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 r57158 = x;
        double r57159 = 1.0;
        double r57160 = y;
        double r57161 = r57158 * r57160;
        double r57162 = r57159 - r57161;
        double r57163 = r57158 * r57162;
        return r57163;
}
↓
double f(double x, double y) {
        double r57164 = x;
        double r57165 = 1.0;
        double r57166 = r57164 * r57165;
        double r57167 = y;
        double r57168 = r57164 * r57167;
        double r57169 = -r57168;
        double r57170 = r57164 * r57169;
        double r57171 = r57166 + r57170;
        return r57171;
}

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 2020083 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))