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 r58504 = x;
        double r58505 = 1.0;
        double r58506 = y;
        double r58507 = r58504 * r58506;
        double r58508 = r58505 - r58507;
        double r58509 = r58504 * r58508;
        return r58509;
}
↓
double f(double x, double y) {
        double r58510 = x;
        double r58511 = 1.0;
        double r58512 = r58510 * r58511;
        double r58513 = y;
        double r58514 = r58510 * r58513;
        double r58515 = -r58514;
        double r58516 = r58510 * r58515;
        double r58517 = r58512 + r58516;
        return r58517;
}

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 2020060 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))