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 r74761 = x;
        double r74762 = 1.0;
        double r74763 = y;
        double r74764 = r74761 * r74763;
        double r74765 = r74762 - r74764;
        double r74766 = r74761 * r74765;
        return r74766;
}
↓
double f(double x, double y) {
        double r74767 = x;
        double r74768 = 1.0;
        double r74769 = r74767 * r74768;
        double r74770 = y;
        double r74771 = r74767 * r74770;
        double r74772 = -r74771;
        double r74773 = r74767 * r74772;
        double r74774 = r74769 + r74773;
        return r74774;
}

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 2019353 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))