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 r88021 = x;
        double r88022 = 1.0;
        double r88023 = y;
        double r88024 = r88021 * r88023;
        double r88025 = r88022 - r88024;
        double r88026 = r88021 * r88025;
        return r88026;
}
↓
double f(double x, double y) {
        double r88027 = x;
        double r88028 = 1.0;
        double r88029 = r88027 * r88028;
        double r88030 = y;
        double r88031 = r88027 * r88030;
        double r88032 = -r88031;
        double r88033 = r88027 * r88032;
        double r88034 = r88029 + r88033;
        return r88034;
}

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 2020039 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))