Average Error: 0.1 → 0.1
Time: 12.6s
Precision: 64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[x \cdot 1 + \left(-y \cdot x\right) \cdot x\]
x \cdot \left(1 - x \cdot y\right)
↓
x \cdot 1 + \left(-y \cdot x\right) \cdot x
double f(double x, double y) {
        double r3574615 = x;
        double r3574616 = 1.0;
        double r3574617 = y;
        double r3574618 = r3574615 * r3574617;
        double r3574619 = r3574616 - r3574618;
        double r3574620 = r3574615 * r3574619;
        return r3574620;
}
↓
double f(double x, double y) {
        double r3574621 = x;
        double r3574622 = 1.0;
        double r3574623 = r3574621 * r3574622;
        double r3574624 = y;
        double r3574625 = r3574624 * r3574621;
        double r3574626 = -r3574625;
        double r3574627 = r3574626 * r3574621;
        double r3574628 = r3574623 + r3574627;
        return r3574628;
}

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

    \[\leadsto x \cdot 1 + \left(-y \cdot x\right) \cdot x\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  (* x (- 1.0 (* x y))))