Average Error: 0.1 → 0.1
Time: 3.0s
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 r74447 = x;
        double r74448 = 1.0;
        double r74449 = y;
        double r74450 = r74447 * r74449;
        double r74451 = r74448 - r74450;
        double r74452 = r74447 * r74451;
        return r74452;
}
↓
double f(double x, double y) {
        double r74453 = x;
        double r74454 = 1.0;
        double r74455 = r74453 * r74454;
        double r74456 = y;
        double r74457 = r74453 * r74456;
        double r74458 = -r74457;
        double r74459 = r74453 * r74458;
        double r74460 = r74455 + r74459;
        return r74460;
}

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 2020083 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))