Average Error: 0.0 → 0.0
Time: 4.2s
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 r664478 = 2.0;
        double r664479 = x;
        double r664480 = r664479 * r664479;
        double r664481 = y;
        double r664482 = r664479 * r664481;
        double r664483 = r664480 + r664482;
        double r664484 = r664478 * r664483;
        return r664484;
}
↓
double f(double x, double y) {
        double r664485 = x;
        double r664486 = y;
        double r664487 = r664485 + r664486;
        double r664488 = r664485 * r664487;
        double r664489 = 2.0;
        double r664490 = r664488 * r664489;
        return r664490;
}

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 
(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))))