Average Error: 0.0 → 0.0
Time: 24.0s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[y \cdot y + \left(y + \left(y + x\right)\right) \cdot x\]
\left(x + y\right) \cdot \left(x + y\right)
↓
y \cdot y + \left(y + \left(y + x\right)\right) \cdot x
double f(double x, double y) {
        double r30107922 = x;
        double r30107923 = y;
        double r30107924 = r30107922 + r30107923;
        double r30107925 = r30107924 * r30107924;
        return r30107925;
}
↓
double f(double x, double y) {
        double r30107926 = y;
        double r30107927 = r30107926 * r30107926;
        double r30107928 = x;
        double r30107929 = r30107926 + r30107928;
        double r30107930 = r30107926 + r30107929;
        double r30107931 = r30107930 * r30107928;
        double r30107932 = r30107927 + r30107931;
        return r30107932;
}

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. Using strategy rm

  3. Applied distribute-rgt-in0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Applied associate-+r+0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 +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)))