Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[y \cdot \left(x + y\right) + \left(x + y\right) \cdot x\]
\left(x + y\right) \cdot \left(x + y\right)
↓
y \cdot \left(x + y\right) + \left(x + y\right) \cdot x
double f(double x, double y) {
        double r550447 = x;
        double r550448 = y;
        double r550449 = r550447 + r550448;
        double r550450 = r550449 * r550449;
        return r550450;
}
↓
double f(double x, double y) {
        double r550451 = y;
        double r550452 = x;
        double r550453 = r550452 + r550451;
        double r550454 = r550451 * r550453;
        double r550455 = r550453 * r550452;
        double r550456 = r550454 + r550455;
        return r550456;
}

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

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"

  :herbie-target
  (+ (* x x) (+ (* y y) (* 2.0 (* y x))))

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