Average Error: 0.1 → 0.1
Time: 4.9s
Precision: 64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[x \cdot \left(1 - y \cdot x\right)\]
x \cdot \left(1 - x \cdot y\right)
↓
x \cdot \left(1 - y \cdot x\right)
double f(double x, double y) {
        double r33428 = x;
        double r33429 = 1.0;
        double r33430 = y;
        double r33431 = r33428 * r33430;
        double r33432 = r33429 - r33431;
        double r33433 = r33428 * r33432;
        return r33433;
}
↓
double f(double x, double y) {
        double r33434 = x;
        double r33435 = 1.0;
        double r33436 = y;
        double r33437 = r33436 * r33434;
        double r33438 = r33435 - r33437;
        double r33439 = r33434 * r33438;
        return r33439;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \left(1 - x \cdot y\right)\]

  2. Taylor expanded around 0 7.8

    \[\leadsto \color{blue}{1 \cdot x - {x}^{2} \cdot y}\]

  3. Simplified0.1

    \[\leadsto \color{blue}{x \cdot \left(1 - y \cdot x\right)}\]

  4. Final simplification0.1

    \[\leadsto x \cdot \left(1 - y \cdot x\right)\]

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))