Average Error: 0.1 → 0.1
Time: 9.7s
Precision: 64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[x \cdot 1 + \left(-y \cdot x\right) \cdot x\]
x \cdot \left(1 - x \cdot y\right)
↓
x \cdot 1 + \left(-y \cdot x\right) \cdot x
double f(double x, double y) {
        double r3294196 = x;
        double r3294197 = 1.0;
        double r3294198 = y;
        double r3294199 = r3294196 * r3294198;
        double r3294200 = r3294197 - r3294199;
        double r3294201 = r3294196 * r3294200;
        return r3294201;
}
↓
double f(double x, double y) {
        double r3294202 = x;
        double r3294203 = 1.0;
        double r3294204 = r3294202 * r3294203;
        double r3294205 = y;
        double r3294206 = r3294205 * r3294202;
        double r3294207 = -r3294206;
        double r3294208 = r3294207 * r3294202;
        double r3294209 = r3294204 + r3294208;
        return r3294209;
}

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

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  (* x (- 1.0 (* x y))))