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 r86989 = x;
        double r86990 = 1.0;
        double r86991 = y;
        double r86992 = r86989 * r86991;
        double r86993 = r86990 - r86992;
        double r86994 = r86989 * r86993;
        return r86994;
}
↓
double f(double x, double y) {
        double r86995 = x;
        double r86996 = 1.0;
        double r86997 = r86995 * r86996;
        double r86998 = y;
        double r86999 = r86995 * r86998;
        double r87000 = -r86999;
        double r87001 = r86995 * r87000;
        double r87002 = r86997 + r87001;
        return r87002;
}

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 2020035 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))