Average Error: 0.0 → 0.0
Time: 5.8s
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 r800445 = 2.0;
        double r800446 = x;
        double r800447 = r800446 * r800446;
        double r800448 = y;
        double r800449 = r800446 * r800448;
        double r800450 = r800447 + r800449;
        double r800451 = r800445 * r800450;
        return r800451;
}
↓
double f(double x, double y) {
        double r800452 = x;
        double r800453 = y;
        double r800454 = r800452 + r800453;
        double r800455 = r800452 * r800454;
        double r800456 = 2.0;
        double r800457 = r800455 * r800456;
        return r800457;
}

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 2020042 
(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))))