Average Error: 0.1 → 0.1
Time: 16.8s
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 r3773587 = x;
        double r3773588 = 1.0;
        double r3773589 = y;
        double r3773590 = r3773587 * r3773589;
        double r3773591 = r3773588 - r3773590;
        double r3773592 = r3773587 * r3773591;
        return r3773592;
}
↓
double f(double x, double y) {
        double r3773593 = x;
        double r3773594 = 1.0;
        double r3773595 = r3773593 * r3773594;
        double r3773596 = y;
        double r3773597 = r3773596 * r3773593;
        double r3773598 = -r3773597;
        double r3773599 = r3773598 * r3773593;
        double r3773600 = r3773595 + r3773599;
        return r3773600;
}

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 2019172 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  (* x (- 1.0 (* x y))))