Average Error: 0.1 → 0.1
Time: 2.7s
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 r59162 = x;
        double r59163 = 1.0;
        double r59164 = y;
        double r59165 = r59162 * r59164;
        double r59166 = r59163 - r59165;
        double r59167 = r59162 * r59166;
        return r59167;
}
↓
double f(double x, double y) {
        double r59168 = x;
        double r59169 = 1.0;
        double r59170 = r59168 * r59169;
        double r59171 = y;
        double r59172 = r59168 * r59171;
        double r59173 = -r59172;
        double r59174 = r59168 * r59173;
        double r59175 = r59170 + r59174;
        return r59175;
}

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 2020024 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))