Average Error: 0.1 → 0.1
Time: 2.8s
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 r79674 = x;
        double r79675 = 1.0;
        double r79676 = y;
        double r79677 = r79674 * r79676;
        double r79678 = r79675 - r79677;
        double r79679 = r79674 * r79678;
        return r79679;
}
↓
double f(double x, double y) {
        double r79680 = x;
        double r79681 = 1.0;
        double r79682 = r79680 * r79681;
        double r79683 = y;
        double r79684 = r79680 * r79683;
        double r79685 = -r79684;
        double r79686 = r79680 * r79685;
        double r79687 = r79682 + r79686;
        return r79687;
}

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))))