Average Error: 0.1 → 0.1
Time: 2.8s
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 r66356 = x;
        double r66357 = 1.0;
        double r66358 = y;
        double r66359 = r66356 * r66358;
        double r66360 = r66357 - r66359;
        double r66361 = r66356 * r66360;
        return r66361;
}
↓
double f(double x, double y) {
        double r66362 = x;
        double r66363 = 1.0;
        double r66364 = r66362 * r66363;
        double r66365 = y;
        double r66366 = r66362 * r66365;
        double r66367 = -r66366;
        double r66368 = r66362 * r66367;
        double r66369 = r66364 + r66368;
        return r66369;
}

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