Average Error: 0.1 → 0.1
Time: 2.6s
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 r71909 = x;
        double r71910 = 1.0;
        double r71911 = y;
        double r71912 = r71909 * r71911;
        double r71913 = r71910 - r71912;
        double r71914 = r71909 * r71913;
        return r71914;
}
↓
double f(double x, double y) {
        double r71915 = x;
        double r71916 = 1.0;
        double r71917 = r71915 * r71916;
        double r71918 = y;
        double r71919 = r71915 * r71918;
        double r71920 = -r71919;
        double r71921 = r71915 * r71920;
        double r71922 = r71917 + r71921;
        return r71922;
}

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 2020002 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))