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 r58459 = x;
        double r58460 = 1.0;
        double r58461 = y;
        double r58462 = r58459 * r58461;
        double r58463 = r58460 - r58462;
        double r58464 = r58459 * r58463;
        return r58464;
}
↓
double f(double x, double y) {
        double r58465 = x;
        double r58466 = 1.0;
        double r58467 = r58465 * r58466;
        double r58468 = y;
        double r58469 = r58465 * r58468;
        double r58470 = -r58469;
        double r58471 = r58465 * r58470;
        double r58472 = r58467 + r58471;
        return r58472;
}

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 2020064 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))