
        double r49845 = r49840 + r49844;
        return r49845;
}

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 2019352 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))