Average Error: 0.1 → 0.1
Time: 2.9s
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 r80993 = x;
        double r80994 = 1.0;
        double r80995 = y;
        double r80996 = r80993 * r80995;
        double r80997 = r80994 - r80996;
        double r80998 = r80993 * r80997;
        return r80998;
}
↓
double f(double x, double y) {
        double r80999 = x;
        double r81000 = 1.0;
        double r81001 = r80999 * r81000;
        double r81002 = y;
        double r81003 = r80999 * r81002;
        double r81004 = -r81003;
        double r81005 = r80999 * r81004;
        double r81006 = r81001 + r81005;
        return r81006;
}

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 2019362 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))