Average Error: 0.0 → 0.0
Time: 8.0s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot \left(y + x\right) + \left(y + x\right) \cdot y\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot \left(y + x\right) + \left(y + x\right) \cdot y
double f(double x, double y) {
        double r419603 = x;
        double r419604 = y;
        double r419605 = r419603 + r419604;
        double r419606 = r419605 * r419605;
        return r419606;
}
↓
double f(double x, double y) {
        double r419607 = x;
        double r419608 = y;
        double r419609 = r419608 + r419607;
        double r419610 = r419607 * r419609;
        double r419611 = r419609 * r419608;
        double r419612 = r419610 + r419611;
        return r419612;
}

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-lft-in0.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(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)))