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 r57561 = x;
        double r57562 = 1.0;
        double r57563 = y;
        double r57564 = r57561 * r57563;
        double r57565 = r57562 - r57564;
        double r57566 = r57561 * r57565;
        return r57566;
}
↓
double f(double x, double y) {
        double r57567 = x;
        double r57568 = 1.0;
        double r57569 = r57567 * r57568;
        double r57570 = y;
        double r57571 = r57567 * r57570;
        double r57572 = -r57571;
        double r57573 = r57567 * r57572;
        double r57574 = r57569 + r57573;
        return r57574;
}

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 2019353 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))