Average Error: 0.1 → 0.1
Time: 10.2s
Precision: 64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[\left(1 - x \cdot y\right) \cdot x\]
x \cdot \left(1 - x \cdot y\right)
↓
\left(1 - x \cdot y\right) \cdot x
double f(double x, double y) {
        double r77697 = x;
        double r77698 = 1.0;
        double r77699 = y;
        double r77700 = r77697 * r77699;
        double r77701 = r77698 - r77700;
        double r77702 = r77697 * r77701;
        return r77702;
}
↓
double f(double x, double y) {
        double r77703 = 1.0;
        double r77704 = x;
        double r77705 = y;
        double r77706 = r77704 * r77705;
        double r77707 = r77703 - r77706;
        double r77708 = r77707 * r77704;
        return r77708;
}

Error

Bits error versus x

Bits error versus y

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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

    \[\leadsto \left(1 - x \cdot y\right) \cdot x\]

Reproduce

herbie shell --seed 2019294 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))