Average Error: 0.0 → 0.0
Time: 7.7s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[\left(\left(x \cdot 2\right) \cdot y + y \cdot y\right) + x \cdot x\]
\left(x + y\right) \cdot \left(x + y\right)
↓
\left(\left(x \cdot 2\right) \cdot y + y \cdot y\right) + x \cdot x
double f(double x, double y) {
        double r537653 = x;
        double r537654 = y;
        double r537655 = r537653 + r537654;
        double r537656 = r537655 * r537655;
        return r537656;
}
↓
double f(double x, double y) {
        double r537657 = x;
        double r537658 = 2.0;
        double r537659 = r537657 * r537658;
        double r537660 = y;
        double r537661 = r537659 * r537660;
        double r537662 = r537660 * r537660;
        double r537663 = r537661 + r537662;
        double r537664 = r537657 * r537657;
        double r537665 = r537663 + r537664;
        return r537665;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{y}^{2} + \left({x}^{2} + 2 \cdot \left(x \cdot y\right)\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{x \cdot x + \left(\left(2 \cdot x\right) \cdot y + y \cdot y\right)}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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)))