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 r64546 = x;
        double r64547 = 1.0;
        double r64548 = y;
        double r64549 = r64546 * r64548;
        double r64550 = r64547 - r64549;
        double r64551 = r64546 * r64550;
        return r64551;
}
↓
double f(double x, double y) {
        double r64552 = x;
        double r64553 = 1.0;
        double r64554 = r64552 * r64553;
        double r64555 = y;
        double r64556 = r64552 * r64555;
        double r64557 = -r64556;
        double r64558 = r64552 * r64557;
        double r64559 = r64554 + r64558;
        return r64559;
}

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 2020057 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))