Average Error: 0.1 → 0.1
Time: 3.1s
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 r42465 = x;
        double r42466 = 1.0;
        double r42467 = y;
        double r42468 = r42465 * r42467;
        double r42469 = r42466 - r42468;
        double r42470 = r42465 * r42469;
        return r42470;
}
↓
double f(double x, double y) {
        double r42471 = x;
        double r42472 = 1.0;
        double r42473 = r42471 * r42472;
        double r42474 = y;
        double r42475 = r42471 * r42474;
        double r42476 = -r42475;
        double r42477 = r42471 * r42476;
        double r42478 = r42473 + r42477;
        return r42478;
}

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 2020036 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))