Average Error: 0.0 → 0.1
Time: 2.3s
Precision: 64
\[2 \cdot \left(x \cdot x - x \cdot y\right)\]
↓
\[x \cdot \left(\left(x - y\right) \cdot 2\right)\]
2 \cdot \left(x \cdot x - x \cdot y\right)
↓
x \cdot \left(\left(x - y\right) \cdot 2\right)
double f(double x, double y) {
        double r530546 = 2.0;
        double r530547 = x;
        double r530548 = r530547 * r530547;
        double r530549 = y;
        double r530550 = r530547 * r530549;
        double r530551 = r530548 - r530550;
        double r530552 = r530546 * r530551;
        return r530552;
}
↓
double f(double x, double y) {
        double r530553 = x;
        double r530554 = y;
        double r530555 = r530553 - r530554;
        double r530556 = 2.0;
        double r530557 = r530555 * r530556;
        double r530558 = r530553 * r530557;
        return r530558;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.1
\[\left(x \cdot 2\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x - x \cdot y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(x \cdot \left(x - y\right)\right) \cdot 2}\]
  3. Using strategy rm

  4. Applied associate-*l*0.1

    \[\leadsto \color{blue}{x \cdot \left(\left(x - y\right) \cdot 2\right)}\]

  5. Final simplification0.1

    \[\leadsto x \cdot \left(\left(x - y\right) \cdot 2\right)\]

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (* (* x 2) (- x y))

  (* 2 (- (* x x) (* x y))))