Average Error: 0.1 → 0.1
Time: 3.1s
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 r55794 = x;
        double r55795 = 1.0;
        double r55796 = y;
        double r55797 = r55794 * r55796;
        double r55798 = r55795 - r55797;
        double r55799 = r55794 * r55798;
        return r55799;
}
↓
double f(double x, double y) {
        double r55800 = x;
        double r55801 = 1.0;
        double r55802 = r55800 * r55801;
        double r55803 = y;
        double r55804 = r55800 * r55803;
        double r55805 = -r55804;
        double r55806 = r55800 * r55805;
        double r55807 = r55802 + r55806;
        return r55807;
}

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