Average Error: 0.1 → 0.1
Time: 6.9s
Precision: 64
\[x \cdot \left(1.0 - x \cdot y\right)\]
↓
\[x \cdot 1.0 + \left(-y \cdot x\right) \cdot x\]
x \cdot \left(1.0 - x \cdot y\right)
↓
x \cdot 1.0 + \left(-y \cdot x\right) \cdot x
double f(double x, double y) {
        double r726463 = x;
        double r726464 = 1.0;
        double r726465 = y;
        double r726466 = r726463 * r726465;
        double r726467 = r726464 - r726466;
        double r726468 = r726463 * r726467;
        return r726468;
}
↓
double f(double x, double y) {
        double r726469 = x;
        double r726470 = 1.0;
        double r726471 = r726469 * r726470;
        double r726472 = y;
        double r726473 = r726472 * r726469;
        double r726474 = -r726473;
        double r726475 = r726474 * r726469;
        double r726476 = r726471 + r726475;
        return r726476;
}

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

    \[x \cdot \left(1.0 - x \cdot y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.1

    \[\leadsto x \cdot \color{blue}{\left(1.0 + \left(-x \cdot y\right)\right)}\]

  4. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{x \cdot 1.0 + x \cdot \left(-x \cdot y\right)}\]

  5. Final simplification0.1

    \[\leadsto x \cdot 1.0 + \left(-y \cdot x\right) \cdot x\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  (* x (- 1.0 (* x y))))