Average Error: 0.1 → 0.1
Time: 16.7s
Precision: 64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[x \cdot 1 + \left(-y \cdot x\right) \cdot x\]
x \cdot \left(1 - x \cdot y\right)
↓
x \cdot 1 + \left(-y \cdot x\right) \cdot x
double f(double x, double y) {
        double r2414110 = x;
        double r2414111 = 1.0;
        double r2414112 = y;
        double r2414113 = r2414110 * r2414112;
        double r2414114 = r2414111 - r2414113;
        double r2414115 = r2414110 * r2414114;
        return r2414115;
}
↓
double f(double x, double y) {
        double r2414116 = x;
        double r2414117 = 1.0;
        double r2414118 = r2414116 * r2414117;
        double r2414119 = y;
        double r2414120 = r2414119 * r2414116;
        double r2414121 = -r2414120;
        double r2414122 = r2414121 * r2414116;
        double r2414123 = r2414118 + r2414122;
        return r2414123;
}

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

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  (* x (- 1.0 (* x y))))