Average Error: 0.0 → 0.0
Time: 6.7s
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[\left(x \cdot \left(x + y\right)\right) \cdot 2\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
\left(x \cdot \left(x + y\right)\right) \cdot 2
double f(double x, double y) {
        double r589572 = 2.0;
        double r589573 = x;
        double r589574 = r589573 * r589573;
        double r589575 = y;
        double r589576 = r589573 * r589575;
        double r589577 = r589574 + r589576;
        double r589578 = r589572 * r589577;
        return r589578;
}
↓
double f(double x, double y) {
        double r589579 = x;
        double r589580 = y;
        double r589581 = r589579 + r589580;
        double r589582 = r589579 * r589581;
        double r589583 = 2.0;
        double r589584 = r589582 * r589583;
        return r589584;
}

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
Herbie0.0
\[\left(x \cdot 2\right) \cdot \left(x + y\right)\]

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

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

  (* 2 (+ (* x x) (* x y))))