Average Error: 0.1 → 0.1
Time: 11.9s
Precision: 64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[x \cdot 1 + \left(y \cdot x\right) \cdot \left(-x\right)\]
x \cdot \left(1 - x \cdot y\right)
↓
x \cdot 1 + \left(y \cdot x\right) \cdot \left(-x\right)
double f(double x, double y) {
        double r56270 = x;
        double r56271 = 1.0;
        double r56272 = y;
        double r56273 = r56270 * r56272;
        double r56274 = r56271 - r56273;
        double r56275 = r56270 * r56274;
        return r56275;
}
↓
double f(double x, double y) {
        double r56276 = x;
        double r56277 = 1.0;
        double r56278 = r56276 * r56277;
        double r56279 = y;
        double r56280 = r56279 * r56276;
        double r56281 = -r56276;
        double r56282 = r56280 * r56281;
        double r56283 = r56278 + r56282;
        return r56283;
}

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. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  (* x (- 1.0 (* x y))))