Average Error: 0.1 → 0.1
Time: 2.6s
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 r61439 = x;
        double r61440 = 1.0;
        double r61441 = y;
        double r61442 = r61439 * r61441;
        double r61443 = r61440 - r61442;
        double r61444 = r61439 * r61443;
        return r61444;
}
↓
double f(double x, double y) {
        double r61445 = x;
        double r61446 = 1.0;
        double r61447 = r61445 * r61446;
        double r61448 = y;
        double r61449 = r61445 * r61448;
        double r61450 = -r61449;
        double r61451 = r61445 * r61450;
        double r61452 = r61447 + r61451;
        return r61452;
}

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 2019352 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))